sea island explorer yacht cruise

DEJONG & LEBET, INC.

Naval Architects & Marine Engineers

Serving the Marine Industry with Naval Architecture  since 1983

Sea island explorer.

71ft x 21ft x 4.5ft Passenger Vessel

New Passenger Vessel for Sea Island Resort in Coastal Georgia

SEA ISLAND EXPLORER, a 71’ yacht style passenger vessel, was recently delivered to the Sea Island Resort located on the southeastern Georgia coast. Sea Island is a well-known luxury resort destination and is home to a PGA TOUR event each year, the RSM Classic.  The vessel has a beam of 21’ and a limited draft of 4’-6” to navigate the shallow creeks and rivers around Georgia’s Barrier Islands.  The vessel was designed by DeJong & Lebet, Inc., Naval Architects, Jacksonville, FL and was built by J&M Metal Works in Green Cove Springs, FL.

The vessel styling was designed by DeJong & Lebet to resemble a classic yacht from the 1930’s.  She is US Coast Guard certificated under Subchapter T for 49 passengers plus 11 crew and measures less than 100 gross tons.  The vessel features include a main deck enclosed salon with a bar, aft fantail semi-enclosed lounge, and open 2nd deck with a canopy aft of the pilothouse.  Below decks features a bride’s room/passenger area with 2 heads and a galley.  A 3rd head is located in the main deck salon.

The main passenger salon, pilothouse and below decks passenger area on SEA ISLAND EXPLORER have a beautiful mahogany finish.  The aft main deck features a NuTeak synthetic wood covering.  The vessel is fully heated and air-conditioned with a system furnished by Dometic.

The vessel is constructed of welded steel with an aluminum pilothouse.

The vessel is powered by a pair of John Deere 6068 diesel engines developing 265 HP each.  The engines are coupled to ZF gear boxes driving 32” HS Marine stainless steel propellers.  Engines and gears are electronically controlled using ZF controls.  Also featured is a 40 HP electric bow thruster furnished by IMTRA.  The power steering system was furnished by Jastram.

Electrical power is provided by (2) Kohler 53 kW gensets which are also driven by John Deere engines.  The main switchboard was furnished by IEM Marine.  The vessel has underwater lights around the transom furnished by Underwater Lights USA.

SEA ISLAND EXPLORER carries 1,200 gallons of fuel, 1,000 gallons of water, and 535 gallons of waste water.

About Sea Island

Since 1928, Sea Island has been known as an exceptional destination appealing to those who appreciate gracious service and heartfelt hospitality.  With four Forbes Five-Star experiences -- The Cloister at Sea Island, The Lodge at Sea Island, The Spa at Sea Island, and the Georgian Room restaurant – Sea Island entices families, outdoor enthusiasts, and those simply wanting to refresh. It is the only resort in the world to have received four Forbes Five-Star awards for ten consecutive years.  As the only U.S. resort to host a G-8 Summit of world leaders, Sea Island provides exceptional settings and service for conferences and executive retreats.

Located on the southeastern coast of Georgia, Sea Island features five miles of private beach, a Beach Club, tennis center, Yacht Club, Shooting School, and children’s programs, as well as three championship golf courses, including Seaside and Plantation, home of the PGA TOUR’s RSM Classic.  Located on St. Simons Island, The Inn at Sea Island offers casual accommodations with access to many Sea Island amenities.  Broadfield, a Sea Island Sporting Club and Lodge, offers seasonal hunting and fishing opportunities.

Enhancements now underway at The Lodge include six new cottages with 14 sleeping rooms, an oceanfront pool, and pool house, opening in November 2018, and a recently opened 18-hole putting course.  Early 2019 brings an all-new, 17,000-square-foot, state-of-the-art Golf Performance Center.

22 August 2018

SEA ISLAND UNVEILS SPECIALLY DESIGNED CLASSIC YACHT

Posted August 9, 2018 in Travel by Morgan Crowe

Built by J&M Metal Works in Green Cove Springs, Florida, and DeJong & Lebet, Inc., Naval Architects in Jacksonville, Florida, the SEA ISLAND EXPLORER blends traditional flare with modern finishes, including arched, wrap-around windows that provide sweeping views of Sea Island’s natural setting. Accommodating up to 49 passengers, the yacht features a double living room on the main deck, a covered top deck and a prep kitchen and additional event space on the bottom level, making it ideal for scenic nature tours, pre-dinner cocktail cruises, customized private events and more.  Food and beverage choices can be customized for each the occasion. Clay Fordham, a naturalist and Sea Island captain with more than 10 years’ of experience in local waters, will lead all operations aboard SEA ISLAND EXPLORER.

“We are always looking for ways to further enhance our guests’ experiences, especially experiences that provide the opportunity to see Sea Island and our expansive salt marsh from the water,” said Scott Steilen, President and CEO of Sea Island Company. “The SEA ISLAND EXPLORER will live up to its name, allowing guests of all ages to get an up-close look at and better understanding of our amazing ecosystem.”

In addition to unveiling the new yacht, Sea Island is celebrating its 90th “Emerald” Anniversary throughout 2018. Currently, The Lodge at Sea Island is undergoing a multi-million-dollar enhancement project that will debut six new cottages this fall, an oceanfront pool, pool house and 18-hole putting course this summer, and a new state-of-the-art Golf Performance Center (early 2019).  

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What’s New on Sea Island, Georgia

Some things change and plenty stays the same on the jewel of the Golden Isles

By Gwen Pratesi

October 2, 2023

Photo: courtesy of sea island

Sea Island, a five-mile-long, half-mile-wide barrier island in Georgia’s Golden Isles, has all the burnished marsh grasses, brilliant sunsets, and sparkling white beaches that give the area its nickname, but it stands apart from neighboring communities.

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After relocating from Boston to Atlanta in 2001, I got a taste of what it was like to live in the private enclave long before I visited. One of the first friends I made in Georgia had a home there, and after hearing her stories about “the island,” I felt I understood the vibe of this exclusive playground of the wealthy few.

But you can’t fully appreciate Sea Island until you see it yourself—the stately waterfront mansions (known as cottages), the lavish landscaping, the dramatic change in scenery as you cross the causeway from St. Simons Island and through the gates. After hearing so much about the property for so long, I felt as though I had been there before when I visited as a guest at  the Cloister  this past July. The well-preserved history and grandeur reminded me of  the Great Gatsby , especially when I looked back at the resort from the shoreline of the Black Banks River. After exploring the property over the course of several days, I saw just how much is new at this timeless resort, but also how the essence of “the island” remains unchanged.

A look back

For nearly one hundred years, Sea Island has hosted generations of families as they’ve celebrated weddings, birthdays, and other milestones, or simply escaped for a vacation. (I learned much of the following history from the delightful cookbook Soul of the South by Sarah Anschutz Hunt.)

Howard Coffin, the founder of Hudson Motor Company, purchased Sea Island (named Glynn Isle at that time) in 1926. He hired Addison Mizner, known for his architectural work in Boca Raton and Palm Beach, Florida, to design the Cloister. The small luxury property, billed as “a friendly little hotel,” opened in October 1928 with a beach club, tennis courts, a shooting school, and a fishing dock. A yacht club, riding stables, and a golf club were built not far away on St. Simons Island, where Coffin also owned property.

During World War II, the Cloister hosted weekly mixers for honeymooning couples, including former president George H.W. Bush and his wife, Barbara, who married in 1945. They returned several times over the years, including in 1991 when Bush was in office and again on their fiftieth wedding anniversary. Sea Island also hosted the G8 Summit—and dignitaries from around the world—in 2004.

Sea Island has seen many transformations over the years, including a complete rebuild of the original 1928 Mizner main building and wings of the Cloister in 2006; a redesign of the golf courses; resort expansions; and several changes in ownership. That evolution continues today—more on that below.

A sample itinerary

Two favorite experiences during my recent visit included the scenic cruise on the Cloister’s two-story passenger yacht, the Sea Island Explorer, and taking a hawk walk with one of the resort’s falconers and his Harris hawk. If you’re as fascinated by the history of the island as I am, you’ll also want to book a walking tour of the Cloister with the resident historian in which you’ll pass through hallways lined with black and white photos chronicling the history of the island and the many famous guests who have walked these passageways.

Stop for a morning coffee and pastry or an afternoon cookie at the Cloister Solarium , a beautiful, light-filled space home to cozy seating areas, lush plants, and the sweet chirping  of a pair of lovebirds . Sea Island has always kept birds at the property; the first known feathered residents were finches that lived in the loggia of the original building in 1928.

I spent an evening at Tavola, the Cloister’s Italian restaurant, and notable dishes included seared scallops over a mélange of fava beans and seasonal vegetables, and a braised lamb shank with polenta. Our Tibetan terrier, Rhythm, also enjoyed his visit, especially sitting out on the balcony at night and taking long shaded walks through the grounds.

The revamped Georgian Rooms

The original Georgian Room, the property’s fine-dining venue, opened to guests in 2006 with hand-painted china, European linens, silver flatware, an impressive wine list, and smart tableside service. The restaurant closed in 2020 to accommodate a reimagined and extensively renovated concept—the Georgian Rooms, plural. The new spac e recently debuted and features multiple stylistically distinct areas.

There’s an intimate lounge serving sushi, Japanese-style dishes, cocktails, sakes, and whiskies. The venue is casual, and you can dine without a reservation. The main dining room and bar is a more formal space designed in a rich palette of dark greens and reds and leather seating (inspired by a classic American grill) and leads into the beautiful glass-enclosed Orangery. This naturally lit space, with its neutral tones and subtle décor, is brighter and airier than the clubby main dining room, especially during the day.

The menu, created by the new chef de cuisine of the Georgian Rooms, Chris Damskey, offers vintage spirits, classic cocktails, and an impressive wine list paired with such standout dishes as caviar service; Angus beef from Linz Heritage in Indiana; and regionally inspired seafood, such as roasted halibut with sweet pea purée and succotash.

New fun for kids

The Sea Island Sea-fari combines several of the resort’s signature activities so young adventurers can see the island’s “Big Five” wildlife: horses, falcons, turtles, dolphins, and shorebirds. The self-guided tour comes with a Sea-fari Passport so children can record their experiences. A free Golden Brick Sundae from Wonderland, the ice cream shop at the Beach Club, awaits future nature explorers who have completed their journey.

Pickleball pro

Eight standalone pickleball courts opened in 2021, and on-staff pickleball pro and former golf prodigy Tadd Fujikawa coordinates the programming, which includes private lessons, beginner and intermediate clinics, leagues for men and women, and round robins for larger groups. Sea Island also hosts pickleball tournaments for various charitable organizations.

An exclusive brew

Beer aficionados will want to check out Sea Island’s 1928 Classic Lager, a new addition to the resort’s lineup of brews made by Georgia-based Creature Comforts Brewing. On island time (hopefully soon!),  the new brew will be offered on draft and in the can.

New at the Lodge

The Lodge , located just minutes away on St. Simons Island, is reachable by car or complimentary shuttle from the Cloister. The intimate, forty-three-room luxury property, situated at the end of an oak-lined road, recently refreshed the guest rooms and restaurants with new décor, art, and furniture. Lodge guests have access to all the amenities of the Cloister and Sea Island, several dining options, an on-site pool, and twenty-four-hour butler service.

The Lodge is also where you’ll find Sea Island’s three championship golf courses and the Golf Performance Center. The most recent redesign of one of the original 1928 courses came in 2019 by professional golfer and St. Simons resident Davis Love III and his brother Mark of Love Golf Design. Guests familiar with the Men’s Locker Room, dubbed “the greatest locker room in golf” by PGA pros, will also find a redesigned traditional barbershop inspired by a 1936 photograph discovered in the archives. Women and children are welcome.

Colt & Alison , the property’s classic American steakhouse, was completely renovated in recent months, including an overhaul of the kitchen. The outdoor veranda is now a glass-enclosed space for year-round dining.

The Lodge attracts more golfers and couples than families since it’s a drive by car (rather than a walk or a golf cart ride) to the Beach Club and all of Sea Island’s family-friendly amenities. The property has an elegant, club-like feel, with dark wood paneling and traditional interior design. It was very quiet during our visit, though you can count on it being busy during golf tournaments and events, including the annual weeklong RSM Classic hosted by David Love III in mid-November.

No matter where you choose to stay when visiting Sea Island, don’t miss saying farewell to the day at the Sea Island Golf Club. This daily tradition at the Lodge includes a bagpiper performing a memorable Scottish sunset serenade.

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Sea Explorer

Eco marine adventures along fraser island’s remote north west coastline....

Step aboard our custom-built fast boat, the ‘Osprey' and explore the untouched paradise of K'gari's remote western coastline.  Cruise along the crystal-clear waters, discover the remote surrounding islands and spot marine life within the Great Sandy National Park, with these unique eco marine experiences exclusive to Kingfisher Bay Resort.  

This experience is available until 12th May 2024.

WEST COAST EXPLORER

Cruise along the western coast of K'gari and experience the remarkable sights of the UNESCO-awarded Great Sandy Biosphere - a remarkable habitat for many species of sea turtles, dolphins, dugongs and a range of coastal and migratory birds. Sharing their expert knowledge, our local skipper and Resort Ranger will offer guided walks and talks as you explore this idyllic natural paradise. Plus, our crew will stop off at some spectacular spots along the way for you to truly immerse yourself and explore!  

Wander along the wondrous white sands, learn about this pristine environment and take the opportunity to swim through crystal-clear waterways, on this surreal eco adventure.

Departure: 12:30pm, from the end of the Kingfisher Bay Resort jetty, near the ferry landing (Boarding time at 12:15pm) Duration: 3 hours

Inclusions: Water permit fees, expert marine guide, light refreshments and onboard bar available.

Cruise itinerary is subject to availability and weather conditions. SUNSET SESSIONS

Set out across the calm waters of the Great Sandy Strait and bask in K'gari's iconic golden glow, for the ultimate ‘sunset chill’ experience. Say ‘cheers’ to life in paradise with our on-board bar, sip complimentary drinks and relax with friends, as the sun dips below the horizon. 

Departure: 17:00pm, from the end of the Kingfisher Bay Resort jetty, near the ferry landing. Boarding time at 16:45pm. Inclusions: Light refreshments and beverages.

Please note that cruise itinerary is subject to availability and weather conditions.

West Coast Explorer $149 per adult, $95 per child Departs at 12:30pm

Sunset Cruise $99 per person Departs at 17:00pm Boarding at 16:45pm from the ocean end of the jetty

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Reservations Open Four Weeks in Advance

SARASOTA BAY EXPLORERS

Eco boat tours & bay cruises in sarasota.

LOCATED AT MOTE AQUARIUM

A HANDS-ON, EDUCATIONAL & FUN EXPERIENCE!

• most popular!
• Clock Arrive 30 min before departure
• Hour Glass Approx. 2 hours
• Users All ages

Sea Life Encounter Eco Tour

Observe our Florida manatees and resident population of bottlenose dolphins on this approximately 2 hour sea life cruise while learning about the ecology, history, and folklore of the area.

• Users Maximum of 6 people
• Hour Glass Custom

Miss Explorer Private Charter - Small Groups

Looking for an unforgettable day? Let our captain help you create your own custom cruise that is perfect for special events. Choose one activity or combine activities to make a full day of fun!

• Family Friendly
• Users Max of 40 people
• Hour Glass 2 hours

Sarasota Sunset Cruise

Join us on a relaxed trip to BIG PASS where we will observe a breathtaking Sarasota sunset over the Gulf of Mexico.

SEA LIFE ENCOUNTER ECO TOUR

About sarasota bay explorers.

Embark on an fun and educational journey through the clear waters of Sarasota, Florida, and discover the wonders of marine science and eco-conservation on one of our unforgettable boat tours.

Our expert guides will take you on a thrilling adventure, showcasing the breathtaking natural beauty of Sarasota Bay while teaching you about the local marine life and the efforts to preserve it.

We are located in beautiful Sarasota, Florida and work in conjunction with Mote Marine Laboratory to provide interactive marine science boat trips for both public and private use.

We offer several types of eco-tours including our renowned  Sea Life Encounter Cruise  and private charters aboard the Miss Explorer.

In addition to our regular cruises, you may charter a trip on one of our 40-foot pontoon boats for a private group. Private charters are available for anything from school field trips to company outings to birthday parties.

GUESTS LOVE OUR FAMILY-FRIENDLY CRUISES!

We enjoyed a wonderful multi-generational Sea Encounter trip on a HOT July Sunday...It’s hard to imagine how much everyone can learn, while having so much fun, in less than 2 hours. I wish I had taken one of these tours in the past and will definitely take one again. Well done!

This was the 6th or 7th trip I’ve done with these guys and it’s always great. An absolute blast and relatively inexpensive. If you like the ocean, sea life and are in the area it’s a ‘must experience’. Bring a camera.

This was an amazing experience and the next time my great nieces and nephews come down from Michigan we our going on this extremely well done educational and interactive boat ride!!! The marine biologist that was onboard did such an amazing job explaining things and the kids that were on the boat absolutely loved it also!!!

I love being out on the water, so this seemed like a natural fit. Our guides were very informative as we toured Sarasota bay. I loved seeing the fish and also the birds. It was a great way to spend the morning.

My mom and I really enjoyed this boat ride! The captain and biologist were professional and informative. It was the perfect amount of time spent on the water, and we got to see lots of wildlife.

Just moved to Sarasota and friends came to visit. Wanted to show them the beauty of the area and friend recommended this tour. We all had a fabulous experience with Martha. The trip was fun and educational. Loved learning about the different birds on bird island (saw my first spoonbill) and all the sea creatures. Definite must for any age. My husband and I bought membership to the Mote Marine and Laboratory so we can bring guests that visit. We will also be doing the tour again.

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The ultimate bucket list expeditions for explorer yacht owners

Related articles, superyacht directory.

With the rise of explorer yachts, reaching far-flung corners of the globe is suddenly possible. Here’s where to add to your adventure bucket list if you're looking for the best destinations to visit on an explorer yacht expedition cruise. 

Turn the clock back to the last century and the term “ explorer yacht ” didn’t really exist. There was a smattering of commercial vessels converted and fitted out to take intrepid owners to remote or difficult environments, but there weren’t really any private yachts specifically built to undertake expeditions. Then in 2003 came the launch of Octopus , the 126-metre prodigy built by Lürssen for diving enthusiast Paul Allen . Fast forward 18 years, and the world’s oceans are bristling with expedition yachts, triggering a dedicated Explorer Yachts Summit to be held at BOAT's International Festival of Yachting .

BOAT Pro data classifies 197 40-metre-plus superyachts as Explorer Class, but there are 32 more in build, with 28 due for launch in 2022. However you look at it, the growth is phenomenal. “It’s a 300 per cent increase over only a few years,” says EYOS Expeditions co-founder Ben Lyons, whose business has boomed alongside the growth in explorer yachts. “Fifteen years ago when the company started, the idea of taking a yacht to an expedition destination was seen as foolhardy and crazy. Now it’s the hot industry trend. As more and more people see the amazing experiences their friends are having, we are seeing more yachts being built for these locations.”

The boom we’ve seen in recent years has its roots in the search for authenticity. A growing cadre of yacht owners are no longer content to while away their summer days sipping cocktails at the quay in the French Riviera. “People want a more meaningful experience,” says Lyons. In the meantime, boatyards have raised their game to offer phenomenal luxury within a very capable explorer wrapper. “An explorer can also have a softer approach with a high-quality yacht finish,” explains Oceanco’s Emy Artolli, pointing to 91.5-metre Tranquility . “She is a true opulent explorer, but with Ice Class certification and extended range capability.”

EYOS Expeditions is one of the biggest integrated expedition organisers in the business, and has been behind some of the most iconic yachting adventures of the last few years – from the Five Deeps Expedition to Papua New Guinea and the Ross Ice Shelf. In a planning process that can take a year or more, EYOS will assess your boat’s suitability for your chosen destination and help the captain develop an itinerary.

“One of the things we pride ourselves on is being thorough and honest,” says Lyons when I ask whether he has ever refused to take a client exploring. “There are times when you have to say to people, ‘That extreme destination is not achievable for your vessel.’ More often, we have to adjust the itinerary and the programme to fit within the vessel’s capabilities.” Then there are the permits and paperwork – an unseen symphony directed by the exploration team. The owner will ideally not be aware of the minutiae of this process, but it can be laborious.

“These locations can be under various different jurisdictions above and beyond what you’d think because of their remote nature – governing what you can do with black and grey water, provisions and getting fuel in,” says Kelvin Murray, director of EYOS’s expedition operations and undersea projects and a Fellow of the Royal Geographical Society. “For a yacht used to cruising in a well-supplied area, this can be a challange, but we manage to make just about anything happen with a bit of creative thinking.”

Deepest explorer destinations

It is a truism to point out that we know more about the surface of the Moon than we do about our own planet’s seabed. But it’s still astonishing to think that no human had been to the deepest point in each ocean until two years ago. Those milestones were passed by Victor Vescovo , funding his own 10-month expedition to reach the lowest point in the five oceans from the refitted 68-metre research vessel DSSV Pressure Drop .

“Eighty-plus per cent of the ocean floor is unmapped and unexplored, so there are wide-open areas to go,” Vescovo tells me. “As best we know, there are several huge ocean trenches that have never had a crewed descent to their bottoms before, like the Peru-Chile or Mid-American trenches. I would love to dive those. Perhaps they have unique features we have not seen anywhere else.”

The lowest point of the Peru-Chile Trench is believed to be 8,065 metres below sea level in the Richards Deep, but it is the scale which defies belief. At 5,900 kilometres long, the trench is twice the length of the Himalayas. It is a vast feature of the ocean floor and yet, it has been scarcely explored. The little-known Middle America Trench at the intersection of four tectonic plates off Honduras reaches a staggering depth of 6,669 metres.

In addition to distinctive features, there are plenty of unique creatures, too. Vescovo’s dive off Puerto Rico uncovered four suspected new species, including a hadal snailfish and a stalked ascidian – a gelatinous animal like a sea squirt. Another science-minded owner, Mark Dalio, has used his private Alucia research vessel to capture the first footage ever of a giant squid, and discovered five new species, including two corals in deep waters off Boston. He has just invested in refitting an even more capable vessel to intensify his marine science effort under the OceanX initiative .

Dalio used a Triton submarine with an operating floor of 1,000 metres, while Vescovo also had his own submersible, DSV Limiting Factor , built for the job by Triton. Director James Cameron dived to 10,908-metre depth in the c in 2012 using another custom-built submersible, designed by Australian diving legend Ron Allum. Fortunately, Triton now offers its most capable sub as a series model, and if you don’t fancy waiting to have one built, you can always charter a yacht with its own submersible .

Highest explorer destinations

Most of the world’s highest mountains are well inland and inaccessible by yacht, but there are some intriguing exceptions. Higher latitudes in particular offer some world-class climbing straight off the boat, notably the sea-cliffs of Greenland and North Baffin Island. Just north west of Cape Farewell on Greenland’s southern tip is the redoubtable Thumbnail climb, for instance, rising to 1,490 metres straight out of the icy waters of the fjord.

“I like the fact that it’s pretty much as far away from everything as you could ever get,” says expedition leader Cecila Vanman. “It’s a true wilderness – a place where you can still walk up a valley and down the other side of a mountain and see something that very, very few other people have ever seen.”

Serial explorer Victor Vescovo took a different tack with the first full ascent of Mauna Kea in Hawaii. At 4,207 metres above sea level, the summit is challenging enough, but geologists consider that the mountain actually begins 5,116 metres below the waves. Launching from his vessel Pressure Drop , Vescovo took a submersible to the seabed, reascended, then paddled ashore in a kayak, took to a bike to reach the mountain’s base station at 2,743 metres up and climbed the rest of the way on foot.

Antarctica also offers skiing and climbing opportunities in some of the most extreme conditions on Earth. In fact, any trip to the South Pole would involve a 3,000-metre ascent, and some mountain ranges have peaks over 4,500 metres. “The ice over the Pole is approximately 2,700 metres thick, so the rock of the continent below is almost at sea level,” says Murray.

But it is not so much the height that counts here. A favourite of Murray’s is Mount Scott on the Antarctic Peninsula, which feels very alpine, although it rises to just 880 metres. “On a clear day you can see well up towards the islands of Gerlache Strait to the north, and Crystal Sound to the south,” he says. “Clients gain a different perspective at sea or deck level and the clear, pollution-free skies give a breathtaking panorama. Point being, you don’t have to go super-high to have an extraordinary experience.”

The continent’s unique climate is drier than a desert in some places, meaning climbs are mysteriously ice-free. Not so the world’s southernmost active volcano, Mount Erebus, which towers 3,794 metres above Ross Island. Despite the lava lake in its crater, its flanks are covered with snow and ice caves form around its numerous fumaroles.

A helicopter is a real asset here, getting you to the base of a climb or into the heart of a wilderness to explore. But it also serves another purpose, as adventurer and guide Richard White explains. While the roar of two 500kW turboshaft engines can send many animals running for cover, it is great for watching large, solitary animals. “My best experience with wildlife helicopters so far has been whale watching,” he says. “Seeing a whale from a boat is like looking at an iceberg – the majority is below the surface. Getting up high and looking down, the whole animal, nose to tail, is revealed and gives a completely different sense of it. Our understanding of some species, such as narwhal and beluga, have been transformed by viewing from above.”

White says he aims to heighten the experience of simply viewing an animal into something far more dynamic. “To find an animal actively hunting or to witness a kill elevates a more typical sighting, which can still be very special, into something fascinating and relatively rarely seen.”

Farthest explorer destinations

When it comes to remoteness, chief among the top spots is the Antarctic Peninsula, also known as Graham Land in the UK. Resembling a long arm reaching north from the South Pole, it is actually a string of bedrock islands covered by ice and scored with deep channels, which make it a varied and exciting landscape to explore. Its proximity to the inhabited areas of Tierra del Fuego is handy for provisioning and joining ship.

“The Antarctic Peninsula is the hottest destination,” says Lyons with a smile. “We’ll have seven yachts down there this Austral summer.” At the bottom of the world, there are penguins galore – seals and other seabirds, too, and cold-water diving for the hardy. But the scenery is the greatest pull. With chiselled mountain peaks, glaciers, frozen lakes and rocky outcrops, the landscape is awe-inspiring and also offers unparalleled skiing opportunities.

You will need two helicopters in this part of the world – one to fly you in and the other as back-up for search and rescue. “There is no SAR or infrastructure in Antarctica. It’s not a playground,” says Murray. What’s more, permits to travel there may place limits on what you can do.  “It’s the only continent dedicated to peace and science. Activities there are required by law to help you appreciate the aesthetic of the place, so jet skis are not permitted.”

The Northwest Passage and the Canadian Arctic also offer phenomenal remote cruising in an environment that, retreating ice notwithstanding, humans have done little to alter. There is excellent fishing and the opportunity to spot polar bears, Arctic foxes, musk oxen, wolves, as well as whales, belugas and narwhals. Expect to see plenty of ice, from mighty glaciers to vast icebergs and loose pack ice. There’s the opportunity to get up close to all of it, and even to set foot on icebergs. As few as 300 boats of any kind are thought to have navigated this tricky, ice-choked branching waterway. “It’s iconic and people want to say ‘My yacht has done this,’ but it is becoming more challenging in terms of permissions,” says Murray.

It’s not all about sub-zero climates, though. A well fitted-out explorer can find plenty of adventure in the Pacific Ocean, exploring wild islands and diving the world’s clearest waters, teeming with life. There are parts of Indonesia, Melanesia and Micronesia that are so far off the beaten track that the only visitors they see are the occasional supply boats. “We often view the globe by looking from our centralised European perspective, but if you spin the planet it reveals a blue marble of ocean,” says Murray. “Out in the middle of the Pacific you can feel truly far from home ground, especially if you have sailed there.”

Fabled destinations such as the Pitcairn Islands and Easter Island are thousands of kilometres from the next inhabited place and, in the case of Pitcairn, the only access is by boat. “These are really isolated places and don’t have the resources or facilities to cater for the needs of a superyacht,” Murray explains. “But then of course, that is a reason to visit – it’s truly off the beaten track.”

A large number of isolated atolls are completely uninhabited, such as Kiribati’s Millennium Atoll. With almost no human intervention to this day, it is reckoned to be as close to a pristine habitat as you can find. “Like some of the remote diving atolls in the South Pacific, it offers exceptional diving, and is totally unspoilt with no infrastructure,” says Murray.

But the jewel in the crown here is Papua New Guinea. This huge island and its waters are home to five per cent of the planet’s species, with what is without a doubt the finest snorkelling and diving the world has to offer. The country also hosts some 5,000 different communities speaking 850 distinct languages and has very little infrastructure. This makes it ideal for exploring by yacht, particularly if you have a helicopter on board.

An EYOS itinerary might begin in the ruins of Rabaul, a town destroyed by the Tavurvur volcano in 1994 and is now said to resemble Pompeii. Then it would move on via some of Papua New Guinea’s unspoiled diving sites to Baia, where the hidden springs and waterfalls of the interior are only accessible by aircraft. There are the cultural performances of the Witu islanders, whose spectacular masks and customs remain largely untouched by the outside world. Vibrant-coloured corals and white sand beaches abound at Kimbe Bay and the islands of New Ireland and New Hanover. And a lucky few have a chance to stay among the people of the Western Highlands, who knew nothing of the outside world until the 1930s, and their way of life has remained largely unchanged for millennia.

The islands of the Mid-Atlantic Ridge are also extremely remote and rarely visited, although there are permanent inhabitants. Tristan da Cunha is perhaps the most interesting, with an array of fine hiking, interesting wildlife and diving in the kelp forests among seals, rays and sharks. “It’s a five- to six-day steam from Cape Town,” says Murray. “It is a rather surreal combination of volcanic sub-tropical island and British influences, complete with red post boxes, and the superintendent wears a police uniform.”

In some ways, the location of these places is becoming secondary, according to EYOS. The next big expeditions may be more about scientific accomplishment than fulfilling a purely personal goal. “We have seen our clients become so engaged with ‘bigger picture’ impact and having the opportunity to give something back to humankind,” says Murray. “I can envision large-scale voyages covering multi-disciplinary sciences, where the notion of citizen science is dramatically upscaled.”

This feature is taken from the September 2021 issue of BOAT International. To buy tickets for the Explorer Yachts Summit , click the button below. 

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Sea Life Safari Nature Tour

Island explorer i & ii.

A hands-on experience unlike any other cruise. View natural habitats & an island bird sanctuary, collect shells and touch sea life. The only tour licensed to pull a net and guided by a Marine Specialist from the Clearwater Marine Aquarium. Kids and adults of all ages will love this unique marina life adventure! This tour only departs from the CLEARWATER MARINE AQUARIUM .

This tour only departs from the CLEARWATER MARINE AQUARIUM .

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Out Island Charters: The Best day tours and cruise ship excursions on St. Maarten

As the premier shore excursion company in St. Maarten we operate the Golden Eagle sailing catamarans, powerboats, Explorer Lagoon cruises, land and sea island tours or fully customizable private tours

Explorer Cruise

Embrace the variety that St. Maarten has to offer on a narrated drive, free time in the charming French capital, and a lively cruise of the lagoon. 

During the bus ride on an air-conditioned bus you will learn history of St. Maarten. A narrated tour is available in 6 languages (English, French, German, Italian, Portuguese and Spanish). You will stop above Orient Bay for a chance to take photos of this world famous beach. Upon arriving in the French capital of Marigot you will have one hour to explore the shops, bakeries, cafes and restaurants.

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24 Luxury Cruise Facts That Might Surprise You

Posted: November 7, 2023 | Last updated: December 10, 2023

Sumptuous escapes at sea

Some Oceania Cruises suites have walk-in closets and grand pianos

No expense has been spared when it comes to suite decor on luxury ships. For ultimate opulence, opt for the Owner’s suites which you’ll find on Oceania Cruises ' ships. These cover 1,991 square feet, have two walk-in closets and entrance foyers with a grand piano and a mahogany bar. A 15-day Svalbard & Arctic Passage cruise with accommodation in the Grand Owner’s suite costs from $23,044 per person.

Regent Seven Seas Cruises’ Seven Seas Explorer had a big design budget

We’re increasingly seeing bigger budgets for ships’ decor. Huge amounts of cash are being splashed on sprucing up interiors, and one example of this decadence is Regent Seven Seas Cruises ' Seven Seas Explorer, which has 473 Swedish-designed chandeliers, 45,876 square feet of marble, Versace-designed dinnerware, crystal glasses from Eastern Europe and a $12 million art collection which includes several Picassos.

Orient Express is set to launch a seriously luxurious ship

After launching the world’s most luxurious train 140 years ago, Orient Express will launch an opulent ship to match. Orient Express Silenseas, which will take to the waves in 2026, will have 54 suites (including a 15,231-square-foot Presidential Suite), two swimming pools, two restaurants and a speakeasy bar. Oh, and a recording studio. Prices are to be confirmed (but will inevitably be eye-watering).

Windstar Cruises’ Star Legend offers themed suites

Sail on Windstar Cruises’ Star Legend and you can book a suite inspired by exotic destinations and hotels. We recommend the suite inspired by the Sea Island resort in Georgia. Expect ocean-inspired colourways and plenty of sea-glass green. A Treasures of the Greek Isles cruise with Windstar starts from $3,745 per person.

Now discover amazing facts about cruise ships you might not know

There are butlers onboard with a Silversea cruise

Book a sailing with  Silversea  and you’re guaranteed your own butler. They'll be on hand to help with everything from the unpacking of luggage to the opening of the Champagne bottles. They’re not just any butlers, either – they’ve undertaken a 108-point training programme created for the cruise line by the London-based School for Butlers. An 11-day Mediterranean Cruise in 2024 costs from $8,092 per person.

You can go beneath the ocean's surface with Scenic Cruises

An abundance of onboard kit means that luxury ships don’t just help passengers get to the world’s most remote places – they help them get below the waves and into the skies too. Take Scenic Cruises – their Scenic Eclipse ship recently became the first vessel to offer both helicopter flights and submarine dives in the Canadian Arctic. An Antarctica in Depth cruise costs from $16,310 per person.

Seven Seas Grandeur has in-suite spas

Love a session in the spa but value your personal space? Book Regent Seven Seas Cruises ’ Regent Suite, which you’ll find on Seven Seas Grandeur, due to launch in November 2023. Highlights include the two enormous bedrooms and the whirlpool bath on the balcony, although the pièce de resistance is the suite’s very own spa retreat.

North America's best river cruises and steamboat journeys

You can sleep under the stars with the SeaDream Yacht Club

Set sail on one of SeaDream Yacht Club ’s yacht-style vessels and you’ll be able to spend a night under the stars. At night, staff transform the upper deck’s huge Balinese day beds by adding luxurious bed linens and fluffy pillows, allowing you to drift off to the sound of the ocean. Expect to pay around $3,700 for a seven-day cruise.

SeaDream Yacht Club has one of the highest crew-to-guest ratios at sea

Some cruise lines offer boats on boats

Zodiacs – small, fast boats carried on ships – make it easy to explore different landscapes, whether it’s the frozen tundra or the Galapagos’ wildlife-dotted islands. Special mentions go to Quark , which uses environmentally friendly four-stroke engine zodiacs; Silversea , famous for its expert-led zodiac excursions, and AE Expeditions – the line’s new expedition ship Sylvia Earle has 15 zodiacs. A seven-day Spitsbergen sailing with Quark costs from $5,547.

Aurora Expeditions and AE Expeditions ships have science laboratories onboard

If peering at distant shorelines through binoculars doesn’t cut it, sign up for a sailing with Aurora Expeditions or AE Expeditions . AE Expeditions ships have tech-filled laboratories and lecture theaters, making it easy to gain new perspectives on the destinations in question. Guests can contribute to a wide range of research projects, including ones relating to micro-plastics and sea life. A 15-day Svalbard In Depth sailing starts from $12,137 per person.

You can have your very own Dom Perignon Experience on Oceania Cruises’ Vista ship

Is spaciousness a priority? Consider Oceania Cruises . Their newest ship Vista (which set sail in May 2023) is tipped as having the largest entry-level staterooms at sea (280 square feet, if you were wondering). We’re equally excited about the Dom Perignon Experience – during this six-course extravaganza you’ll sip Dom Perignon Champagnes chosen to suit the various dishes. A 10-day Bangkok to Singapore cruise starts from $5,335 per person.

Celebrity Cruises’ Celebrity Flora has a stargazing platform

Celebrity Cruises ’ Celebrity Flora, which has space for just 100 passengers and is based permanently in the Galapagos Islands, is a pint-sized ship that can effortlessly access the areas other vessels can’t reach. But our favorite feature is the stargazing platform. Head here for stargazing sessions led by the ship’s onboard astronomer. You’ll pay from $7,796 for a Galapagos Inner Loop sailing on Celebrity Flora.

The naming ceremonies are often spectacular

Simply swinging a bottle against the side of a ship is so passé. In January 2023 Viking christened new luxury ship Viking Neptune. The ship’s godmother Nicole Stott (a retired NASA astronaut) used a traditional Viking broad ax to cut the rope, which sent a bottle of fizz smashing into the ship. A 13-day Mediterranean Odyssey cruise with Viking costs $5,911.

Your Abercrombie & Kent guide might be a famous explorer

Abercrombie & Kent Luxury Expedition Cruises – previously known as Crystal Cruises – are famous for their onboard experts. The cruise line’s expedition leaders include explorer James McClintock, recipient of the Antarctica Service Medal, and former Royal Marine Commando Russ Manning, who served as base commander in the South Orkneys and earned the Polar Medal. A 14-night Arctic Cruise Adventure with Abercrombie & Kent costs from $17,922.

You no longer have to wear a ball gown to dinner

You can ride on a magic carpet with Celebrity Cruises

Okay, not the type ridden by Aladdin. We’re talking about Celebrity Cruises’ Magic Carpet – a cantilevered platform which appears to float in thin air, and which glides up and down the side of Celebrity Edge, one of the cruise line’s most luxurious ships. Depending on what level it stops at, the Magic Carpet can become a restaurant, bar or nightclub, although the one constant is breathtaking views.

Check out Spain's most stunning seaside spots

There are luxury ships you can live on

Dread disembarkation day? Why not simply stay onboard? No, we’re not suggesting claiming squatters’ rights at the end of your cruise, but splashing out on a cabin on  The World , described by its owners as a luxury private residence at sea. There are 165 residences available for purchase and the ship sails around the planet – in 2023 it will visit South Asia, the Middle East, the Iberian Peninsula, Greenland, South America and Antarctica. Some residents live on the ship full-time, while others visit throughout the year, and residences start at around $1.2m.

Luxury cruise lines can be fully all-inclusive too

You can feast on cuisine prepared by Michelin-starred chefs

You can learn firsthand about the Polar regions

Luxury cruise lines are going all out to provide fascinating insights into the explorers who first mapped these regions. In 2024, Scenic will launch several East Antarctic cruises focusing on the routes taken by explorer Sir Ernest Shackleton. If you sail through the Arctic on Ponant’s Le Commandant Charcot (the world’s only luxury ice breaker), a team of 23 polar experts will help you gain a whole new perspective on these remote regions.

There’s designer decor on Oceania Cruises’ Vista ship

SeaDream Yacht Club offer a ‘Champagne & Caviar Splash’

You need to book well in advance

If you’re planning on a bucket list-worthy sailing on one of the more luxurious ships, you’ll need to bag your spot early on. Take  Azamara’s World Voyage , a 155-night, 37-country sailing which takes place in 2024 and is currently sold out (there’s a waiting list of passengers hoping for cancellations). Luckily, spots on the 2025 World Voyage are still available – if you’ve got a minimum of $42,622 to spare.

The world's most beautiful ports visited by cruise ships

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Crying Myself to Sleep on the Biggest Cruise Ship Ever

Seven agonizing nights aboard the Icon of the Seas

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Updated at 2:44 p.m. ET on April 6, 2024.

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MY FIRST GLIMPSE of Royal Caribbean’s Icon of the Seas, from the window of an approaching Miami cab, brings on a feeling of vertigo, nausea, amazement, and distress. I shut my eyes in defense, as my brain tells my optic nerve to try again.

The ship makes no sense, vertically or horizontally. It makes no sense on sea, or on land, or in outer space. It looks like a hodgepodge of domes and minarets, tubes and canopies, like Istanbul had it been designed by idiots. Vibrant, oversignifying colors are stacked upon other such colors, decks perched over still more decks; the only comfort is a row of lifeboats ringing its perimeter. There is no imposed order, no cogent thought, and, for those who do not harbor a totalitarian sense of gigantomania, no visual mercy. This is the biggest cruise ship ever built, and I have been tasked with witnessing its inaugural voyage.

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“Author embarks on their first cruise-ship voyage” has been a staple of American essay writing for almost three decades, beginning with David Foster Wallace’s “A Supposedly Fun Thing I’ll Never Do Again,” which was first published in 1996 under the title “Shipping Out.” Since then, many admirable writers have widened and diversified the genre. Usually the essayist commissioned to take to the sea is in their first or second flush of youth and is ready to sharpen their wit against the hull of the offending vessel. I am 51, old and tired, having seen much of the world as a former travel journalist, and mostly what I do in both life and prose is shrug while muttering to my imaginary dachshund, “This too shall pass.” But the Icon of the Seas will not countenance a shrug. The Icon of the Seas is the Linda Loman of cruise ships, exclaiming that attention must be paid. And here I am in late January with my one piece of luggage and useless gray winter jacket and passport, zipping through the Port of Miami en route to the gangway that will separate me from the bulk of North America for more than seven days, ready to pay it in full.

The aforementioned gangway opens up directly onto a thriving mall (I will soon learn it is imperiously called the “Royal Promenade”), presently filled with yapping passengers beneath a ceiling studded with balloons ready to drop. Crew members from every part of the global South, as well as a few Balkans, are shepherding us along while pressing flutes of champagne into our hands. By a humming Starbucks, I drink as many of these as I can and prepare to find my cabin. I show my blue Suite Sky SeaPass Card (more on this later, much more) to a smiling woman from the Philippines, and she tells me to go “aft.” Which is where, now? As someone who has rarely sailed on a vessel grander than the Staten Island Ferry, I am confused. It turns out that the aft is the stern of the ship, or, for those of us who don’t know what a stern or an aft are, its ass. The nose of the ship, responsible for separating the waves before it, is also called a bow, and is marked for passengers as the FWD , or forward. The part of the contemporary sailing vessel where the malls are clustered is called the midship. I trust that you have enjoyed this nautical lesson.

I ascend via elevator to my suite on Deck 11. This is where I encounter my first terrible surprise. My suite windows and balcony do not face the ocean. Instead, they look out onto another shopping mall. This mall is the one that’s called Central Park, perhaps in homage to the Olmsted-designed bit of greenery in the middle of my hometown. Although on land I would be delighted to own a suite with Central Park views, here I am deeply depressed. To sail on a ship and not wake up to a vast blue carpet of ocean? Unthinkable.

Allow me a brief preamble here. The story you are reading was commissioned at a moment when most staterooms on the Icon were sold out. In fact, so enthralled by the prospect of this voyage were hard-core mariners that the ship’s entire inventory of guest rooms (the Icon can accommodate up to 7,600 passengers, but its inaugural journey was reduced to 5,000 or so for a less crowded experience) was almost immediately sold out. Hence, this publication was faced with the shocking prospect of paying nearly $19,000 to procure for this solitary passenger an entire suite—not including drinking expenses—all for the privilege of bringing you this article. But the suite in question doesn’t even have a view of the ocean! I sit down hard on my soft bed. Nineteen thousand dollars for this .

The viewless suite does have its pluses. In addition to all the Malin+Goetz products in my dual bathrooms, I am granted use of a dedicated Suite Deck lounge; access to Coastal Kitchen, a superior restaurant for Suites passengers; complimentary VOOM SM Surf & Stream (“the fastest Internet at Sea”) “for one device per person for the whole cruise duration”; a pair of bathrobes (one of which comes prestained with what looks like a large expectoration by the greenest lizard on Earth); and use of the Grove Suite Sun, an area on Decks 18 and 19 with food and deck chairs reserved exclusively for Suite passengers. I also get reserved seating for a performance of The Wizard of Oz , an ice-skating tribute to the periodic table, and similar provocations. The very color of my Suite Sky SeaPass Card, an oceanic blue as opposed to the cloying royal purple of the standard non-Suite passenger, will soon provoke envy and admiration. But as high as my status may be, there are those on board who have much higher status still, and I will soon learn to bow before them.

In preparation for sailing, I have “priced in,” as they say on Wall Street, the possibility that I may come from a somewhat different monde than many of the other cruisers. Without falling into stereotypes or preconceptions, I prepare myself for a friendly outspokenness on the part of my fellow seafarers that may not comply with modern DEI standards. I believe in meeting people halfway, and so the day before flying down to Miami, I visited what remains of Little Italy to purchase a popular T-shirt that reads DADDY’S LITTLE MEATBALL across the breast in the colors of the Italian flag. My wife recommended that I bring one of my many T-shirts featuring Snoopy and the Peanuts gang, as all Americans love the beagle and his friends. But I naively thought that my meatball T-shirt would be more suitable for conversation-starting. “Oh, and who is your ‘daddy’?” some might ask upon seeing it. “And how long have you been his ‘little meatball’?” And so on.

I put on my meatball T-shirt and head for one of the dining rooms to get a late lunch. In the elevator, I stick out my chest for all to read the funny legend upon it, but soon I realize that despite its burnished tricolor letters, no one takes note. More to the point, no one takes note of me. Despite my attempts at bridge building, the very sight of me (small, ethnic, without a cap bearing the name of a football team) elicits no reaction from other passengers. Most often, they will small-talk over me as if I don’t exist. This brings to mind the travails of David Foster Wallace , who felt so ostracized by his fellow passengers that he retreated to his cabin for much of his voyage. And Wallace was raised primarily in the Midwest and was a much larger, more American-looking meatball than I am. If he couldn’t talk to these people, how will I? What if I leave this ship without making any friends at all, despite my T-shirt? I am a social creature, and the prospect of seven days alone and apart is saddening. Wallace’s stateroom, at least, had a view of the ocean, a kind of cheap eternity.

Worse awaits me in the dining room. This is a large, multichandeliered room where I attended my safety training (I was shown how to put on a flotation vest; it is a very simple procedure). But the maître d’ politely refuses me entry in an English that seems to verge on another language. “I’m sorry, this is only for pendejos ,” he seems to be saying. I push back politely and he repeats himself. Pendejos ? Piranhas? There’s some kind of P-word to which I am not attuned. Meanwhile elderly passengers stream right past, powered by their limbs, walkers, and electric wheelchairs. “It is only pendejo dining today, sir.” “But I have a suite!” I say, already starting to catch on to the ship’s class system. He examines my card again. “But you are not a pendejo ,” he confirms. I am wearing a DADDY’S LITTLE MEATBALL T-shirt, I want to say to him. I am the essence of pendejo .

Eventually, I give up and head to the plebeian buffet on Deck 15, which has an aquatic-styled name I have now forgotten. Before gaining entry to this endless cornucopia of reheated food, one passes a washing station of many sinks and soap dispensers, and perhaps the most intriguing character on the entire ship. He is Mr. Washy Washy—or, according to his name tag, Nielbert of the Philippines—and he is dressed as a taco (on other occasions, I’ll see him dressed as a burger). Mr. Washy Washy performs an eponymous song in spirited, indeed flamboyant English: “Washy, washy, wash your hands, WASHY WASHY!” The dangers of norovirus and COVID on a cruise ship this size (a giant fellow ship was stricken with the former right after my voyage) makes Mr. Washy Washy an essential member of the crew. The problem lies with the food at the end of Washy’s rainbow. The buffet is groaning with what sounds like sophisticated dishes—marinated octopus, boiled egg with anchovy, chorizo, lobster claws—but every animal tastes tragically the same, as if there was only one creature available at the market, a “cruisipus” bred specifically for Royal Caribbean dining. The “vegetables” are no better. I pick up a tomato slice and look right through it. It tastes like cellophane. I sit alone, apart from the couples and parents with gaggles of children, as “We Are Family” echoes across the buffet space.

I may have failed to mention that all this time, the Icon of the Seas has not left port. As the fiery mango of the subtropical setting sun makes Miami’s condo skyline even more apocalyptic, the ship shoves off beneath a perfunctory display of fireworks. After the sun sets, in the far, dark distance, another circus-lit cruise ship ruptures the waves before us. We glance at it with pity, because it is by definition a smaller ship than our own. I am on Deck 15, outside the buffet and overlooking a bunch of pools (the Icon has seven of them), drinking a frilly drink that I got from one of the bars (the Icon has 15 of them), still too shy to speak to anyone, despite Sister Sledge’s assertion that all on the ship are somehow related.

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The ship’s passage away from Ron DeSantis’s Florida provides no frisson, no sense of developing “sea legs,” as the ship is too large to register the presence of waves unless a mighty wind adds significant chop. It is time for me to register the presence of the 5,000 passengers around me, even if they refuse to register mine. My fellow travelers have prepared for this trip with personally decorated T-shirts celebrating the importance of this voyage. The simplest ones say ICON INAUGURAL ’24 on the back and the family name on the front. Others attest to an over-the-top love of cruise ships: WARNING! MAY START TALKING ABOUT CRUISING . Still others are artisanally designed and celebrate lifetimes spent married while cruising (on ships, of course). A couple possibly in their 90s are wearing shirts whose backs feature a drawing of a cruise liner, two flamingos with ostensibly male and female characteristics, and the legend “ HUSBAND AND WIFE Cruising Partners FOR LIFE WE MAY NOT HAVE IT All Together BUT TOGETHER WE HAVE IT ALL .” (The words not in all caps have been written in cursive.) A real journalist or a more intrepid conversationalist would have gone up to the couple and asked them to explain the longevity of their marriage vis-à-vis their love of cruising. But instead I head to my mall suite, take off my meatball T-shirt, and allow the first tears of the cruise to roll down my cheeks slowly enough that I briefly fall asleep amid the moisture and salt.

I WAKE UP with a hangover. Oh God. Right. I cannot believe all of that happened last night. A name floats into my cobwebbed, nauseated brain: “Ayn Rand.” Jesus Christ.

I breakfast alone at the Coastal Kitchen. The coffee tastes fine and the eggs came out of a bird. The ship rolls slightly this morning; I can feel it in my thighs and my schlong, the parts of me that are most receptive to danger.

I had a dangerous conversation last night. After the sun set and we were at least 50 miles from shore (most modern cruise ships sail at about 23 miles an hour), I lay in bed softly hiccupping, my arms stretched out exactly like Jesus on the cross, the sound of the distant waves missing from my mall-facing suite, replaced by the hum of air-conditioning and children shouting in Spanish through the vents of my two bathrooms. I decided this passivity was unacceptable. As an immigrant, I feel duty-bound to complete the tasks I am paid for, which means reaching out and trying to understand my fellow cruisers. So I put on a normal James Perse T-shirt and headed for one of the bars on the Royal Promenade—the Schooner Bar, it was called, if memory serves correctly.

I sat at the bar for a martini and two Negronis. An old man with thick, hairy forearms drank next to me, very silent and Hemingwaylike, while a dreadlocked piano player tinkled out a series of excellent Elton John covers. To my right, a young white couple—he in floral shorts, she in a light, summery miniskirt with a fearsome diamond ring, neither of them in football regalia—chatted with an elderly couple. Do it , I commanded myself. Open your mouth. Speak! Speak without being spoken to. Initiate. A sentence fragment caught my ear from the young woman, “Cherry Hill.” This is a suburb of Philadelphia in New Jersey, and I had once been there for a reading at a synagogue. “Excuse me,” I said gently to her. “Did you just mention Cherry Hill? It’s a lovely place.”

As it turned out, the couple now lived in Fort Lauderdale (the number of Floridians on the cruise surprised me, given that Southern Florida is itself a kind of cruise ship, albeit one slowly sinking), but soon they were talking with me exclusively—the man potbellied, with a chin like a hard-boiled egg; the woman as svelte as if she were one of the many Ukrainian members of the crew—the elderly couple next to them forgotten. This felt as groundbreaking as the first time I dared to address an American in his native tongue, as a child on a bus in Queens (“On my foot you are standing, Mister”).

“I don’t want to talk politics,” the man said. “But they’re going to eighty-six Biden and put Michelle in.”

I considered the contradictions of his opening conversational gambit, but decided to play along. “People like Michelle,” I said, testing the waters. The husband sneered, but the wife charitably put forward that the former first lady was “more personable” than Joe Biden. “They’re gonna eighty-six Biden,” the husband repeated. “He can’t put a sentence together.”

After I mentioned that I was a writer—though I presented myself as a writer of teleplays instead of novels and articles such as this one—the husband told me his favorite writer was Ayn Rand. “Ayn Rand, she came here with nothing,” the husband said. “I work with a lot of Cubans, so …” I wondered if I should mention what I usually do to ingratiate myself with Republicans or libertarians: the fact that my finances improved after pass-through corporations were taxed differently under Donald Trump. Instead, I ordered another drink and the couple did the same, and I told him that Rand and I were born in the same city, St. Petersburg/Leningrad, and that my family also came here with nothing. Now the bonding and drinking began in earnest, and several more rounds appeared. Until it all fell apart.

Read: Gary Shteyngart on watching Russian television for five days straight

My new friend, whom I will refer to as Ayn, called out to a buddy of his across the bar, and suddenly a young couple, both covered in tattoos, appeared next to us. “He fucking punked me,” Ayn’s frat-boy-like friend called out as he put his arm around Ayn, while his sizable partner sizzled up to Mrs. Rand. Both of them had a look I have never seen on land—their eyes projecting absence and enmity in equal measure. In the ’90s, I drank with Russian soldiers fresh from Chechnya and wandered the streets of wartime Zagreb, but I have never seen such undisguised hostility toward both me and perhaps the universe at large. I was briefly introduced to this psychopathic pair, but neither of them wanted to have anything to do with me, and the tattooed woman would not even reveal her Christian name to me (she pretended to have the same first name as Mrs. Rand). To impress his tattooed friends, Ayn made fun of the fact that as a television writer, I’d worked on the series Succession (which, it would turn out, practically nobody on the ship had watched), instead of the far more palatable, in his eyes, zombie drama of last year. And then my new friends drifted away from me into an angry private conversation—“He punked me!”—as I ordered another drink for myself, scared of the dead-eyed arrivals whose gaze never registered in the dim wattage of the Schooner Bar, whose terrifying voices and hollow laughs grated like unoiled gears against the crooning of “Goodbye Yellow Brick Road.”

But today is a new day for me and my hangover. After breakfast, I explore the ship’s so-called neighborhoods . There’s the AquaDome, where one can find a food hall and an acrobatic sound-and-light aquatic show. Central Park has a premium steak house, a sushi joint, and a used Rolex that can be bought for $8,000 on land here proudly offered at $17,000. There’s the aforementioned Royal Promenade, where I had drunk with the Rands, and where a pair of dueling pianos duel well into the night. There’s Surfside, a kids’ neighborhood full of sugary garbage, which looks out onto the frothy trail that the behemoth leaves behind itself. Thrill Island refers to the collection of tubes that clutter the ass of the ship and offer passengers six waterslides and a surfing simulation. There’s the Hideaway, an adult zone that plays music from a vomit-slathered, Brit-filled Alicante nightclub circa 1996 and proves a big favorite with groups of young Latin American customers. And, most hurtfully, there’s the Suite Neighborhood.

I say hurtfully because as a Suite passenger I should be here, though my particular suite is far from the others. Whereas I am stuck amid the riffraff of Deck 11, this section is on the highborn Decks 16 and 17, and in passing, I peek into the spacious, tall-ceilinged staterooms from the hallway, dazzled by the glint of the waves and sun. For $75,000, one multifloor suite even comes with its own slide between floors, so that a family may enjoy this particular terror in private. There is a quiet splendor to the Suite Neighborhood. I see fewer stickers and signs and drawings than in my own neighborhood—for example, MIKE AND DIANA PROUDLY SERVED U.S. MARINE CORPS RETIRED . No one here needs to announce their branch of service or rank; they are simply Suites, and this is where they belong. Once again, despite my hard work and perseverance, I have been disallowed from the true American elite. Once again, I am “Not our class, dear.” I am reminded of watching The Love Boat on my grandmother’s Zenith, which either was given to her or we found in the trash (I get our many malfunctioning Zeniths confused) and whose tube got so hot, I would put little chunks of government cheese on a thin tissue atop it to give our welfare treat a pleasant, Reagan-era gooeyness. I could not understand English well enough then to catch the nuances of that seafaring program, but I knew that there were differences in the status of the passengers, and that sometimes those differences made them sad. Still, this ship, this plenty—every few steps, there are complimentary nachos or milkshakes or gyros on offer—was the fatty fuel of my childhood dreams. If only I had remained a child.

I walk around the outdoor decks looking for company. There is a middle-aged African American couple who always seem to be asleep in each other’s arms, probably exhausted from the late capitalism they regularly encounter on land. There is far more diversity on this ship than I expected. Many couples are a testament to Loving v. Virginia , and there is a large group of folks whose T-shirts read MELANIN AT SEA / IT’S THE MELANIN FOR ME . I smile when I see them, but then some young kids from the group makes Mr. Washy Washy do a cruel, caricatured “Burger Dance” (today he is in his burger getup), and I think, Well, so much for intersectionality .

At the infinity pool on Deck 17, I spot some elderly women who could be ethnic and from my part of the world, and so I jump in. I am proved correct! Many of them seem to be originally from Queens (“Corona was still great when it was all Italian”), though they are now spread across the tristate area. We bond over the way “Ron-kon-koma” sounds when announced in Penn Station.

“Everyone is here for a different reason,” one of them tells me. She and her ex-husband last sailed together four years ago to prove to themselves that their marriage was truly over. Her 15-year-old son lost his virginity to “an Irish young lady” while their ship was moored in Ravenna, Italy. The gaggle of old-timers competes to tell me their favorite cruising stories and tips. “A guy proposed in Central Park a couple of years ago”—many Royal Caribbean ships apparently have this ridiculous communal area—“and she ran away screaming!” “If you’re diamond-class, you get four drinks for free.” “A different kind of passenger sails out of Bayonne.” (This, perhaps, is racially coded.) “Sometimes, if you tip the bartender $5, your next drink will be free.”

“Everyone’s here for a different reason,” the woman whose marriage ended on a cruise tells me again. “Some people are here for bad reasons—the drinkers and the gamblers. Some people are here for medical reasons.” I have seen more than a few oxygen tanks and at least one woman clearly undergoing very serious chemo. Some T-shirts celebrate good news about a cancer diagnosis. This might be someone’s last cruise or week on Earth. For these women, who have spent months, if not years, at sea, cruising is a ritual as well as a life cycle: first love, last love, marriage, divorce, death.

Read: The last place on Earth any tourist should go

I have talked with these women for so long, tonight I promise myself that after a sad solitary dinner I will not try to seek out company at the bars in the mall or the adult-themed Hideaway. I have enough material to fulfill my duties to this publication. As I approach my orphaned suite, I run into the aggro young people who stole Mr. and Mrs. Rand away from me the night before. The tattooed apparitions pass me without a glance. She is singing something violent about “Stuttering Stanley” (a character in a popular horror movie, as I discover with my complimentary VOOM SM Surf & Stream Internet at Sea) and he’s loudly shouting about “all the money I’ve lost,” presumably at the casino in the bowels of the ship.

So these bent psychos out of a Cormac McCarthy novel are angrily inhabiting my deck. As I mewl myself to sleep, I envision a limited series for HBO or some other streamer, a kind of low-rent White Lotus , where several aggressive couples conspire to throw a shy intellectual interloper overboard. I type the scenario into my phone. As I fall asleep, I think of what the woman who recently divorced her husband and whose son became a man through the good offices of the Irish Republic told me while I was hoisting myself out of the infinity pool. “I’m here because I’m an explorer. I’m here because I’m trying something new.” What if I allowed myself to believe in her fantasy?

“YOU REALLY STARTED AT THE TOP,” they tell me. I’m at the Coastal Kitchen for my eggs and corned-beef hash, and the maître d’ has slotted me in between two couples. Fueled by coffee or perhaps intrigued by my relative youth, they strike up a conversation with me. As always, people are shocked that this is my first cruise. They contrast the Icon favorably with all the preceding liners in the Royal Caribbean fleet, usually commenting on the efficiency of the elevators that hurl us from deck to deck (as in many large corporate buildings, the elevators ask you to choose a floor and then direct you to one of many lifts). The couple to my right, from Palo Alto—he refers to his “porn mustache” and calls his wife “my cougar” because she is two years older—tell me they are “Pandemic Pinnacles.”

This is the day that my eyes will be opened. Pinnacles , it is explained to me over translucent cantaloupe, have sailed with Royal Caribbean for 700 ungodly nights. Pandemic Pinnacles took advantage of the two-for-one accrual rate of Pinnacle points during the pandemic, when sailing on a cruise ship was even more ill-advised, to catapult themselves into Pinnacle status.

Because of the importance of the inaugural voyage of the world’s largest cruise liner, more than 200 Pinnacles are on this ship, a startling number, it seems. Mrs. Palo Alto takes out a golden badge that I have seen affixed over many a breast, which reads CROWN AND ANCHOR SOCIETY along with her name. This is the coveted badge of the Pinnacle. “You should hear all the whining in Guest Services,” her husband tells me. Apparently, the Pinnacles who are not also Suites like us are all trying to use their status to get into Coastal Kitchen, our elite restaurant. Even a Pinnacle needs to be a Suite to access this level of corned-beef hash.

“We’re just baby Pinnacles,” Mrs. Palo Alto tells me, describing a kind of internal class struggle among the Pinnacle elite for ever higher status.

And now I understand what the maître d’ was saying to me on the first day of my cruise. He wasn’t saying “ pendejo .” He was saying “Pinnacle.” The dining room was for Pinnacles only, all those older people rolling in like the tide on their motorized scooters.

And now I understand something else: This whole thing is a cult. And like most cults, it can’t help but mirror the endless American fight for status. Like Keith Raniere’s NXIVM, where different-colored sashes were given out to connote rank among Raniere’s branded acolytes, this is an endless competition among Pinnacles, Suites, Diamond-Plusers, and facing-the-mall, no-balcony purple SeaPass Card peasants, not to mention the many distinctions within each category. The more you cruise, the higher your status. No wonder a section of the Royal Promenade is devoted to getting passengers to book their next cruise during the one they should be enjoying now. No wonder desperate Royal Caribbean offers (“FINAL HOURS”) crowded my email account weeks before I set sail. No wonder the ship’s jewelry store, the Royal Bling, is selling a $100,000 golden chalice that will entitle its owner to drink free on Royal Caribbean cruises for life. (One passenger was already gaming out whether her 28-year-old son was young enough to “just about earn out” on the chalice or if that ship had sailed.) No wonder this ship was sold out months before departure , and we had to pay $19,000 for a horrid suite away from the Suite Neighborhood. No wonder the most mythical hero of Royal Caribbean lore is someone named Super Mario, who has cruised so often, he now has his own working desk on many ships. This whole experience is part cult, part nautical pyramid scheme.

From the June 2014 issue: Ship of wonks

“The toilets are amazing,” the Palo Altos are telling me. “One flush and you’re done.” “They don’t understand how energy-efficient these ships are,” the husband of the other couple is telling me. “They got the LNG”—liquefied natural gas, which is supposed to make the Icon a boon to the environment (a concept widely disputed and sometimes ridiculed by environmentalists).

But I’m thinking along a different line of attack as I spear my last pallid slice of melon. For my streaming limited series, a Pinnacle would have to get killed by either an outright peasant or a Suite without an ocean view. I tell my breakfast companions my idea.

“Oh, for sure a Pinnacle would have to be killed,” Mr. Palo Alto, the Pandemic Pinnacle, says, touching his porn mustache thoughtfully as his wife nods.

“THAT’S RIGHT, IT’S your time, buddy!” Hubert, my fun-loving Panamanian cabin attendant, shouts as I step out of my suite in a robe. “Take it easy, buddy!”

I have come up with a new dressing strategy. Instead of trying to impress with my choice of T-shirts, I have decided to start wearing a robe, as one does at a resort property on land, with a proper spa and hammam. The response among my fellow cruisers has been ecstatic. “Look at you in the robe!” Mr. Rand cries out as we pass each other by the Thrill Island aqua park. “You’re living the cruise life! You know, you really drank me under the table that night.” I laugh as we part ways, but my soul cries out, Please spend more time with me, Mr. and Mrs. Rand; I so need the company .

In my white robe, I am a stately presence, a refugee from a better limited series, a one-man crossover episode. (Only Suites are granted these robes to begin with.) Today, I will try many of the activities these ships have on offer to provide their clientele with a sense of never-ceasing motion. Because I am already at Thrill Island, I decide to climb the staircase to what looks like a mast on an old-fashioned ship (terrified, because I am afraid of heights) to try a ride called “Storm Chasers,” which is part of the “Category 6” water park, named in honor of one of the storms that may someday do away with the Port of Miami entirely. Storm Chasers consists of falling from the “mast” down a long, twisting neon tube filled with water, like being the camera inside your own colonoscopy, as you hold on to the handles of a mat, hoping not to die. The tube then flops you down headfirst into a trough of water, a Royal Caribbean baptism. It both knocks my breath out and makes me sad.

In keeping with the aquatic theme, I attend a show at the AquaDome. To the sound of “Live and Let Die,” a man in a harness gyrates to and fro in the sultry air. I saw something very similar in the back rooms of the famed Berghain club in early-aughts Berlin. Soon another harnessed man is gyrating next to the first. Ja , I think to myself, I know how this ends. Now will come the fisting , natürlich . But the show soon devolves into the usual Marvel-film-grade nonsense, with too much light and sound signifying nichts . If any fisting is happening, it is probably in the Suite Neighborhood, inside a cabin marked with an upside-down pineapple, which I understand means a couple are ready to swing, and I will see none of it.

I go to the ice show, which is a kind of homage—if that’s possible—to the periodic table, done with the style and pomp and masterful precision that would please the likes of Kim Jong Un, if only he could afford Royal Caribbean talent. At one point, the dancers skate to the theme song of Succession . “See that!” I want to say to my fellow Suites—at “cultural” events, we have a special section reserved for us away from the commoners—“ Succession ! It’s even better than the zombie show! Open your minds!”

Finally, I visit a comedy revue in an enormous and too brightly lit version of an “intimate,” per Royal Caribbean literature, “Manhattan comedy club.” Many of the jokes are about the cruising life. “I’ve lived on ships for 20 years,” one of the middle-aged comedians says. “I can only see so many Filipino homosexuals dressed as a taco.” He pauses while the audience laughs. “I am so fired tonight,” he says. He segues into a Trump impression and then Biden falling asleep at the microphone, which gets the most laughs. “Anyone here from Fort Leonard Wood?” another comedian asks. Half the crowd seems to cheer. As I fall asleep that night, I realize another connection I have failed to make, and one that may explain some of the diversity on this vessel—many of its passengers have served in the military.

As a coddled passenger with a suite, I feel like I am starting to understand what it means to have a rank and be constantly reminded of it. There are many espresso makers , I think as I look across the expanse of my officer-grade quarters before closing my eyes, but this one is mine .

A shocking sight greets me beyond the pools of Deck 17 as I saunter over to the Coastal Kitchen for my morning intake of slightly sour Americanos. A tiny city beneath a series of perfectly pressed green mountains. Land! We have docked for a brief respite in Basseterre, the capital of St. Kitts and Nevis. I wolf down my egg scramble to be one of the first passengers off the ship. Once past the gangway, I barely refrain from kissing the ground. I rush into the sights and sounds of this scruffy island city, sampling incredible conch curry and buckets of non-Starbucks coffee. How wonderful it is to be where God intended humans to be: on land. After all, I am neither a fish nor a mall rat. This is my natural environment. Basseterre may not be Havana, but there are signs of human ingenuity and desire everywhere you look. The Black Table Grill Has been Relocated to Soho Village, Market Street, Directly Behind of, Gary’s Fruits and Flower Shop. Signed. THE PORK MAN reads a sign stuck to a wall. Now, that is how you write a sign. A real sign, not the come-ons for overpriced Rolexes that blink across the screens of the Royal Promenade.

“Hey, tie your shoestring!” a pair of laughing ladies shout to me across the street.

“Thank you!” I shout back. Shoestring! “Thank you very much.”

A man in Independence Square Park comes by and asks if I want to play with his monkey. I haven’t heard that pickup line since the Penn Station of the 1980s. But then he pulls a real monkey out of a bag. The monkey is wearing a diaper and looks insane. Wonderful , I think, just wonderful! There is so much life here. I email my editor asking if I can remain on St. Kitts and allow the Icon to sail off into the horizon without me. I have even priced a flight home at less than $300, and I have enough material from the first four days on the cruise to write the entire story. “It would be funny …” my editor replies. “Now get on the boat.”

As I slink back to the ship after my brief jailbreak, the locals stand under umbrellas to gaze at and photograph the boat that towers over their small capital city. The limousines of the prime minister and his lackeys are parked beside the gangway. St. Kitts, I’ve been told, is one of the few islands that would allow a ship of this size to dock.

“We hear about all the waterslides,” a sweet young server in one of the cafés told me. “We wish we could go on the ship, but we have to work.”

“I want to stay on your island,” I replied. “I love it here.”

But she didn’t understand how I could possibly mean that.

“WASHY, WASHY, so you don’t get stinky, stinky!” kids are singing outside the AquaDome, while their adult minders look on in disapproval, perhaps worried that Mr. Washy Washy is grooming them into a life of gayness. I heard a southern couple skip the buffet entirely out of fear of Mr. Washy Washy.

Meanwhile, I have found a new watering hole for myself, the Swim & Tonic, the biggest swim-up bar on any cruise ship in the world. Drinking next to full-size, nearly naked Americans takes away one’s own self-consciousness. The men have curvaceous mom bodies. The women are equally un-shy about their sprawling physiques.

Today I’ve befriended a bald man with many children who tells me that all of the little trinkets that Royal Caribbean has left us in our staterooms and suites are worth a fortune on eBay. “Eighty dollars for the water bottle, 60 for the lanyard,” the man says. “This is a cult.”

“Tell me about it,” I say. There is, however, a clientele for whom this cruise makes perfect sense. For a large middle-class family (he works in “supply chains”), seven days in a lower-tier cabin—which starts at $1,800 a person—allow the parents to drop off their children in Surfside, where I imagine many young Filipina crew members will take care of them, while the parents are free to get drunk at a swim-up bar and maybe even get intimate in their cabin. Cruise ships have become, for a certain kind of hardworking family, a form of subsidized child care.

There is another man I would like to befriend at the Swim & Tonic, a tall, bald fellow who is perpetually inebriated and who wears a necklace studded with little rubber duckies in sunglasses, which, I am told, is a sort of secret handshake for cruise aficionados. Tomorrow, I will spend more time with him, but first the ship docks at St. Thomas, in the U.S. Virgin Islands. Charlotte Amalie, the capital, is more charming in name than in presence, but I still all but jump off the ship to score a juicy oxtail and plantains at the well-known Petite Pump Room, overlooking the harbor. From one of the highest points in the small city, the Icon of the Seas appears bigger than the surrounding hills.

I usually tan very evenly, but something about the discombobulation of life at sea makes me forget the regular application of sunscreen. As I walk down the streets of Charlotte Amalie in my fluorescent Icon of the Seas cap, an old Rastafarian stares me down. “Redneck,” he hisses.

“No,” I want to tell him, as I bring a hand up to my red neck, “that’s not who I am at all. On my island, Mannahatta, as Whitman would have it, I am an interesting person living within an engaging artistic milieu. I do not wish to use the Caribbean as a dumping ground for the cruise-ship industry. I love the work of Derek Walcott. You don’t understand. I am not a redneck. And if I am, they did this to me.” They meaning Royal Caribbean? Its passengers? The Rands?

“They did this to me!”

Back on the Icon, some older matrons are muttering about a run-in with passengers from the Celebrity cruise ship docked next to us, the Celebrity Apex. Although Celebrity Cruises is also owned by Royal Caribbean, I am made to understand that there is a deep fratricidal beef between passengers of the two lines. “We met a woman from the Apex,” one matron says, “and she says it was a small ship and there was nothing to do. Her face was as tight as a 19-year-old’s, she had so much surgery.” With those words, and beneath a cloudy sky, humidity shrouding our weathered faces and red necks, we set sail once again, hopefully in the direction of home.

THERE ARE BARELY 48 HOURS LEFT to the cruise, and the Icon of the Seas’ passengers are salty. They know how to work the elevators. They know the Washy Washy song by heart. They understand that the chicken gyro at “Feta Mediterranean,” in the AquaDome Market, is the least problematic form of chicken on the ship.

The passengers have shed their INAUGURAL CRUISE T-shirts and are now starting to evince political opinions. There are caps pledging to make America great again and T-shirts that celebrate words sometimes attributed to Patrick Henry: “The Constitution is not an instrument for the government to restrain the people; it is an instrument for the people to restrain the government.” With their preponderance of FAMILY FLAG FAITH FRIENDS FIREARMS T-shirts, the tables by the crepe station sometimes resemble the Capitol Rotunda on January 6. The Real Anthony Fauci , by Robert F. Kennedy Jr., appears to be a popular form of literature, especially among young men with very complicated versions of the American flag on their T-shirts. Other opinions blend the personal and the political. “Someone needs to kill Washy guy, right?” a well-dressed man in the elevator tells me, his gray eyes radiating nothing. “Just beat him to death. Am I right?” I overhear the male member of a young couple whisper, “There goes that freak” as I saunter by in my white spa robe, and I decide to retire it for the rest of the cruise.

I visit the Royal Bling to see up close the $100,000 golden chalice that entitles you to free drinks on Royal Caribbean forever. The pleasant Serbian saleslady explains that the chalice is actually gold-plated and covered in white zirconia instead of diamonds, as it would otherwise cost $1 million. “If you already have everything,” she explains, “this is one more thing you can get.”

I believe that anyone who works for Royal Caribbean should be entitled to immediate American citizenship. They already speak English better than most of the passengers and, per the Serbian lady’s sales pitch above, better understand what America is as well. Crew members like my Panamanian cabin attendant seem to work 24 hours a day. A waiter from New Delhi tells me that his contract is six months and three weeks long. After a cruise ends, he says, “in a few hours, we start again for the next cruise.” At the end of the half a year at sea, he is allowed a two-to-three-month stay at home with his family. As of 2019, the median income for crew members was somewhere in the vicinity of $20,000, according to a major business publication. Royal Caribbean would not share the current median salary for its crew members, but I am certain that it amounts to a fraction of the cost of a Royal Bling gold-plated, zirconia-studded chalice.

And because most of the Icon’s hyper-sanitized spaces are just a frittata away from being a Delta lounge, one forgets that there are actual sailors on this ship, charged with the herculean task of docking it in port. “Having driven 100,000-ton aircraft carriers throughout my career,” retired Admiral James G. Stavridis, the former NATO Supreme Allied Commander Europe, writes to me, “I’m not sure I would even know where to begin with trying to control a sea monster like this one nearly three times the size.” (I first met Stavridis while touring Army bases in Germany more than a decade ago.)

Today, I decide to head to the hot tub near Swim & Tonic, where some of the ship’s drunkest reprobates seem to gather (the other tubs are filled with families and couples). The talk here, like everywhere else on the ship, concerns football, a sport about which I know nothing. It is apparent that four teams have recently competed in some kind of finals for the year, and that two of them will now face off in the championship. Often when people on the Icon speak, I will try to repeat the last thing they said with a laugh or a nod of disbelief. “Yes, 20-yard line! Ha!” “Oh my God, of course, scrimmage.”

Soon we are joined in the hot tub by the late-middle-age drunk guy with the duck necklace. He is wearing a bucket hat with the legend HAWKEYES , which, I soon gather, is yet another football team. “All right, who turned me in?” Duck Necklace says as he plops into the tub beside us. “I get a call in the morning,” he says. “It’s security. Can you come down to the dining room by 10 a.m.? You need to stay away from the members of this religious family.” Apparently, the gregarious Duck Necklace had photobombed the wrong people. There are several families who present as evangelical Christians or practicing Muslims on the ship. One man, evidently, was not happy that Duck Necklace had made contact with his relatives. “It’s because of religious stuff; he was offended. I put my arm around 20 people a day.”

Everyone laughs. “They asked me three times if I needed medication,” he says of the security people who apparently interrogated him in full view of others having breakfast.

Another hot-tub denizen suggests that he should have asked for fentanyl. After a few more drinks, Duck Necklace begins to muse about what it would be like to fall off the ship. “I’m 62 and I’m ready to go,” he says. “I just don’t want a shark to eat me. I’m a huge God guy. I’m a Bible guy. There’s some Mayan theory squaring science stuff with religion. There is so much more to life on Earth.” We all nod into our Red Stripes.

“I never get off the ship when we dock,” he says. He tells us he lost $6,000 in the casino the other day. Later, I look him up, and it appears that on land, he’s a financial adviser in a crisp gray suit, probably a pillar of his North Chicago community.

THE OCEAN IS TEEMING with fascinating life, but on the surface it has little to teach us. The waves come and go. The horizon remains ever far away.

I am constantly told by my fellow passengers that “everybody here has a story.” Yes, I want to reply, but everybody everywhere has a story. You, the reader of this essay, have a story, and yet you’re not inclined to jump on a cruise ship and, like Duck Necklace, tell your story to others at great pitch and volume. Maybe what they’re saying is that everybody on this ship wants to have a bigger, more coherent, more interesting story than the one they’ve been given. Maybe that’s why there’s so much signage on the doors around me attesting to marriages spent on the sea. Maybe that’s why the Royal Caribbean newsletter slipped under my door tells me that “this isn’t a vacation day spent—it’s bragging rights earned.” Maybe that’s why I’m so lonely.

Today is a big day for Icon passengers. Today the ship docks at Royal Caribbean’s own Bahamian island, the Perfect Day at CocoCay. (This appears to be the actual name of the island.) A comedian at the nightclub opined on what his perfect day at CocoCay would look like—receiving oral sex while learning that his ex-wife had been killed in a car crash (big laughter). But the reality of the island is far less humorous than that.

One of the ethnic tristate ladies in the infinity pool told me that she loved CocoCay because it had exactly the same things that could be found on the ship itself. This proves to be correct. It is like the Icon, but with sand. The same tired burgers, the same colorful tubes conveying children and water from Point A to B. The same swim-up bar at its Hideaway ($140 for admittance, no children allowed; Royal Caribbean must be printing money off its clientele). “There was almost a fight at The Wizard of Oz ,” I overhear an elderly woman tell her companion on a chaise lounge. Apparently one of the passengers began recording Royal Caribbean’s intellectual property and “three guys came after him.”

I walk down a pathway to the center of the island, where a sign reads DO NOT ENTER: YOU HAVE REACHED THE BOUNDARY OF ADVENTURE . I hear an animal scampering in the bushes. A Royal Caribbean worker in an enormous golf cart soon chases me down and takes me back to the Hideaway, where I run into Mrs. Rand in a bikini. She becomes livid telling me about an altercation she had the other day with a woman over a towel and a deck chair. We Suites have special towel privileges; we do not have to hand over our SeaPass Card to score a towel. But the Rands are not Suites. “People are so entitled here,” Mrs. Rand says. “It’s like the airport with all its classes.” “You see,” I want to say, “this is where your husband’s love of Ayn Rand runs into the cruelties and arbitrary indignities of unbridled capitalism.” Instead we make plans to meet for a final drink in the Schooner Bar tonight (the Rands will stand me up).

Back on the ship, I try to do laps, but the pool (the largest on any cruise ship, naturally) is fully trashed with the detritus of American life: candy wrappers, a slowly dissolving tortilla chip, napkins. I take an extra-long shower in my suite, then walk around the perimeter of the ship on a kind of exercise track, past all the alluring lifeboats in their yellow-and-white livery. Maybe there is a dystopian angle to the HBO series that I will surely end up pitching, one with shades of WALL-E or Snowpiercer . In a collapsed world, a Royal Caribbean–like cruise liner sails from port to port, collecting new shipmates and supplies in exchange for the precious energy it has on board. (The actual Icon features a new technology that converts passengers’ poop into enough energy to power the waterslides . In the series, this shitty technology would be greatly expanded.) A very young woman (18? 19?), smart and lonely, who has only known life on the ship, walks along the same track as I do now, contemplating jumping off into the surf left by its wake. I picture reusing Duck Necklace’s words in the opening shot of the pilot. The girl is walking around the track, her eyes on the horizon; maybe she’s highborn—a Suite—and we hear the voice-over: “I’m 19 and I’m ready to go. I just don’t want a shark to eat me.”

Before the cruise is finished, I talk to Mr. Washy Washy, or Nielbert of the Philippines. He is a sweet, gentle man, and I thank him for the earworm of a song he has given me and for keeping us safe from the dreaded norovirus. “This is very important to me, getting people to wash their hands,” he tells me in his burger getup. He has dreams, as an artist and a performer, but they are limited in scope. One day he wants to dress up as a piece of bacon for the morning shift.

THE MAIDEN VOYAGE OF THE TITANIC (the Icon of the Seas is five times as large as that doomed vessel) at least offered its passengers an exciting ending to their cruise, but when I wake up on the eighth day, all I see are the gray ghosts that populate Miami’s condo skyline. Throughout my voyage, my writer friends wrote in to commiserate with me. Sloane Crosley, who once covered a three-day spa mini-cruise for Vogue , tells me she felt “so very alone … I found it very untethering.” Gideon Lewis-Kraus writes in an Instagram comment: “When Gary is done I think it’s time this genre was taken out back and shot.” And he is right. To badly paraphrase Adorno: After this, no more cruise stories. It is unfair to put a thinking person on a cruise ship. Writers typically have difficult childhoods, and it is cruel to remind them of the inherent loneliness that drove them to writing in the first place. It is also unseemly to write about the kind of people who go on cruises. Our country does not provide the education and upbringing that allow its citizens an interior life. For the creative class to point fingers at the large, breasty gentlemen adrift in tortilla-chip-laden pools of water is to gather a sour harvest of low-hanging fruit.

A day or two before I got off the ship, I decided to make use of my balcony, which I had avoided because I thought the view would only depress me further. What I found shocked me. My suite did not look out on Central Park after all. This entire time, I had been living in the ship’s Disneyland, Surfside, the neighborhood full of screaming toddlers consuming milkshakes and candy. And as I leaned out over my balcony, I beheld a slight vista of the sea and surf that I thought I had been missing. It had been there all along. The sea was frothy and infinite and blue-green beneath the span of a seagull’s wing. And though it had been trod hard by the world’s largest cruise ship, it remained.

This article appears in the May 2024 print edition with the headline “A Meatball at Sea.” When you buy a book using a link on this page, we receive a commission. Thank you for supporting The Atlantic.

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8 Norwegian Cruise Passengers Stranded on African Island Catch Up to Ship After Traversing 7 Countries

The group of stranded American and Australian passengers included four elderly people, one with a heart condition and a pregnant woman

Natalia Senanayake is an Editorial Assistant, Lifestyle at PEOPLE. She covers all things travel and home, from celebrities' luxury mansions to breaking travel news.

Sipa via AP

• Nine Norwegian Cruise Line passengers were reportedly left behind on the African island of São Tomé and Príncipe on March 27 
• The group was on a guided excursion that got delayed, leading them to miss the ship’s "all aboard" call 
• A statement from Norwegian Cruise Lines noted that all guests are responsible for returning to the docked ship at the designated call time 
• Eight people were able to catch up to the ship on Tuesday morning after reportedly traversing seven countries.
• One, who had fallen ill before the incident, has safely returned to the U.S.

Multiple passengers were stranded on an island in Africa after their Norwegian Cruise Line ship reportedly left them behind. After several days of uncertainty and a trek across seven countries, they're now back on board the vessel.

On Wednesday, March 27, South Carolina couple Jill and Jay Campbell were enjoying a guided tour on the island of São Tomé and Príncipe located off the continent's western coast, ABC15 News reported at the time. The pair was with six other American and Australian passengers when they realized they wouldn’t make it back to the ship on time due to their tour taking longer than planned.

Though the tour operator contacted the cruise ship’s captain to inform them of the delay, the captain refused to let them back on the still-anchored ship when they arrived at the port because it was after the "all aboard" call, per the outlet. 

The São Tomé and Príncipe Coast Guard allegedly then took them by boat directly to the ship where the captain again did not permit them to board. 

The group later encountered another stranded passenger, an 80-year-old woman, who was hospitalized on the island after a cruise line tour, the outlet stated. The woman reportedly experienced memory and vision loss due to a medical emergency. 

In addition to the ill passenger, the group also includes one person who is pregnant, one with a heart condition and four elderly travelers. 

The majority of the group left their medications and credit cards on the ship except for the Campbells, who have reportedly paid over $5,000 for food, accommodations, and other necessities for their fellow passengers. 

On Sunday, the U.S. Embassy in Angola allegedly arranged for the group to fly to the West African country of Gambia, the ship's next planned port of call, so they could reboard. 

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Unfortunately, the group discovered the cruise ship wasn’t docked at the port in Gambia as planned because it had to spend another day at sea due to low tides. ABC News 4 reports the passengers spent fifteen hours traveling through six countries to make it to the port on Sunday. 

“We have to cross the ferry to get into Senegal,” Campbell told the outlet on Monday, marking their seventh country. “We just learned from the gentleman that the ferry hadn’t been working, but he said no problem, if the ferry is not working we will get another little boat and then pick up a car on the other side. And then once we get on the other side of Senegal, it’s another four-hour drive.” 

In a statement to PEOPLE, Norwegian Cruise Line said, “On the afternoon of March 27, 2024, while the ship was in São Tomé and Príncipe, an African island nation, eight guests who were on the island on a private tour not organized through us missed the last tender back to the vessel, therefore not meeting the all aboard time of 3 p.m. local time."

The statement continued, “While this is a very unfortunate situation, guests are responsible for ensuring they return to the ship at the published time, which is communicated broadly over the ship’s intercom, in the daily print communication and posted just before exiting the vessel.”

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories. 

The cruise line added that guests are “responsible for any necessary travel arrangements” to meet the ship at the next port and that they had each of their passports “delivered to the local port agents to retrieve” when they missed their all aboard call.

The group was finally able to catch up to the vessel. They reached Dakar, Senegal, its next port, on Monday night, PEOPLE confirmed.

After what they'd been through, Jill told NBC News in a story published on Tuesday, "We are considering whether or not we are going to board the ship. We believe there was a basic duty of care that they had forgotten about, so it does concern us." While she allowed that Norwegian technically followed protocol, she says, "I believe that they really forgot that they are people working in the hospitality industry and really the safety and well-being of the customers should be their first priority."

On Tuesday morning, the eight passengers, less the person who had fallen ill and later safely returned home to the United States, chose to board the cruise. Norwegian confirmed the news to PEOPLE in a statement.

"Despite the series of unfortunate events outside of our control, we will be reimbursing these eight guests for their travel costs from Banjur, Gambia to Dakar, Senegal. We remain in communication with the guests and are providing additional information as it becomes available,"

The Norwegian Dawn departed from Cape Town, South Africa, on March 20 for a 21-day trip that will end in Barcelona on April 10.

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Combo Cruise

South sea island half day trip and boat cruise.

Spend the morning at South Sea Island and after lunch, board a vessel for a tour around some of the other Mamanuca Islands as we drop off/pick up people from resorts in those areas.

• Description

South Sea Island is Fiji’s most popular day cruise island and is a short high-speed catamaran ride with South Sea Cruises from Port Denarau. Being so close to Denarau means you can make the most of your time lazing on the beach, snorkelling, swimming, and enjoying the many activities on offer.

After a few hours to explore the tiny island and a buffet lunch, jump back onboard our high-speed catamaran and enjoy a few hours sightseeing through the beautiful Mamanuca Islands as we stop to drop off/pick up passengers along the way.

Plenty to do Being small in size, it means you can explore it in the just under 2 hours you have on the island before boarding the island cruise, with plenty to keep you entertained such as a semi-submersible submarine for underwater viewing, a saltwater swimming pool and complimentary use of all non-motorised water sports equipment such as snorkelling gear, stand up paddle boards and kayaks.

Food and drinks Lunchtime is a highlight on the island when everyone gathers around rustic tables at the open-air restaurant to watch Fijian performances and craft market (both daily except Sundays). Enjoy a delicious buffet lunch and complimentary local beer, house wine, and soft drinks while on the island.

Additional options For an additional cost while on the island treat yourself to an island massage and be sure to try one of our handmade cocktails or grab a snack at the Tipsy Turtle Bar.

Passengers travel from/to Port Denarau with the following schedule:

• Return pre-booked coach transfers to/from Port Denarau to/from most Nadi, Denarau, Wailoaloa hotels/resorts. Check the coach timetable  here  for times
• Vessel transfers from Port Denarau to South Sea Island on our high-speed catamaran
• A delicious BBQ buffet lunch, local beer, house wine, filtered water, and soft drinks are all included while on South Sea Island
• An island sightseeing cruise around the Mamanuca Islands onboard our resort transfer vessel service
• Complimentary Kids Club (for 3 – 12 year olds)
• Subsea Adventure in our semi-submersible coral viewer (note that in the event this is not available due to maintenance or repairs, no refund will be given)
• Use of non-motorised water sports equipment (snorkelling gear, paddle boards, kayaks)
• Saltwater swimming pool and fantastic swimming/snorkelling in the sea, even at low tide
• Fijian ‘Meke’ performance at lunchtime (daily except Sundays)
• Massage, premium bar, and scuba diving are all available at an additional cost

What to bring:

• Cash or credit/debit card for optional purchases (premium bar, merchandise, diving, massage, shell market)
• Sunscreen and hat
• Footwear for the beach

*Children are aged 5-15 years inclusive.  Infants 4 and under are free of charge. **Family Pass = a family of 4 (2 adults and 2 children) and a family of 5 (2 adults and 3 children) All pricing is in FJD, includes taxes, and is valid for travel until 31 March 2025. Bookings paid by credit card or international debit card will incur a 2.5-3% non-refundable administration fee.

Other Popular Fiji Island Day Trips

Most popular

Malamala beach club.

Experience true tropical island bliss. Passes include transfers, towel service and the use of non-motorised water sports equipment. Full and half day options available.

from FJ$159

Book Now Find out more

South Sea Sailing

Enjoy a full day sailing experience around Fiji’s Mamanuca Islands onboard our custom-built sailing catamaran including lunch and drinks.

from FJ$255

South Sea Island

A day spent on a tiny tropical island including drinks, lunch, snorkelling gear, SUP’s and kayaks. Relax and chill or get busy with activities! A Half Day option is also available for those who prefer a later start to their day.

from FJ$215

South Sea Island Finding Nemo

Great for young families with an early start and midday return. Swim in the crystal clear waters and take the kids to see the underwater world in a semi-submersible coral viewer.

from FJ$125

Ultimate Encounters: Snorkel With Sharks

Get up close and personal with reef sharks in their natural environment in the Yasawa Islands. Includes lunch at Barefoot Kuata Island Resort.

from FJ$375

Manta Ray Experience

Journey to Mantaray Island Resort on select dates from May to October for the chance to swim with these majestic creatures. A bucket list experience!

from FJ$399

Mamanuca Island Explorer

Relax onboard our high-speed catamaran vessel for 3 hours taking in the sights around the Mamanuca Islands as we drop off/pick up at the various island resorts.

from FJ$149

Yasawa Island Explorer

Take in the stunning Yasawa Islands as our high-speed catamaran does its daily run north through the islands and back as we drop off/pick up at the various island resorts.

from FJ$235

Barefoot Kuata Island Resort

See the spectacular scenery the majestic beauty of the Yasawa Islands. Take in the sights as you cruise 2 hours each way to this island. Lunch is included.

from FJ$279

Castaway Island Fiji

Spend the day at one of Fiji’s most popular resorts. Lunch and snorkelling gear are also included. Optional Kids Club.

from FJ$299

Serenity Island Resort

Mana Island Resort & Spa

Visit this popular and expansive resort with lunch included. Swim in the lagoon or explore the three different beaches as you soak up the sun. Full and Half Day options available.

One of the best experiences I've had in a long time. The island was beautiful, super friendly staff always ready to help. Snorkeling and kayak equipment were complimentary. The food was great, and the infinity pool was something I'd never experienced. Highly recommended!

Best day trip in Fiji! Lots of activities, easy access to bus transfers and wonderful staff – very open and accommodating. If you're in Fiji it is a must do trip!

It was an amazing cruise with a delicious lunch and wine. We got to snorkel with colourful fish. We then spent the afternoon island hopping seeing other places we could stay. The Fijian show was excellent. We had a wonderful day.

This was so much fun. Staff were awesome. Island is great with plenty to do. Lots of room to sit around relaxing. Trip was well priced.

Sabre was an absolute dream experience. The boat is amazing and a real asset for Fiji, the crew were accommodating and fun. There was plenty of seating on the ship. I would recommend it to all. Thank you South Sea Cruise, yet another great trip with your company.

This was an absolutely fantastic trip and a lifetime highlight for us!!! We were greeted on the island with music and singing! The guides were exceptional and we saw sharks and turtles. Highly recommend!

Join @southseasailingfiji on board Sabre as they sail around the Mamanucas in search of the best swimming spots - no day is ever the same! ⛵ https://southseacruisesfiji.com/day-trips/south-sea-sailing/ 📽️: @skatesail

Postcards from South Sea Island 🌴☀️🏖️ #SouthSeaCruises #DayTrip #mustdofiji #southseaisland #holiday #bucketlist #fijiislands #idyllic #holidaytime #FijiAdventure

If you`re looking for a sign...this is it...see you soon at one of the best day trip destinations in Fiji: Malamala Beach Club Fiji - Reopening March 1st. #SouthSeaCruises #DayTrip #welcome #mustdofiji #islandlife #bucketlist #fijiislands #holidaytime #EscapeToParadise #idyllic

The best welcome when you arrive at @barefoot_kuata 💙 #SouthSeaCruises #DayTrip #mustdofiji #bula #welcome #holiday #tropical #seas #fijihappy #scenic

Our fishy friends can`t wait to meet you! 🐠🦈 #SouthSeaCruises #DayTrip #mustdofiji #fijihappy #instatravel #holiday #tropical #FijiBound #seas #snorkelling

Our full and half-day Island Explorer cruises are the perfect way to take in the sights around the stunning Mamanuca and Yasawa Islands ⛵ #SouthSeaCruises #DayTrip #mustdofiji #tropical #welcome #instatravel #holiday #bucketlist #fijihappy #fijiislands

Looking for the perfect day trip while you`re on holiday in Fiji? South Sea Sailing is the perfect combo of fun, relaxing and adventurous! Come sail away with us ⛵ 📹: @skatesail #SouthSeaCruises #DayTrip #mustdofiji #seas #Snorkelling #travelgram #wanderlust #scenic #boat #holiday

Dreaming of turquoise waters and palm-fringed beaches? Dive into the beauty of Fiji with Awesome Adventures - make 2024 your year! 🎥: @millie.beesley thanks for sharing!

Who`s up for a blissful island escape in 2024? 🏝️ Discover the untouched beauty of Fiji - including this little gem, South Sea Island, where every moment feels like a dream come true! #Paradise #FijiBound #UnforgettableHoliday #SouthSeaCruises

📍 @barefoot_kuata Kuata Island is the perfect place to spend a day exploring, swimming, snorkelling, or simply relaxing under a palm tree 🌴 #SouthSeaCruises #mustdofiji #FijiAdventure #holiday #islandlife #fiji #travelgoals #tropical

good cover letter for sales resume

How to write a sales cover letter (examples & templates) for all sales positions.

If a cover letter seems a bit old school to you, think again. According to a recent survey by ResumeLab , cover letters are still an important component of the decision-making process among 83 percent of hiring managers, recruiters and HR staff. Moreover, 83 percent of respondents claimed that they would interview a candidate with a great cover letter, even if their resume isn’t up to par.

That said, you’ll still need a solid track record or educational background to snag the interest of an employer. But with a sales cover letter in hand, your next job search will become that much easier, whether you’re an entry-level job seeker or you’ve cultivated a LinkedIn resume that turns heads.

Why is a Sales Cover Letter Important?

Cover letters tell your potential employer who you are before you even walk in the door for a sales job interview , and it makes said interview that much more likely. Even if writing such a letter feels uncomfortable and you’d prefer to let your experience do the talking, this is still an invaluable skill to have.

5 Cover Letter Tips for Today’s Sales Professionals

Writing a professional cover letter for a sales job might not feel intuitive yet, but that doesn’t mean it has to be hard. The following tips will start you off on the right foot.

Be Clear And Concise

A cover letter is not an aria. It’s not a soliloquy or a monologue. It’s certainly not a rant. No, you can think of it as a short informational pamphlet—and the subject is you.

Rather than waxing poetic about your thoughts, feelings, or even your goals, stick to the main points, including who you are, what you’ve done so far, and what you can do for the company for which you’d like to work. Keeping your letter short and sweet can increase application success.

Make it Easy to Read

Hiring managers go through hundreds of resumes at a time. The way you format your cover letter can either help or hurt your chances of standing out.

No, that doesn’t mean it’s time to throw in the fancy fonts and fun colors. Instead, format your cover letter with the goal of making it easy to read.

Follow best practices such as:

• Write short, concise sentences and remove unnecessary adjectives
• Make your paragraphs shorter, or use bullet points to make key ideas stand out
• Use clean, professional fonts at a size that’s easy to read

The overall goal is for hiring managers to quickly and easily see what makes you stand out beyond the rest of the applicants. Don’t hide your strongest selling points in small, swirly fonts and huge blocks of text!

Highlight Your Skills

It’s very important to highlight your sales skills in a cover letter. This is different from accomplishments, which we’re covering next. Your skills are a separate category, in which you describe what you bring to the table, regardless of whether you’ve used those skills in the past or not. Include such details as the apps, sales tools or programs you know how to use, languages you speak, and areas in which you’ve trained.

While it is appropriate to include some reference to soft skills in your cover letter, limit it to a few. Any job applicant will claim they are a good problem-solver and a team player; it’s more important to share which skills make you stand out as a salesperson.

Showcase Relevant Achievements

In addition to putting your achievements on a professional resume , include a quick recap of them in your cover letter. Make those achievements quantifiable, using numbers and statistics from your sales reports or the company’s, and don’t hold back or engage in false modesty. This is no time to sell yourself short.

5 Steps To Writing A Sales Representative Cover Letter

So it’s time to write that letter and nail that sales representative position! But how exactly are you going to fit all the awesomeness that is you onto one page, single-spaced, in 12-point Helvetica font, without leaving anything out?

Good question, and as with all good answers, an analogy is called for: think of your cover letter as if it’s a highlight reel on your social media account. While your highlight reel can’t stand in for the hours you spend crafting witty tweets, it can give people a quick glance at who you are. And just like a highlight reel, the goal for your cover letter is to make others want to dig a little bit deeper.

A good sales representative cover letter should make your readers curious enough to learn more about you as a sales professional that they will want to ask you about yourself in person. Let’s take a look at how to make them do just that, in five easy steps.

1. The Header

Think of yourself as a sales hiring manager. How hard are you going to look for the contact information of a candidate if they can’t even bother to provide it somewhere obvious in the sales cover letter?

Answer: not very hard. That’s why every sales position cover letter needs a header. Usually, you’ll find it across the top, though sometimes the header runs along the side of the page. It needs to include your name, phone number, address, and any other contact information you might have.

Note that while cover letters to clients or professional colleagues might include your company name, a sales job cover letter should not. Under your info, put the date.

Note that the header is different from the salutation, which includes the hiring manager’s contact information. Don’t confuse the two.

2. How To Greet the Employer

Here is where you greet your potential employer. It has two parts: the contact info and the salutation. First, include the same contact info you included for yourself, but relevant to the hiring manager: their name, basic info and company name.

Then greet them.

You can pick from a number of ways to do this, but if you know the manager’s name, that’s the simplest. “Dear Ms. Lannister” is always better than a “Hi there,” “Greetings,” “Dear Sir or Madam” or “To Whom It May Concern.” The former two are too casual, while the latter couple are old-fashioned and make it look like you haven’t bothered to look up their name.

Note: If you can’t be sure of someone’s pronouns, opt for a neutral “Dear Hiring Manager Lannister” or their full name.

3. The Introduction

As with anything else, you have very little time to make a good impression if you want the job. Whether you’re in software sales or yacht sales, you need to punch it right from the beginning.

The introductory paragraph should emphasize why you are an ideal candidate. Remember that this paragraph needs to entice the employer to read further, and readers will lose interest in a boring introduction. Include why you’re applying, any notable sales goals you’ve met or awards you’ve won, and a lead-in to the following paragraph.

4. The Body

Here’s where you flesh out your skills and achievements in more detail. Include items such as:

• Work experience
• Sales experience and sales skills
• Communication skills
• Time management abilities
• Achievement or award track record

Note that you should avoid bullet points, though you can use them in your sales resume. The same goes for detailing aspects of your education, with the exception being your degree (associate’s, bachelor’s, master’s, etc.), which is appropriate to mention.

Mostly, this is a sales pitch that should include why you’re the best candidate for the job. Your existing knowledge and abilities are critical to whether or not you can land the role you’re looking for, so don’t hold back. While you should never brag or pass on compliments you’ve gotten, you should share exactly why you would be a good fit for the position.

5. The Conclusion

The last paragraph of your sales cover letter should include a summation, references, and the fond wish that you hear from the hiring manager again. It’s okay to use humor here as long as it is tasteful and doesn’t become the focus on the letter.

If you prefer a more serious tone, simply express your gratitude and desire to hear from them again.

• Cover Letter Examples

There exist a wide variety of job positions in the sales world, with different focuses, locations and levels of seniority. No one size fits all when it comes to sales jobs, which is why you need to tailor your sales cover letter to the exact position you’re looking for.

Naturally, we can’t cover every possible job title in a single post. However, the following sales cover letter example list should give you a fairly good idea of what employers are looking for. Feel free to browse both the resume templates and the cover letter templates for ideas before writing your own.

Sales Associate Cover Letter

If you’re just beginning your career in sales , then chances are good you might find yourself at a retail location. From cell phone stores to electronics outlets, car dealerships to boutiques that pay on commission, these are great places to cut your sales teeth.

Just because they’re good for entry-level employees doesn’t mean employers don’t expect a good showing, however. You’ll still need a cover letter that impresses. Go through the sales cover letter sample list below to see what we’re talking about:

• Sales Associate Cover Letter 1
• Sales Associate Cover Letter 2
• Sales Associate Cover Letter 3

Inside Sales Rep Cover Letter

Responsible for selling products and services from company headquarters or satellite offices rather than retail locations where customers walk in, inside sales reps spend a lot of time on the phone and using email. (Ideally for the company, they’re also spending plenty of time using smart automated sales software , but that’s another subject.)

If you hope to become an inside sales rep, you’ll need a sales representative cover letter that demonstrates related abilities. That includes good customer service, the ability to focus under pressure, and a solid background in sales or its theory. Take a look at these examples:

• Inside Sales Rep Cover Letter 1
• Inside Sales Rep Cover Letter 2
• Inside Sales Rep Cover Letter 3

Outside Sales Rep Cover Letter

While their inside counterparts work at a company building, outside sales reps travel to various locations to meet with clients on their turf. The two jobs have much in common, but an outside sales rep must demonstrate a skill set specific to traveling and meeting people in person.

This includes great one-on-one people skills, excellent personal grooming, and account growth. It is sales, after all. Here are a few excellent samples:

• Outside Sales Rep Cover Letter 1
• Outside Sales Rep Cover Letter 2
• Outside Sales Rep Cover Letter 3

Sales Manager Cover letter

Whether you’re already a manager hoping for a position at a new company, or you want to get a managerial job for the first time, the competition is stiff. You’ll need to show you not only have sales chops, but that you can manage people at the same time.

A sales manager cover letter should include how long you’ve been in the industry, how many people you’ve managed, your previous positions, your sales quota history and any related stats. These letters showcase exactly how to present professionally and put yourself in the running for manager:

• Sales Manager Cover Letter 1
• Sales Manager Cover Letter 2
• Sales Manager Cover Letter 3

You may have noticed that most of the above cover letter examples come with offers from their sites to help you craft your own cover letter (and often resume). If you don’t feel confident that you can do a stellar job yourself, go ahead and use one of those templates. Over time, you can use those skills to begin writing cover letters yourself, but there’s no pressure to do so now.

Why Are Sales Cover Letters Effective?

Again, writing a sales cover letter might feel daunting when you first set out to do it. In addition to making you look responsible and organized, however, a cover letter will immediately push you further up in the queue because a full 45 percent of job applicants don’t even include one. If you can get ahead of nearly half of the competition that easily, why wouldn’t you?

At the end of the day, a cover letter just isn’t that hard, and the potential rewards are indisputable. Take this opportunity to write the best cover letter you can, tailoring it to the job description and using a cover letter builder if necessary. There’s nothing wrong with getting a little help, but there’s everything wrong with leaving an opportunity on the table. That’s just not how salespeople roll, right?

Finally, keep learning. Increase your sales skills, learn to build remote teams , and practice your writing and communication skills as often as possible. Do this when you’re on the job hunt and when you’re not, because in the end, it will make you a better worker who is more appreciated by your employer. And that in turn is bound to pay off for life.

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How to Write an Effective Sales Manager Cover Letter and Resume

Many job applicants write cover letters without much thought. However, this is a big mistake. When writing your sales manager cover letter, it will boost your job application if you can sell yourself as the ultimate candidate. A great cover letter, along with a great sales manager resume, is essential to acing the hiring process. 

In your sales manager cover letter, you can highlight your experience in sales manager positions that you have previously held as well as the successful strategies you used in those positions. Overall, your cover letter should establish yourself as a valuable asset to the company. The cover letter tips in this article will show you how to do exactly that. 

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Sales manager cover letter guide.

An impactful sales manager cover letter follows a fairly specific formula. In this section, we break down the necessary components and share some cover letter writing practices you can use when writing your own. You will also find an example that will help you showcase your sales manager skills. 

Why Does Your Sales Manager Cover Letter Matter? 

A sales manager cover letter is a key document because it acts as your initial sales pitch for why you should be hired. Your cover letter is your opportunity to distinguish yourself from other job seekers and tell the company about your sales training, exceptional qualifications, and past successful sales. Furthermore, it is a great time to show the company that you share its goals.

All of this is extremely valuable during the competitive application process. In fact, the Bureau of Labor Statistics estimates that jobs for sales managers will increase by seven percent between 2020 and 2030. This is on par with the growth of the United States economy as a whole, which means that the supply of sales managers is projected to keep pace with demand.

In a sales manager cover letter, you can add accomplishments and academic qualifications that you think will help you perform well in the job, and explain how the sales techniques you’ve mastered can increase company revenue. To write a powerful cover letter, you should highlight your strong work ethic and detail how you would contribute to a creative sales team. 

Essential Components of Your Sales Manager Cover Letter

To write a strong cover letter, you need to incorporate several components. Make sure that the following four things are included somewhere in your letter.

• Soft skills. In the context of sales management, the most important soft skills are leadership qualities such as integrity, listening skills, reliability, and team-building. These are skills that you must have to be part of the sales staff of any company.
• Sales management skills. It is good to provide evidence of your sales manager skills when writing your cover letter, as companies closely evaluate these skills when considering a candidate. These skills include coaching, selling, innovation, and other core sales management behaviors.
• Sales skills. Of course, you need to establish yourself as an excellent salesperson. You can do this by mentioning your track record and prior experience. You can discuss a successful email campaign you ran in a previous role, different sales pipelines that you established, or your use of effective sales tactics. 
• Accomplishments. You should also highlight the professional accomplishments you have achieved throughout your career. These may include being an award-winning sales manager or achieving a high percentage of sales growth after implementing successful campaigns.

5 Tips for Writing a Strong Sales Manager Cover Letter

Use the following tips to create a strong sales management cover letter that will impress anyone who reads it and improve your chances of landing an interview. 

• Be professional. When writing your sales manager cover letter, you must maintain a professional tone in your writing. Remember that you cannot write the way you speak and that the hiring manager whom you are addressing is also a professional. The tone of your letter should be warm and friendly without being too casual.
• Show your passion. A perfect cover letter will show how much you want to work for the company in question, why you have always admired it, how it aligns with your career goals, and what you like most about your career as a sales manager.
• Be honest.  It is best to be honest when writing your cover letter, as lies can easily be discovered. Make sure that you are honest about the clients you have worked with, the teams you have led, and the sales you have made. Your references may be checked and, if any deceit is uncovered, you may ruin your chances of being hired. 
• Research the company. One of the best ways to get information about the company is to read its annual report, which you can typically download from its website. This way, you can learn about its activities, accomplishments, mission, vision, and goals for the future. These are very important points that can impact future sales decisions. This strategy will also ensure that you align yourself with the company in your cover letter.
• Proofread. Before sending your cover letter, you should read it many times to check for errors. Do this ahead of time so that you can make corrections. Your sales manager cover letter must not have spelling or grammatical errors. It must be fluid, and you should remember to write in an active voice. 

Sales Manager Cover Letter Example

Use the following sample cover letter to help write yours. This will aid you in finding your next job as a sales manager at the company you’ve always dreamed of working for.

Sales Manager Cover Letter Sample

[Your Name]

[Your Phone Number]

[Your Email Address]

Dear [Hiring Manager’s Name],

I am writing this letter to apply for the sales manager position at [company name]. I am very excited for this opportunity and I believe that I am the perfect candidate due to my extensive experience in the field.

Thanks to my studies and the hands-on professional experience I have gained in previous positions, I have developed extensive sales knowledge. In addition, I have increased the annual revenue of each client to whom I have offered my services, by an average of [X] percent.

I have worked closely with marketing managers from different industries throughout my career to develop effective sales strategies. I consider myself a professional with problem-solving, communication, and leadership skills. I can make decisions with sound judgment as needed. 

I possess a great work ethic that can contribute to your company as part of your sales team. As a sales manager at [Name of the Previous Company You Worked For], I have been able to facilitate online promotional campaigns for a wide variety of products and services, while also being in charge of a high-level and highly productive team.

Thank you for your attention and for the opportunity. I invite you to read my resume and learn a little more about my experience, studies, and training. I look forward to hearing from you.

Sales Manager Resume Guide

In this section, we will show you important tips, suggestions, and examples so that you can create an impressive sales manager resume. 

Why Does Your Sales Manager Resume Matter?

A sales manager’s resume includes all the details of a person’s professional life. Through a resume, the employer can determine if a candidate is a good fit for the company’s objectives. Once a hiring manager understands your relevant experience, they will have a better idea of how you will perform in the job.  

It is important to list any courses in sales training in addition to any bachelor’s or master’s degrees you hold. It is also important to mention your successful sales campaigns. This is also a suitable time to mention noteworthy clients you have worked with in the past.

Essential Components of Your Sales Manager Resume

Below are the components that your sales manager resume should include. You must follow these recommendations to write a successful resume.

• Header. In the header of your sales manager resume, you must place your name in a larger font than the rest of the text. Then you can place your contact details, including your phone number, address, and email. Make sure that all your data is correct so that the company can contact you easily.
• Executive summary. When writing your sales manager resume, make sure to include an executive summary that is impactful and communicates your achievements, experience, skills, and qualifications.
• Professional experience. Make a list of your previous sales jobs, and include the position you held in the company as well as the years you were in that position. Also, include a list of the activities and achievements you carried out in that position.
• Key skills. Knowing what skills to add to a resume can be hard. Focus on skills that a sales manager must have to perform well in their field. Include hard skills such as software management, financial forecasting, and sales planning, and some soft skills such as analytical skills, leadership, and critical thinking.
• Key achievements. A key way to stand out from other sales managers is to show your accomplishments, so include industry-relevant achievements on your resume. It is important to be as specific as possible in this section. 

5 Tips for Writing a Strong Sales Manager Resume

Below are some tips for creating an impressive resume. Remember to pay attention to details, and focus on demonstrating why you are the ideal sales candidate.

• Write an excellent summary. The executive summary is the first impression anyone who reads your resume has of you. Concentrate on writing a compelling summary that will make the hiring manager want to read on and learn more about your experience and training.
• Quantify your achievements. It is good to include your achievements by quantifying them. As a sales manager, you should back up your achievements with references that show the results in measurable terms, such as the overall monetary worth of your campaigns or the number of employees you have been in charge of. 
• Read the job description.  Make sure you read the company’s job post carefully. You can include keywords found in the job post so that your resume will pass through the applicant tracking systems (ATS). This way, you can be sure your resume will get into the hiring manager’s hands.
• Focus on your sales experience. It is unnecessary to include all the information regarding non-sales jobs you had before starting your career as a sales manager. It is better to focus on the sales jobs you have held, even if you have only had an entry-level position, and describe all your accomplishments in detail. 
• Design. You should use designs that look professional, clean, and minimalistic. That’s why we recommend that you look at sample resume templates and choose one that you feel comfortable with. In the next section, we look at some specific examples. 

Sales Manager Resume Examples

Below is an example of a sales manager’s resume and an example of the executive summary. As you’ll be able to see, our examples adhere to the components and tips discussed above.

"Career Karma entered my life when I needed it most and quickly helped me match with a bootcamp. Two months after graduating, I found my dream job that aligned with my values and goals in life!"

Venus, Software Engineer at Rockbot

Sales Manager Resume Sample: The Executive Summary Section

Executive Summary

Sales professional with five years of experience leading successful marketing campaigns, including digital marketing, email marketing, and partner marking campaigns. Experience working with diverse clients, including several Fortune 500 companies. Highly qualified, proactive, and responsible, with strong leadership and negotiation skills .

Sample Sales Manager Resume Template

[Your Full Name]

[Your Address]

[Write a brief summary of your Sales Manager experience and accomplishments. This should be no more than a few sentences.]

[List your skills in bullet-point format, including managerial skills and soft skills.]

Professional Experience

[Company Name] | [Location] [Job Title] [Date Started – Date Ended]

• [List your key responsibilities and accomplishments for each role.]
• [Be specific and detail-oriented to show your impact.]

[Company Name, Location] [Job Title] [Date Started – Date Ended]

[Institution Name] | [Location] [Graduation Date] [Degree]

• [Add details about relevant coursework, special achievements, and any honors.] 

Sales Manager Resume Template Resources

• Sales manager resume . This is a Word resume template. The template is specially designed for a sales professional to list work experience chronologically. 
• Marketing resume . This is a Word marketing resume template. This is an eye-catching template to list your studies, skills, and work experience. This is a bold design, but you can change the font and colors.
• Minimalist resume . This is a Word template that you can use for your sales manager resume. The template has a minimalist style that you can customize, and you can also combine it with a minimalist cover letter template.

Importance of a Sales Manager Cover Letter and Resume

A compelling cover letter and a sleek resume are a sales manager’s way of communicating their sales experience to employers. You must have these documents ready and well-curated to get your next job in the industry.

Sales Manager Cover Letter and Resume FAQ

To write your sales manager cover letter, you should, first of all, address the hiring manager of the company directly. Start by explaining why you would be a good fit for the sales manager position. Describe how your skills and accomplishments will help you meet the company’s goals and how your vision aligns with their ideals.

In your sales manager resume, it is very important that you create a list of your skills. This list should include the skills you have in reporting, statistical analysis, use of systems, and soft skills such as communication, coaching, and leadership skills. You can also detail management skills on your resume .

When you are following an application process, you must follow the steps indicated by the recruiter or hiring manager. If the job ad suggests that you send the cover letter and resume together, then do it. They are sometimes kept separate in the application process, in which case they will be individually requested at different times.

A sales manager is a highly trained professional who must have skills in leadership, coaching, communication, customer relations, management, and personnel management skills, including hiring and recruiting sales representatives.

About us: Career Karma is a platform designed to help job seekers find, research, and connect with job training programs to advance their careers. Learn about the CK publication .

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Professional Sales Associate Cover Letter Example

Writing a cover letter for a job as a professional sales associate can be an intimidating task, but it doesn’t have to be. With the right approach, you can craft an effective cover letter that impresses prospective employers and gets your resume to the top of the pile. In this guide, you’ll find tips and advice on how to write a professional sales associate cover letter and a sample letter to help you get started.

If you didn’t find what you were looking for, be sure to check out our complete library of cover letter examples .

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Professional Sales Associate Cover Letter Sample

Dear [Hiring Manager’s Name],

I am writing to apply for the position of Sales Associate at [Company name]. After reading through the job description provided, I am confident I possess the necessary qualifications and experience that make me an ideal candidate for the role.

I am an enthusiastic, customer- focused professional with a proven track record of success in providing high- level sales services. I have several years of retail sales experience, which has allowed me to develop strong customer service and communication skills. I am confident in my ability to assess customer needs and provide solutions that meet their expectations. Additionally, I have a comprehensive understanding of sales techniques, product knowledge, and best practices that have helped me develop successful sales strategies.

I also have experience in developing and executing successful merchandising strategies and product displays. My experience in working with various vendors and suppliers has allowed me to effectively collaborate within a team environment. I am also able to work independently and with minimal supervision, which has helped me build a comprehensive understanding of inventory management.

My commitment to meeting customer expectations and my drive to exceed sales targets are what I believe sets me apart from other candidates. I am eager to join a team of like- minded professionals and leverage my experience to make an immediate impact within the team.

I have enclosed my resume and would happily provide additional information if required. I look forward to discussing this opportunity in further detail. Thank you for your time and consideration.

[Your name]

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What should a Professional Sales Associate cover letter include?

A professional sales associate cover letter should include information that highlights the applicant’s relevant skills and experience to the position. It should also demonstrate the applicant’s enthusiasm for the role and express their interest in the company.

The cover letter should start with a brief introduction and provide a brief overview of why the applicant believes that they are the best fit for the job. This should be followed by a discussion of the applicant’s relevant skills and experience, such as their knowledge of sales techniques and customer service, their ability to work with others and their success in previous sales positions.

The cover letter should end with a closing statement that reiterates the applicant’s interest in the job and expresses appreciation for the time taken to consider the application. The applicant should also provide contact information so that the employer can get in touch with them.

Professional Sales Associate Cover Letter Writing Tips

Writing a professional sales associate cover letter can be a daunting task, especially if you don’t have a lot of experience in the role. However, it’s important to make sure your cover letter stands out from other applicants and introduces you as a qualified candidate. Here are some tips to help you write a winning sales associate cover letter:

• Research: Take the time to research the company and learn about the job you are applying for. Make sure you include details in your cover letter that demonstrate your knowledge and understanding of the company and the role.
• Highlight Skills: Use the cover letter to highlight the skills and experience that make you the best fit for the role. Mention any relevant job experience and training you have that is related to sales and customer service.
• Be Specific: Be sure to mention examples of successful sales campaigns or customer service initiatives you have been involved in. Having specific examples will make your cover letter more compelling to the employer.
• Tailor Your Letter: Make sure you tailor your cover letter to the job you are applying for. Highlight any transferable skills and experiences that are relevant to the job.
• Proofread: Take the time to proofread your cover letter for any typos or errors. It’s important to make sure your letter is professional and free of any mistakes.

Following these steps will help you write a successful sales associate cover letter. A well- written cover letter can make you stand out from the competition and increase your chances of getting the job. Good luck with your job search!

Common mistakes to avoid when writing Professional Sales Associate Cover letter

Writing a successful cover letter for a Professional Sales Associate position can be challenging. It can be difficult to know what to include and how to make your letter stand out from the rest. To ensure that your letter is effective and persuasive, there are some important mistakes to avoid.

• Not doing enough research: Before writing your letter, it’s important to research the company and their products or services. This will give you an idea of the company’s values and tone and help you tailor your letter to the specific organization.
• Not customizing the letter: To make sure your letter stands out, it’s important to tailor it to the specific company and position. Make sure to include specific examples of how your skills and experiences can benefit the organization.
• Focusing too much on your qualifications: Your cover letter should be more than just a list of your qualifications. It should highlight your enthusiasm for the job and show why you are the right person for the position.
• Not showing enthusiasm: Your letter should show your enthusiasm for the job and the organization. Make sure to include specific examples of how your skills and experiences can benefit the organization and make sure to express your excitement for the job.
• Not proofreading: Before sending your application, it’s important to proofread your letter. This will help ensure that there are no typos or grammatical errors.

By avoiding these common mistakes, you can create an effective and persuasive cover letter for a Professional Sales Associate position. Good luck!

Key takeaways

Writing a cover letter to apply for a Professional Sales Associate position can be an intimidating and challenging task. But with the right tips and tricks, you can create a cover letter that will give you an edge over other applicants. Here are some key takeaways to write an impressive cover letter for a Professional Sales Associate position:

• Start off by introducing yourself and explaining why you are the perfect fit for the position. Highlight how your experience and skills make you an ideal candidate.
• Focus on how your strengths align with the company’s goals, values, and culture. Show that you are familiar with the company and show that you can bring value to the team.
• Showcase your knowledge of the industry and emphasize your sales skills. Show that you have the tools and strategies to achieve their sales goals.
• Explain why you are passionate about sales and why this job is a good fit for you. Show off your enthusiasm and dedication for the job.
• Finish off your cover letter with a call to action. Provide a way for the employer to contact you, such as an email address or phone number.

Following these key takeaways will help you craft a successful cover letter that will make you stand out from other applicants. Good luck!

Frequently Asked Questions

1. how do i write a cover letter for an professional sales associate job with no experience.

Writing a cover letter for an Professional Sales Associate job with no experience can be a daunting challenge. However, there are certain strategies you can employ to create a powerful and effective cover letter. First of all, start by introducing yourself and your interest in the job. Explain why you believe you are the right person for the job, even without experience. Then, focus on the skills and qualities you possess which could make you successful in the role. For example, highlight any related qualifications, such as in customer service or communication, as well as any transferable skills from other roles. Finally, be sure to thank the employer for their time and consideration.

2. How do I write a cover letter for an Professional Sales Associate job experience?

Writing a cover letter for an Professional Sales Associate job with experience is a different task. Here you should focus on how your past experience has prepared you for this position. Start by drawing on your previous experiences, such as successfully meeting targets or providing excellent customer service. Then, discuss the skills that you have developed over time, such as your ability to work as a team, handle challenging situations, and make decisions. Finally, explain why your past experiences make you the ideal candidate for the job and why you would be a great fit.

3. How can I highlight my accomplishments in Professional Sales Associate cover letter?

When writing a Professional Sales Associate cover letter, it is important to highlight your accomplishments. Begin by describing the successes you have achieved in previous roles or projects. This could include meeting sales targets, providing excellent customer service, or successfully negotiating deals. Additionally, you can use concrete figures to demonstrate your value, such as how much revenue you brought in or how many new clients you acquired. Finally, make sure to emphasize how these achievements make you the ideal candidate for the role.

4. What is a good cover letter for an Professional Sales Associate position?

A good cover letter for an Professional Sales Associate position should be concise, yet thorough. Begin by introducing yourself and expressing your enthusiasm for the position. Then, focus on the skills and qualities that make you the ideal candidate for the job. Be sure to draw from your past experiences and accomplishments to demonstrate why you are the right person for the role. Finally, express your interest in learning more and thank the employer for their time and consideration.

In addition to this, be sure to check out our cover letter templates , cover letter formats ,  cover letter examples ,  job description , and  career advice  pages for more helpful tips and advice.

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60+ Cover Letter Examples in 2024 [For All Professions]

No matter where you are in your career, or what job you’re applying for, submitting a cover letter with your resume is a must . 

Done right, a cover letter will effectively complement your resume and explain to the hiring manager in more detail why you’re the right person for the job.

Writing a cover letter, however, is easier said than done. 

You have to effectively demonstrate that you’ll be able to perform the responsibilities listed in the job description and that you’d be a better fit for the company compared to other candidates. 

And unless you’re a professional writer, this can be a very hard task.

Fortunately, we created these cover letter examples to inspire you and help you get started with your own cover letter!

Let’s dive in!

21 Cover Letter Examples 

#1. career change cover letter example .

Here’s what this cover letter does right:

• Has an ideal length. This cover letter includes all the relevant information for the hiring manager without getting into too much detail.
• Relevant introduction. The candidate explains that they’re changing careers and why they want to work in this new field from the get-go.
• Explains their related experience. The candidate explains how their previous experience in retail sales can help them succeed in PR.

Check out our guide video guide to learn how to write a Cover Letter that gets you HIRED!

#2. Recent Graduate Cover Letter Example 

• Personally greets the hiring manager. The candidate has taken the time to find the hiring manager’s name and address them by it, which makes the opening of the cover letter much more personal.
• Wraps up with a call to action. The candidate wraps up the cover letter by suggesting a meeting with the hiring manager, which makes them more memorable.
• Explains why the candidate is the right person for the internship. In this cover letter for an internship , the candidate explains how they’ve previously interned in a different firm, which gives them the experience to succeed in this role.

Have you just graduated from college? Make sure to check out our guide on writing an entry-level cover letter from start to finish! 

#3. Middle Management Cover Letter Example

• Use of bullet points. The candidate presents the information in a concise and reader-friendly way, making it easy for the hiring manager to find their key achievements. 
• Formal closing. The candidate has used a formal and polite tone to conclude their cover letter, which combined with a call to action makes them look professional and passionate about getting the job. 
• Explains how the company would benefit from hiring them. The candidate outlines exactly what they could do for the company, which not only highlights their skills but also shows they’ve done their research on the company’s needs. 

#4. Business Manager Cover Letter Example

• Detailed header. In addition to the must-have contact details, this candidate has also included their professional Twitter and LinkedIn profiles, making it easy for the hiring manager to look more closely into their career. 
• Concise and to the point. This candidate has used short paragraphs and bullet points to make the cover letter easy to skim through. 
• Wraps up with a call to action. By letting the hiring manager know they’ll be contacting them soon, they’re more likely to make an impression.

Check out this article for a complete writing guide and an inspiring business manager resume sample. 

#5. Ph.D. Cover Letter Example

Here’s what this cover letter does right: 

• Attention-grabbing introduction. In the opening paragraph, this candidate explains why they’re passionate about pursuing a Ph.D. in great detail. 
• Explains the candidate’s qualifications in detail. The candidate builds on their passion by explaining how they’re also qualified for the degree because of their education history and academic achievements. 

#6. Senior Executive Cover Letter Example

• Professional and minimalistic template. This senior executive has used a professional but minimalistic template that lets their work experience do the talking. 
• Achievement-oriented opening paragraph. Right from the get-go, this candidate explains what makes them so good at their job, effectively grabbing the hiring manager’s attention.  
• Wraps up with a call to action. By suggesting to have a meeting and discussing how they can help the company meet its goals, the candidate stands more chance to make a positive lasting impression. 

#7. Architect Cover Letter Example 

• Modern resume template. This architect has picked a template that perfectly matches his industry, as it is professional and modern at the same time. 
• A personal greeting to the HR. They address the hiring manager by their first name, which helps make a better first impression. 
• Measurable achievements. By quantifying their achievements, the candidate proves their achievements instead of just claiming them.

Struggling with your architect resume ? Check out our full guide!

#8. Business Analyst Cover Letter Example 

• Detailed contact information. The candidate has listed both their LinkedIn and Twitter profiles, providing the HR manager an opportunity to learn more about the candidate.  
• Mentions what the candidate can do for the company. This cover letter doesn’t just explain why the job would be great for the candidate, but also how the candidate would benefit the company. Win-win, right? 
• Error-free and reader-friendly. It’s super important for the cover letter to have no spelling or grammatical errors and be reader-friendly. This candidate made sure they did both.

Need a resume alongside your cover letter? Check out our guide on how to write a business analyst resume . 

#9. Consultant Cover Letter Example 

• Professional cover letter template. Being an experienced consultant, this candidate has picked a professional template that doesn’t steal the spotlight from their achievements. 
• Experience and achievement-oriented. The candidate has effectively elaborated on their top achievements relevant to the job. 
• Highlights the candidate’s passion. To show they want the job, this candidate has also explained how passionate they are about their profession.

For more advice on landing a job as a consultant, check out our guide to writing a consultant resume .

#10. Digital Marketing Cover Letter Example

• Creative cover letter template. This digital marketer highlights their originality by picking a creative cover letter template. 
• Lists the candidate’s awards. The candidate has taken advantage of the cover letter to list their most noteworthy awards in the industry. 
• Concludes with a call to action. As they used a call to action to conclude their cover letter, the HR manager will be more likely to remember them.

Want to take your digital marketing resume to the next level? Check out our guide!

#11. Graphic Designer Cover Letter Example 

• Detailed contact information. The candidate has included additional contact information such as their website link, as well as their LinkedIn and Twitter profiles.  
• Ideal length. This cover letter is concise, which means that the HR manager is more likely to read it from start to finish.  
• Draws attention to the candidate’s strong points. Although this candidate is a recent college graduate, they’ve managed to effectively show that they have enough knowledge and experience to do the job right.

Read this guide to write a graphic designer resume that’s just as good as your cover letter!

#12. Administrative Assistant Cover Letter Example

• Minimalistic cover letter template. The candidate picked a well-designed but minimalistic template for their cover letter. 
• Focused on skills and achievements. This cover letter is packed with the candidate’s skills and achievements, proving he can be an excellent employee. 
• Formal closing. Politeness can go a long way and the candidate has used this to their advantage to make an impression. 

Our article on how to write an administrative assistant resume can help you take your job application to the next level.

#13. Front Desk Cover Letter Example

• Modern cover letter template. This template incorporates memorable colors and clear lines, which make the cover letter very visually appealing. 
• Attention-grabbing introduction. Using an attention-grabbing intro, the candidate is more likely to make an impression. 
• Calls the HR to action. By including a call to action, the candidate is reminding the HR of their immediate availability. 

#14. Human Resources Cover Letter Example

• It is concise and to the point. The candidate doesn’t dwell on unimportant details the HR won’t be interested in. 
• Uses a traditional cover letter template. The cover letter design is more on the conventional side, which fits the industry better. 
• Highlights the candidate’s strong points. The candidate has rich work experience and they use the cover letter to elaborate on it. 

This HR resume guide can help you get your resume just right.

#15. Sales Agent Cover Letter Example 

• Attention-grabbing cover letter template. As a salesperson, this candidate knows how important first impressions are, so they’ve picked a catchy cover letter template. 
• Has an ideal length. At the same time, they’ve also made sure to keep their cover letter at just the right length. 
• Lists the candidate’s career highlights. The candidate has made perfect use of the space by mentioning their most impressive professional achievements. 

Check out this sales agent resume guide to create an attention-grabbing sales resume .

#16. Receptionist Cover Letter Example

• Modern but minimalistic cover letter template. The template’s design hints the candidate is creative but professional at the same time. 
• Uses a catchy introduction. The candidate has used an attention-grabbing opening paragraph to catch HR’s attention. 
• Concludes the cover letter formally. The candidate proves that they’re polite and well-spoken, a quality very much important for the role they’re applying for. 

Take your receptionist resume to the next level with this receptionist resume guide .

#17. Information Technology Cover Letter Example

• Mentions measurable achievements. Numbers make an impact, which is why this candidate has included measurable achievements. 
• Lists both soft and hard skills. The candidate has mentioned a great mix of soft and hard skills, showing how well-rounded they are. 
• Contains relevant contact information. The candidate’s GitHub, website name, LinkedIn, and Twitter profiles are all great additions to the resume. 

Looking for tips to help you write a great IT resume ? Check out our guide!

#18. Real Estate Cover Letter Example

• Ideal length. Short and to the point, this cover letter is bound to get noticed by the HR manager. 
• Wraps up with a call to action. This candidate reinforces the HR to call them back through a final call to action. 
• Mentions the right skills. On top of their sales accomplishments, the candidate touch upon important soft skills such as customer service and communication . 

This real estate resume guide will help you take your resume from good to great.

#19. Teacher Cover Letter Example

• Mentions relevant contact information details. This candidate has included optional (but relevant) contact information details, such as their LinkedIn, Quora, and Medium profiles. 
• Achievement-oriented. The candidate has elaborated on their achievements in more detail throughout their cover letter. 
• Highlights the candidate’s passion. For some jobs, being passionate is much more important than for others. Teaching is one of these jobs, which is why this candidate explains their passion for the job. 

Our guide on how to write a teacher resume has all the tips you need to land the job.

#20. Project Manager Cover Letter Example

• Leverages a catchy introduction. Through a catchy introductory paragraph, this candidate is sure to grab the HR’s attention and get them to read the rest of their cover letter.
• Lists measurable accomplishments. This candidate explains exactly what they’ve achieved using numbers and hard data. 
• Personally greets the HR. A personal greeting sounds much better than “Dear Sir/Madam,” and the candidate knows this. 

This guide on how to write a project manager resume can help you perfect your appication.

#21. Paralegal Cover Letter Example

• Minimalistic cover letter template. This cover letter design looks good but doesn’t steal the show from the candidate’s abilities.
• Mentions the candidate’s academic achievements and extracurricular activities. Although the candidate is a recent graduate, they’ve used the cover letter to explain they have enough skills and achievements to do the job.
• Lists measurable achievements. The candidate proves they did well in their internship by mentioning quantifiable achievements.

Check out this paralegal resume guide to perfect yours.

40+ More Cover Letter Examples and Guides 

Couldn’t find a cover letter example for your field? Do not worry.

Below you can find a number of other cover letter examples for different fields and industries:

• Acting Cover Letter Examples
• Accounting Cover Letter Examples
• Administrative Assistant Cover Letter Examples
• Architecture Cover Letter Examples
• Attorney Cover Letter Examples
• Barista Cover Letter Examples
• Bartender Cover Letter Examples
• Business Cover Letter Examples
• Business Analyst Cover Letter Examples
• College Student Cover Letter Examples
• Computer Science Cover Letter Examples
• Construction Cover Letter Examples
• Consultant Cover Letter Examples
• Customer Service Cover Letter Examples
• Data Analyst Cover Letter Examples
• Data Entry Cover Letter Examples
• Dental Assistant Cover Letter Examples
• Digital Marketing Cover Letter Examples
• Elementary Teacher Cover Letter Examples
• Engineering Cover Letter Examples
• Executive Assistant Cover Letter Examples
• Finance Cover Letter Examples
• Graphic Design Cover Letter Examples
• Healthcare Cover Letter Examples
• Human Resources Cover Letter Examples
• IT Cover Letter Examples
• Law Cover Letter Examples
• Management Cover Letter Examples
• Marketing Cover Letter Examples
• Mechanical Engineering Cover Letter Examples
• Medical Assistant Cover Letter Examples
• Nurse Practitioner Cover Letter Examples
• Physician Cover Letter Examples
• Project Manager Cover Letter Examples
• Receptionist Cover Letter Examples
• Retail Cover Letter Examples
• Sales Cover Letter Examples
• Social Work Cover Letter Examples
• Software Engineer Cover Letter Examples
• Substitute Teacher Cover Letter Examples
• Teacher Assistant Cover Letter Examples
• Team Leader Cover Letter Example

What is a Cover Letter? 

A cover letter is a one-page document that you submit as part of your job application, alongside your resume . 

Its purpose is to introduce you and briefly summarize your professional background. On average, your cover letter should be from 250 to 400 words long .

A good cover letter can give the hiring manager more insight into what makes you a good candidate and help them make up their mind about whether they should invite you for an interview. A bad cover letter, though, will get ignored (at best) and lose you the job (at worst).

So, to make sure this doesn’t happen, it’s essential to know how to write a convincing cover letter.

The first thing to remember is that a cover letter is a supplement to your resume, not a replacement. Meaning, you shouldn’t just repeat whatever is mentioned in your resume and call it a day. 

Optimally, you should use your cover letter to shed more light on your skills and qualifications, as well as explain anything you didn’t have space for in your resume (e.g. a career gap or why you’re changing careers).

If you’re writing a cover letter for the first time, though, putting all this together might seem pretty tough. 

Fortunately, you can follow our tried-and-tested format to make the experience much easier:

• Header - Input your contact information.
• Greeting the hiring manager - Open the cover letter with a “Dear Sir or Madam,” or use the hiring manager’s name if you know what that is.
• Opening paragraph - Grab the hiring manager’s attention by getting straight to the point. Mention what your professional experiences are, and what role you’re applying for.
• The second paragraph - Explain why you’re the perfect candidate for the job. Mention your top 2-3 achievements, your top skills, why you want to work in that specific industry, and whatever else is relevant.
• The third paragraph - End your cover letter with a call to action. E.g. “I would love to meet personally and discuss how I can help Company X.”
• Formal closing - Something like this: “Thank you for your consideration. Best, John Doe.”

Here’s what this looks like in practice:

9 Tips to Write a Cover Letter (the Right Way)

Now that we've covered the basics, let's talk about cover letter tips . Below, we'll give you all the knowledge you need to take your cover letter from "OK" to "great."

#1. Pick the right template

A good cover letter is all about leaving the right first impression.

And what’s a better way to leave a good impression than through a professional, well-formatted, and visual template?

You can simply pick one of our tried-and-tested cover letter templates and you’ll be all set!

#2. Add your contact details on the header

The best way to start your cover letter is through a header. 

Here’s what you want to include there:

• Phone Number
• Name of the hiring manager / their professional title
• Name of the company you’re applying to

Optionally, you can also include the following:

• Social Media Profiles - Any type of profile that’s relevant to your field. Social Profiles on websites like LinkedIn, GitHub (for developers), Medium (for writers), etc.
• Personal Website - If you have a personal website that somehow adds value to your application, you can mention it. Let’s say you’re a professional writer. In that case, you’d want to link to your content portfolio site or blog.

#3. Greet the hiring manager the right way

Once you’ve listed all your relevant contact information, it’s time to address the hiring manager reading your cover letter. 

A good practice here is to find the hiring manager’s name and address them directly instead of using the traditional “dear sir or madam.” This shows that you’re really invested in the company and that you took your time to do some research about the job.

So, how can you find out the hiring manager’s name?

One way to do this is by looking up the head of the company’s relevant department on LinkedIn. Let’s say you’re applying for the position of Communication Specialist at Novoresume. The hiring manager is probably the Head of Communications or the Chief Communications Office.

Or let’s say you’re applying for the position of server at a restaurant. In that case, you’d be looking to find out who the restaurant manager is.

If this doesn’t work, you can also check out the “Team” page on the company website; there’s a good chance you’ll at least find the right person there.

If you still can’t find out the hiring manager’s name, here are several other greetings you can use:

• Dear [Department] Hiring Manager
• Dear Hiring Manager
• To whom it may concern
• Dear [Department] Team

#4. Create an attention-grabbing introduction

Recruiters get hundreds, sometimes even thousands, of applications. Chances are, they’re not going to be reading every single cover letter end-to-end.

So, it’s essential to catch their attention from the very first paragraph.

The problem with most cover letter opening paragraphs, though, is that they’re usually extremely generic, often looking something like this: 

Hey, my name is Jonathan and I’d like to work as a Sales Manager at XYZ Inc. I’ve worked as a sales manager at MadeUpCompany Inc. for 5+ years, so I believe that I’d be a good fit for the position.

As you can probably tell, this opening paragraph doesn’t tell the hiring manager anything other than that you’ve worked the job before - and that’s not really helpful in setting you apart from other candidates. 

What you want to do, instead, is start off with 2-3 of your top achievements to really grab the reader’s attention. Preferably, the achievements should be as relevant as possible to the position. 

For example:

My name’s Michael and I’d like to help XYZ Inc. hit and exceed its sales goals as a Sales Manager. I’ve worked with Company X, a fin-tech company, for 3+ years. As a Sales Representative, I generated an average of $30,000+ in sales per month (beating the KPIs by around 40%). I believe that my previous industry experience, as well as my excellence in sales, makes me the right candidate for the role of X at Company Y.

The second example shows how the candidate is a top performer. The first just shows that they’ve worked a sales job before.

Which one are YOU more likely to invite for an interview?

#5. Show you’re the perfect person for the job

One great thing about cover letters is that they allow you to expand more on the top achievements from your resume and really show the hiring manager that you’re the right person for the job. 

A good way to do that is to first read the job ad and really understand what skills/experiences are required, and then to ensure that your cover letter touches upon the said skills or experiences.

In my previous role as a Facebook Marketing Expert at XYZ Inc. I handled customer acquisition through ads, managing a monthly Facebook ad budget of $20,000+. As the sole digital marketer at the company, I managed the ad creation and management process end-to-end. This means I created the ad copy and images, as well as picked the targeting, ran optimization trials, and so on.

Other than Facebook advertising, I’ve also delved into other online PPC channels, including:

• Google Search

#6. Explain why you’re a great company fit

The HR manager doesn’t only look at whether you’ll be good at the job or not. They’re looking for someone that’s also a good fit for the company culture.

After all, employees that don’t fit in are bound to quit, sooner or later. This ends up costing the company a ton of money, up to 50% of the employee’s annual salary . 

To convince the hiring manager that you’re a great company fit, do some research on the company and find out what it is you like about them, or about working there. You want to know things like:

• What’s the company’s business model?
• What’s the company's product or service? Have you used it?
• What’s the culture like? Will someone micro-manage your work, or will you have autonomy on how you get things done?

Then, turn your top reasons for liking to work there into text and add them to your cover letter! 

#7. Wrap up with a call to action

To make the end of your cover letter as memorable as possible, you want to:

• Wrap up any points you couldn't in the previous paragraphs. Mention anything you’ve left out that you think could help the hiring manager make up your mind.
• Thank the hiring manager for their time. After all, it never hurts to be polite. 
• Finish the cover letter with a call to action. A call to action is a great way to make your cover letter ending as memorable as possible. 

#8. Write a formal closing

Once you’re done with the final paragraph, all you have to do is write down a formal “goodbye” and you’re good to go.

Feel free to use one of the most popular conclusions in a cover letter:

• Best Regards,
• Kind Regards,

#9. Proofread your cover letter

Last but not least, make sure to always proofread each and every document that you’ll be including in your job application - cover letter included. 

The last thing you want is to be claiming you’re a great candidate for the job with a cover letter full of typos! 

For an even more comprehensive guide on how to write an impactful cover letter , check out our article ! 

Cover Letter Writing Checklist 

Do you still have some questions about cover letters? Check out the answers below:

1. How do I write a simple cover letter? 

To write a cover letter that’s simple but also professional, make sure to include a header with your personal information, a formal greeting to the hiring manager, an attention-grabbing opening paragraph, a second paragraph explaining why you’re a good candidate for the job, and a formal closing (preferably with a call to action). 

2. What are the 3 parts of a cover letter? 

The three parts of a cover letter are: 

• The introduction , namely the header, the greeting to the hiring manager, and the opening paragraph. 
• The sales pitch is usually the body of the cover letter. 
• The conclusion involves a formal closing and a signature line.

3. What makes a great cover letter?

A great cover letter should be personalized for each job you’re applying for, instead of being overly generic. It’s also preferable to address the hiring manager by their name and not use the overly-used “Dear Sir/Madam.”

To make a great first impression, you should mention 1-2 of your top achievements in your opening paragraph - the more job-specific they are, the better. Also, don’t stop at showing the hiring manager why you’re a great candidate for the job. Make sure to also talk about how you’re a good culture fit for the company.

Last but not least, wrap up your closing paragraph with a call to action to give the hiring manager a little extra something to remember you by. 

4. When is a cover letter necessary?

Unless the job ad specifically states otherwise, you should always include a cover letter with your job application .

Even if the hiring manager doesn’t read it, you will look more professional simply by including one.

And that’s a wrap! We hope our cover letter examples and writing tips will inspire you to write a cover letter that will land you your next job.

If you’re looking for more invaluable career advice and articles, make sure to check out our career blog , or any of these related articles: 

• How to Write a Resume
• Cover Letter Mistakes to Avoid at All Costs
• Cover Letter Format (w/ Examples & Free Templates)

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21 Sales Resume Examples That Landed Jobs in 2024

• Sales Resume
• Sales Resumes by Experience
• Sales Resumes by Role

Writing Your Sales Resume

Sales are the lifeblood of any growing company. Without sales, companies grow stagnant—or worse, fail. But with a good sales department, a company can truly thrive.

You know how to care for customers, present solutions to problems, and adapt to any situation. Unfortunately, getting a new sales job involves more than just a short resignation letter at your current job and being stellar at what you do.

You shouldn’t have to create an effective resume or write a sales cover letter alone, which is why we’ve analyzed hundreds of professional resumes and created 21 sales resume examples just for you. These examples have helped salespeople get hired by companies like Google and Facebook , and they’re here for you to achieve the next role of your dreams in 2024.

Sales Resume Example

or download as PDF

Why this resume works

• Whether your most significant impact was in total sales, conversion rate, retention rate, or lead generation performance, it doesn’t matter—numbers speak louder than words, so include them whenever you can!

Sales Assistant Resume

• Find a way to include metrics to really sell your skills!
• Don’t just say you used a certain skill; demonstrate how you used that skill. For example, did you use your organization skills to stock many items? 
• Pack your resume objective with proactive language that shows your eagerness for growth and improvement. If you’re looking for a career-building role, then say exactly that!

Entry-Level Sales Representative Resume

• Sales is a people management game. If you have charm and patience, that’s much more valuable in the eyes of the hiring manager than an impressive educational background.
• You can also include a  resume objective  to mention some of your accomplishments and skills right off the bat; if you choose to do so, make sure you tailor it for every job to which you apply.
• If your education is your strongest area, include your minor, GPA, and any relevant courses you’ve taken.
• If you’ve worked on several projects, make room to include them on your resume in place of work experience.

Experienced Sales Associate Resume

• Your true competence as a sales associate shines through the most when you mention how you effectively calmed angry customers and offered practical, compassionate solutions.
• If you’re not overly familiar with a skill, leave it out—honesty is the best policy, and many skills are easy to learn on the job.

Experienced Retail Sales Associate Resume Example

• If you don’t have past retail experience, don’t fret; use the positions you have to highlight transferable skills, like time management, customer service, and problem-solving.
• Instead of just listing responsibilities, include any achievements, too. Were you a top salesperson in your store? Did you increase your customer review rating? Did you cross-sell effectively and increase revenue? All of these are great examples to include!

Senior Sales Analyst Resume

• Include a  resume summary  (also called a career summary) if you can boast 10+ years of field experience. Make it a concise, customized snapshot of yourself by including your specializations, defining expertise, and mentioning the target business by name.
• You can include the number of employees you manage or mentor, the rate at which you’ve increased revenue, the rate at which employees have hit sales targets during your tenure, the number of departments you collaborate with, the number of monthly presentations you give, and any other metrics that showcase how you’ve improved company performance.

VP of Sales Resume

• A good example is the training program you initiated, which boosted team morale and overall productivity by 38 percent.

Pharmaceutical Sales Resume

• Did you help expand market share? Did you leverage technology to help close more sales deals? Add all that in and sit back as your past success elevates your candidacy to the top of the shortlisted applicants.

Insurance Sales Resume

• Highlight how you’ve tapped InsurGrid, NowCerts, ClearSlide, etc. to improve customer service, and attract and retain customers. Also, back your competencies with realistic figures that underscore your impact.

Tech Sales Resume

• Be bold, like Asher, in showing off to what extent your skills and knowledge contributed to the company’s sales department.

Sales Representative Resume

• Make sure every section of your sales representative resume is easy to read and distinguish by either capitalizing them, bolding them, or using a colored font.
• Any mistakes will be easy to see and will hurt your chances of getting an interview. So, always  check your resume  before you submit it!

Sales Manager Resume

• Focus your work experience on your sales achievements and management expertise. Even if you have no sales management experience, you can still show off your sales skills and leadership qualities wherever it was that you worked. 
• When you can, include metrics that quantify your success. Saying you conducted meetings is one thing, but conducting meetings that resulted in a 14% increase in leads is another.

Digital Sales Representative Resume

• A  good resume template  will help you structure your content effectively, but be aware of spacing—even a good resume template won’t help if your text is too tiny to read or spreads into the margins.
• If you’re stumped on what numbers to include, consider these options: response time, the number of active accounts, size of the average account, churn dollars, team size, ROI, social media post engagement, the number of products you know, and how many awards you’ve won.

Sales Strategist Resume

• There are many  good resume examples  if you know where to look, and they can help you break out of your writer’s block funk. Take a look and get some inspiration!
• Moreover, you can ask some co-workers to help you, too! They can help you decide what metrics to include and how to sound confident but not arrogant.
• For example, if you’re a senior-level employee, you don’t need to include much in your education section, but you should include more work experience bullet points.
• However, if you’re new to the field, you can include your GPA and educational awards while minimizing your work experience in favor of projects.

Sales Consultant Resume

• A strong network on LinkedIn indicates that you’re good at building professional relationships, which is an essential element of sales.
• If you haven’t updated your LinkedIn in a while, make sure you do that as soon as possible.
• For example, you can talk about unveiling events for clients, creating working relationships, and building up networks. These details demonstrate that strong customer rapport is, in fact, a skill you possess.

Sales Engineer Resume

• For example, if the job you’re applying to emphasizes the importance of using CRM software or building long-lasting relationships with customers, emphasize these skills in your skills section. 
• Focus on including hard skills similar to the ones used in the  sales job description .
• If you’re just starting your career in sales engineering OR transitioning to a different type of role, include an objective.
• If none of the above applies, leave it out in favor of more work experience.

Director Of Sales Resume

• Don’t forget to list accomplishments related to leading people and building customer relationships, starting by recording how many customers you helped or how many people you led. Then look for percentages relating to KPIs from there.
• If you’re stuck on what to include in your  resume skills section , go back to the  sales job description  and see what soft skills they require, whether explicitly stated or implied.

Outside Sales Representative Resume

• Good examples include the number of new accounts you opened, conversion rate, retention rate, lead generation performance, and overall growth.
• Sales revenue is the main statistic related to every sales position, but make sure you venture outside the box to include other metrics, too.
• You’d be amazed at what tiny typos and punctuation errors can slip through without your noticing, and employers will appreciate your attention to detail!
• Run your resume through a  resume checker  or spellcheck system, then proofread it again with your own eyes.

Software Sales Representative Resume

• For example, did you exceed your sales quotes, and if so, how many times? How much did you increase profits for the company? 
• Provide details that prove you can boost numbers at the next company you’ll work for!
• If you can, shoot for half and half between technical and soft skills, but if you’re an entry-level candidate, it’s okay to have more soft skills.
• As a software sales rep, you should include the programming languages you know, plus soft skills like “negotiation” and “interpersonal communication.”

Fragrance Sales Associate Resume

• For a successful career in sales, you’ll want your communication and persuasion skills to shine just as brightly as your technical knowledge. Be sure you include some of both in your fragrance sales associate resume .

Sales Development Representative Resume

• Sales are all about the numbers. When you’ve brought about tangible positive results at your past workplaces, it speaks to how effective you are as a salesperson and should be touted in your sales development representative resume .

Related resume guides

• Sales Associate
• Sales Representative
• Sales Manager

Proper formatting ensures your resume is readable, logical, and complete. If you neglect the formatting, you risk potential employers not taking your application seriously (or not even seeing your resume). When it comes to formatting, remember the following: 

• Choose one of three resume format options 
• Draw attention to your resume header 
• Make your sales resume accessible for the ATS and employers

Overall resume format options

Hiring managers’ preferences tend to change over time, but for 2024, it’s clear that three  resume formats  are the most popular:

• Reverse-chronological format:  This format emphasizes your most recent experience by placing work experience toward the top of your resume. Ordering your experience this way highlights career growth and development.
• Functional format:  A functional format stresses skills over work experience. This type of format may be appealing if you have little work experience or if there are gaps in your employment. 
• Combination/hybrid format:  This type combines reverse-chronological and functional formatting, placing equal weight on job history  and  skills, but it can be hard to read because of this.

Though all three types are popular,  hiring managers prefer   the reverse-chronological format . It’s easy to read, underscores career growth, and looks honest regarding your job experience. 

Draw attention to your resume header

Presenting your contact information may seem unimportant. However, this is the most important information in your resume; without it, how can you expect hiring managers to tell you “you’re hired?” Don’t make the mistake of underestimating the importance of an accurate and beautiful resume header.

Start by aligning your header either to the left or center. Then write your name in a large font size so you can see it from far away.

Right below your name, include your job title in a slightly smaller font. Then if you like, you can tastefully add some color to show your personality. (We love cobalt blue and buttercup yellow, but we’re a bit biased.)

Underneath your name and title, list your contact information. Keep the text the same font size as the body of your resume, and consider including a border (with or without color) to make it pop. This section should include:

• Your email (make sure it’s professional and not something like “ [email protected] ”)
• Phone number (with an area code)
• City & State (optional but recommended)
• Professional links to portfolios or sites like LinkedIn (optional but recommended)

Make your sales resume accessible to the ATS and employers

Once you upload your resume to an online job application, it won’t go straight to a hiring manager’s desk. Instead, it will go through the ATS, or Applicant Tracking System software.

This system uses keywords in your resume to determine your likelihood of being a good fit for a particular sales job. If you don’t pass the ATS scan, it’s doubtful you’ll get an interview.

To get past the software and reach human eyes, pay attention to:

• Margins:  Use standard half-inch or one-inch margins all around.
• Fonts:  Use professional, easy-to-read fonts like Times New Roman, Arial, or Georgia. 
• Font sizes:  The body of your resume should be the smallest font at around 12-point, your job title should be 20-point font, and your name should be approximately 24-point font.
• Header names:  Instead of adjusting font size for section headers, try bolding them or using all caps. 
• Skills:  You can list them in a horizontal or vertical list; we recommend using bullet points in a vertical list unless you lack space. 
• Logical order:  As we suggested earlier, we recommend a reverse-chronological format since it’s easy for the ATS to scan. 
• One page:  You must fill one page  exactly . You can slightly adjust fonts, font sizes (just a touch), vertical spacing, and margins to hit this target.

If you’re struggling to  build your resume  with enough content and proper formatting, remember this: the most important thing is to  ensure your resume is read . If you have to cut content to keep your formatting easy to read, do it.

Do you really need an objective or summary?

Contrary to sources floating around the internet, there  is  a difference between a  resume objective  and a  resume summary . Both are short paragraphs written explicitly for every application you submit, but there are a few key differences between them. 

An  objective  identifies why you’d like to work for the company under the specific job title for which you’re applying. A  summary  highlights the skills you possess and what achievements you’ve earned within your past positions.

Objectives and summaries are strictly optional, but there are a few instances where adding one would help.

• Consider including an objective if you’re seeking an entry-level role or are transitioning careers.
• Consider using a summary best suited if you have 10+ years of sales experience.

Customized resume objective:  Seasoned floor salesperson with 4+ years of experience hitting sales 7% above targets. Seeking a position with Neiman Marcus, where my specialization in high-end retail will continue the tradition of upholding the highest standard of luxury retail experiences for clientele. 

• This objective is specific to the job and includes a customized job title, quantified metrics, specific skill sets, and the company name. It adds real value and will impress any hiring manager.

Poor summary statement:  Dedicated applicant with experience in sales and marketing looking for a sales associate role to improve customer service skills. 

• This statement is anything but specific, and it could be on any number of sales resumes. More than just that, it doesn’t highlight any skills or qualifications beyond dedication. Major yikes.

Customized summary statement:  Results-driven sales associate with 13+ years of experience developing rapport and good customer relations. Leveraged top marketing strategies to yield results, performing in the top 5% of sales associates at all workplaces for over a decade. From informing customers about purchases to designing trending storefront decor, I am confident that my proven excellence in results-driven sales strategies would positively impact the movement of products at Decor 101. 

• This summary statement is customized and unique, including specific skills and quantifiable metrics to support their claims; this candidate is a top choice for an interview.

Know what to include in your job experience section

When writing your sales resume, you may be tempted to include every job you’ve had since you were 16. Though this may be an appropriate choice if you have limited job experience, we recommend including two to four highly relevant jobs on your sales resume if you have more experience. 

Write your work experience bullet points purposefully

When you write your work experience section, remember that space is crucial. To take up less room, use bullet points to break up chunks of text. Start each bullet point with an action verb, such as “oversaw” or “championed,” to drive your value (and cut filler).

Using action verbs will also lay the foundation for using active (rather than passive) voice. For example, a passive sentence like “The store was closed by the sales team” sounds weak and boring. Active voice gives agency to the subject and shortens the statement: “The sales team closed the store.” 

Avoid personal pronouns when writing about your experience, such as “I” or “we.” Ending punctuation is up to you—just be consistent. (Avoid having periods at the end of all your bullet points except for one, for example).

Finally, keep your verb tense in the past, and make sure it’s consistent.

Good bullet points can look like any of these examples:

• Executed an outbound calling strategy to warm leads, leading to a close rate of 16%, which exceeded targets by 50%
• Implemented and expanded the use of Salesforce, saving over 18 hours of weekly manual reporting time by sales staff
• Led initiatives for prospective home buyers to improve brand awareness and increase inbound customer interest, resulting in a $275,000+ increase in incremental revenue

These bullet points are successful because they start with action words, maintain an active voice, avoid personal pronouns, and are consistent with punctuation and tenses. 

Getting these things correct is tricky, but you can return to this guide anytime to review these tips!

Use numbers to your advantage

You may have noticed that all the bullet point examples we included contain numbers. Metrics are essential for any resume, but especially your sales resume. Words tell hiring managers you’re good at your job, but numbers show undeniable value. Include quantified metrics within at least 50 percent of your bullet points. 

Here’s how:

• Performance relative to targets:  Have you ever or do you consistently outperform sales targets? By what percentage do you exceed targets on average? 
• Improvements per customer:  Do your customers have higher purchase totals than others? Are they making more repeat purchases than customers helped by other sales associates? What’s your close rate? 
• Efficiency standards:  How many customers do you help on average, per hour, day, or week? How long does it typically take you to make a sale? How many seconds does it take you to greet customers? 
• Customer relations:  How many customers have reviewed you positively on customer surveys? Have any customers mentioned you by name in positive reviews?

It helps to see these tips in practice, so here are some examples: 

• Improved the shopper-to-customer conversion rate of the store by 6% by prioritizing immediate customer service of inbound customers
• Responded to customer questions with a detailed understanding of products, resulting in a customer satisfaction rating of 96%
• Recognized as a Top 5% Salesperson in the most heavily trafficked Kay’s store in Maine 
• Exceeded annual membership targets by 23% by encouraging a compassionate, customer-centered approach

Select appropriate sales skills for your resume

The skills section is one of the shortest sections on your resume and one of the most mysterious. Unfortunately, the ATS plays a big part in this section since it scans your resume for pre-selected keywords.

Not enough keywords? Not the right keywords? ATS wins, 1 to 0. 

We’re here to shed light on this mystery using a simple trick. When writing your skills, choose those mentioned in the  sales job description . Of course, don’t include every skill they list, but use the job description to guide your strengths.

Ideally, include a mix of both hard and soft skills for a total of six to 10 skills. Hard skills are easier to measure, so we recommend listing mostly hard skills. However, soft skills, such as “organization” and “customer service,” are critical in a sales role, so include a few that match your abilities. 

Let’s put this trick into practice! Here’s an excerpt from a sales job description: 

Seeking qualified sales associates! Our ideal candidate thrives in a fast-paced work environment and can maintain a positive, upbeat attitude with co-workers and customers under stressful situations. Must utilize standard software to track and follow up with leads. Should be charismatic, comfortable with public speaking, and have a solid ability to memorize merchandise details and answer complex customer questions. We serve a predominantly Hispanic population, so Spanish speakers, please apply! 

From this job description, we can create a list of skills that would be particularly appropriate for this job position: 

• Salesforce and HubSpot CRM
• Bilingual (Native English, Fluent Spanish) 
• Customer relations
• Interpersonal communication
• Product knowledge 
• Sales demos and pitches
• Time management 

 No matter the job you’re applying for, you’re likely to see some of these skills: 

• Cold-prospecting 
• Negotiation
• Work stream management
• Trend forecasting
• Traditional lead-generation
• Presentations 

Education, certs, interests, and hobbies

In sales, employers typically only require a high school diploma or equivalent. However, specific educational requirements will vary widely in such a large field. Some employers will seek applicants with a bachelor’s degree in business or even an MBA. 

So in your sales resume, list your highest level of education. If you have a graduate degree, you can include both it and your undergrad degree.

If you have any certifications or additional training, such as software certification for a particular type of CRM, you can include that, too, although it isn’t required.

Typically, sales professionals don’t include an optional  interests and hobbies section on their resumes , but there are a few circumstances where it may be appropriate: 

• Hobbies can demonstrate that you’re the type of person a potential customer might enjoy chatting with, which is a bonus for employers.
• Use projects, like volunteering or academic extracurriculars, in place of work experience if you’re light on jobs. 

Here’s an example of what projects could look like on your sales resume:

Tailor your sales resume to the job description

Remember to customize your resume  every time  you apply for a job. Tailoring your resume to the job description is the best way to land an interview quickly.

Start by reworking your resume objective or summary statement (if you have one). Then adjust your skills section to include skills relevant to the role. Finally, adjust your job description bullet points to include relevant qualifications. 

For instance, if a job description mentions they’re looking for a sales representative who can begin giving presentations on day one, emphasize your comfort in public speaking roles. Highlight your previous presentation experience, and perhaps de-emphasize the data analysis skillset that is less relevant to this job. 

Pro tip:  You can keep a master list of bullet points for each job title in a separate document . Write down as many skills and responsibilities as you can for every job title, and organize them based on their emphasis (time management, customer relations, data analysis, etc.). Then you can pull from this document to create fully-customized resumes quickly. 

Edit and polish your sales resume

When finished  writing your resume , it’s tempting to submit it immediately, but it’s best to take a step away first. Give your eyes and mind a rest for a day, and send your resume to trusted family and friends for review. Then you can adjust your content and  check your resume  for errors before you submit; that way, you don’t miss the little details you may have inadvertently overlooked!

Ready for the Next Step?

The first step to having an interview-ready, professional sales resume is to take the time to research and prepare. Congratulations on helping out your future self by using our guide! 

Our easy-to-use  resume builder  will allow you to build your resume from the ground up with perfect formatting, so you can save serious time and focus on your next sales job. If you’re ready to find out how your resume stacks up, use our  resume checker  to give you AI-powered suggestions to polish your resume to perfection. 

We know that wherever you get hired, you’ll be helping customers and growing revenue in no time!

Land your next job with our AI-powered, user-friendly tool.

Gut the guesswork in your job hunt. Upload your existing resume to check your score and make improvements. Build a resume with one of our eye-catching, recruiter-friendly templates.

• Work in real-time with immediate feedback and tips from our AI-powered experience. • Leverage thousands of pre-written, job-specific bullet points. • Edit your resume in-line like a Google Doc or let us walk you through each section at a time. • Enjoy peace of mind with our money-back guarantee and 5-star customer support.

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How to Write a Cover Letter That Will Get You a Job

I ’ve read thousands, maybe tens of thousands, of cover letters in my career. If you’re thinking that sounds like really boring reading, you’re right. What I can tell you from enduring that experience is that most cover letters are terrible — and not only that, but squandered opportunities. When a cover letter is done well, it can significantly increase your chances of getting an interview, but the vast majority fail that test.

So let’s talk about how to do cover letters right.

First, understand the point of a cover letter.

The whole idea of a cover letter is that it can help the employer see you as more than just your résumé. Managers generally aren’t hiring based solely on your work history; your experience is crucial, yes, but they’re also looking for someone who will be easy to work with, shows good judgment, communicates well, possesses strong critical thinking skills and a drive to get things done, complements their current team, and all the other things you yourself probably want from your co-workers. It’s tough to learn much about those things from job history alone, and that’s where your cover letter comes in.

Because of that …

Whatever you do, don’t just summarize your résumé.

The No. 1 mistake people make with cover letters is that they simply use them to summarize their résumé. This makes no sense — hiring managers don’t need a summary of your résumé! It’s on the very next page! They’re about to see it as soon as they scroll down. And if you think about it, your entire application is only a few pages (in most cases, a one- or two-page résumé and a one-page cover letter) — why would you squander one of those pages by repeating the content of the others? And yet, probably 95 percent of the cover letters I see don’t add anything new beyond the résumé itself (and that’s a conservative estimate).

Instead, your cover letter should go beyond your work history to talk about things that make you especially well-suited for the job. For example, if you’re applying for an assistant job that requires being highly organized and you neurotically track your household finances in a detailed, color-coded spreadsheet, most hiring managers would love to know that because it says something about the kind of attention to detail you’d bring to the job. That’s not something you could put on your résumé, but it can go in your cover letter.

Or maybe your last boss told you that you were the most accurate data processor she’d ever seen, or came to rely on you as her go-to person whenever a lightning-fast rewrite was needed. Maybe your co-workers called you “the client whisperer” because of your skill in calming upset clients. Maybe you’re regularly sought out by more senior staff to help problem-solve, or you find immense satisfaction in bringing order to chaos. Those sorts of details illustrate what you bring to the job in a different way than your résumé does, and they belong in your cover letter.

If you’re still stumped, pretend you’re writing an email to a friend about why you’d be great at the job. You probably wouldn’t do that by stiffly reciting your work history, right? You’d talk about what you’re good at and how you’d approach the work. That’s what you want here.

You don’t need a creative opening line.

If you think you need to open the letter with something creative or catchy, I am here to tell you that you don’t. Just be simple and straightforward:

• “I’m writing to apply for your X position.”

• “I’d love to be considered for your X position.”

• “I’m interested in your X position because …”

• “I’m excited to apply for your X position.”

That’s it! Straightforward is fine — better, even, if the alternative is sounding like an aggressive salesperson.

Show, don’t tell.

A lot of cover letters assert that the person who wrote it would excel at the job or announce that the applicant is a skillful engineer or a great communicator or all sorts of other subjective superlatives. That’s wasted space — the hiring manager has no reason to believe it, and so many candidates claim those things about themselves that most managers ignore that sort of self-assessment entirely. So instead of simply declaring that you’re great at X (whatever X is), your letter should demonstrate that. And the way you do that is by describing accomplishments and experiences that illustrate it.

Here’s a concrete example taken from one extraordinarily effective cover-letter makeover that I saw. The candidate had originally written, “I offer exceptional attention to detail, highly developed communication skills, and a talent for managing complex projects with a demonstrated ability to prioritize and multitask.” That’s pretty boring and not especially convincing, right? (This is also exactly how most people’s cover letters read.)

In her revised version, she wrote this instead:

“In addition to being flexible and responsive, I’m also a fanatic for details — particularly when it comes to presentation. One of my recent projects involved coordinating a 200-page grant proposal: I proofed and edited the narratives provided by the division head, formatted spreadsheets, and generally made sure that every line was letter-perfect and that the entire finished product conformed to the specific guidelines of the RFP. (The result? A five-year, $1.5 million grant award.) I believe in applying this same level of attention to detail to tasks as visible as prepping the materials for a top-level meeting and as mundane as making sure the copier never runs out of paper.”

That second version is so much more compelling and interesting — and makes me believe that she really is great with details.

If there’s anything unusual or confusing about your candidacy, address it in the letter.

Your cover letter is your chance to provide context for things that otherwise might seem confusing or less than ideal to a hiring manager. For example, if you’re overqualified for the position but are excited about it anyway, or if you’re a bit underqualified but have reason to think you could excel at the job, address that up front. Or if your background is in a different field but you’re actively working to move into this one, say so, talk about why, and explain how your experience will translate. Or if you’re applying for a job across the country from where you live because you’re hoping to relocate to be closer to your family, let them know that.

If you don’t provide that kind of context, it’s too easy for a hiring manager to decide you’re the wrong fit or applying to everything you see or don’t understand the job description and put you in the “no” pile. A cover letter gives you a chance to say, “No, wait — here’s why this could be a good match.”

Keep the tone warm and conversational.

While there are some industries that prize formal-sounding cover letters — like law — in most fields, yours will stand out if it’s warm and conversational. Aim for the tone you’d use if you were writing to a co-worker whom you liked a lot but didn’t know especially well. It’s okay to show some personality or even use humor; as long as you don’t go overboard, your letter will be stronger for it.

Don’t use a form letter.

You don’t need to write every cover letter completely from scratch, but if you’re not customizing it to each job, you’re doing it wrong. Form letters tend to read like form letters, and they waste the chance to speak to the specifics of what this employer is looking for and what it will take to thrive in this particular job.

If you’re applying for a lot of similar jobs, of course you’ll end up reusing language from one letter to the next. But you shouldn’t have a single cover letter that you wrote once and then use every time you apply; whatever you send should sound like you wrote it with the nuances of this one job in mind.

A good litmus test is this: Could you imagine other applicants for this job sending in the same letter? If so, that’s a sign that you haven’t made it individualized enough to you and are probably leaning too heavily on reciting your work history.

No, you don’t need to hunt down the hiring manager’s name.

If you read much job-search advice, at some point you’ll come across the idea that you need to do Woodward and Bernstein–level research to hunt down the hiring manager’s name in order to open your letter with “Dear Matilda Jones.” You don’t need to do this; no reasonable hiring manager will care. If the name is easily available, by all means, feel free to use it, but otherwise “Dear Hiring Manager” is absolutely fine. Take the hour you just freed up and do something more enjoyable with it.

Keep it under one page.

If your cover letters are longer than a page, you’re writing too much, and you risk annoying hiring managers who are likely sifting through hundreds of applications and don’t have time to read lengthy tomes. On the other hand, if you only write one paragraph, it’s unlikely that you’re making a compelling case for yourself as a candidate — not impossible, but unlikely. For most people, something close to a page is about right.

Don’t agonize over the small details.

What matters most about your cover letter is its content. You should of course ensure that it’s well-written and thoroughly proofread, but many job seekers agonize over elements of the letter that really don’t matter. I get tons of  questions from job seekers  about whether they should attach their cover letter or put it in the body of the email (answer: No one cares, but attaching it makes it easier to share and will preserve your formatting), or what to name the file (again, no one really cares as long as it’s reasonably professional, but when people are dealing with hundreds of files named “resume,” it’s courteous to name it with your full name).

Approaching your cover letter like this can make a huge difference in your job search. It can be the thing that moves your application from the “maybe” pile (or even the “no” pile) to the “yes” pile. Of course, writing cover letters like this will take more time than sending out the same templated letter summarizing your résumé — but 10 personalized, compelling cover letters are likely to get you more  interview invitations  than 50 generic ones will.

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How To Write a Cover Letter With Examples

Cover letters can help differentiate you from other job applicants and be the determining factor of landing your dream job. By taking the time to craft a custom cover letter, a single sheet of paper can help communicate all the human elements that a resume may fall short of capturing about yourself. 

But what do employers and recruiters have to say about how to write a cover letter? What are the best tips they have to offer for graduate students who are writing a cover letter?

We asked 11 employers for their best cover letter tips. Here is what they had to share.

Let it Set the Stage

In many ways, cover letters should provide background information and context to your resume, while simultaneously addressing how that resume addresses the specific requirements of the job opportunity. The cover letter is your opportunity to "set the stage" and to convince the hiring manager why your specific set of skills, experiences and interests will provide value to their team and its objectives.

Andrew Horrigan '11 BSBA (Management Information Systems), Product Manager at Cisco

Research the Hiring Manager

If possible, find out who the hiring manager is and look them up on LinkedIn. Do your research on the company you're applying for. What's their mission statement and how do they portray their company culture? Hopefully what you're looking for in a job is reflected by those things. Make sure the hiring manager knows that and understands who you are and what drives you. A resume is often about as robotic as things can be. Make sure your cover letter is the opposite—personalize it and let yourself shine through.

Joshua Schlag ’05 BS (Computer Science) ’11 MBA, Digital Marketing Manager at Pyramid Analytics

Utilize Career Development Resources

The University of Arizona and Eller College of Management go to great lengths to make sure students are prepared for their impending career journey. Because cover letters are so important to getting your foot in the door, there are several career development resources online and on campus to take advantage of. The university’s cover letter builder serves as a nice template to get started. And of course, it never hurts to make an appointment with an Eller Career Coach through eSMS to have a professional review your letter before submission. 

Brett Farmiloe, ’06 BSBA (Accounting), Founder, Featured

Discover Past Samples of the Position

Do your research on the company and personalize your cover letter to the role for which you are applying. Don't be afraid to Google, "How to write a good cover letter for X position." Seriously, it helps! There is so much information out there from various perspectives—applicants, hiring managers, etc. Most importantly be yourself and let your personality come through. And don't forget to spell check!

Mariam Nikola '17 MS MIS, Consultant at Point B

Highlight Your Soft Skills

When writing a professional cover letter, there are a couple things you can do to set yourself apart from the pack. First, make sure you tailor your letter to the specific position you are applying for. This should not be a general, "one size fits all" letter—be sure to discuss specific details surrounding the role or the company itself. Secondly, this is an opportunity for you to show a little bit of your personality. Obviously, you want to remain professional, but this is a great time to highlight some of your soft skills that might not be fully conveyed through your resume.  

Brian Ellis ’17 BSBA (Management), Staffing Manager at Randstad Office and Administrative Professionals

Fill in the “Why” Gaps

As a talent advisor, I review a lot of applicants and agree that a cover letter can be a great way to stand apart, if it is done correctly. A great cover letter for me covers the ‘why’ that I cannot understand from just a resume alone. It should clearly state why you are interested in the role, what your goals are for utilizing your graduate degree (if recently graduated) and explain any career pivots reflected on your resume. If you answer those questions in a direct, concise manner it will add value to your application.

Monica Larson , ’11 BSBA (Marketing) ‘20 MBA, Talent Advisor

Tell Your Story

A cover letter is your opportunity to tell your story—tying your experience and personal interests into why you want a position and why you are the best candidate for it. Paint the picture of your journey and what about the position excites you personally and professionally. Similar to your resume, keep it short and sweet. No need to repeat what’s already on your resume. Recruiters and hiring managers don’t have time to comb through a novel, so you need to engage them with as few words as possible while also grabbing their attention.

Kelly Castoro, ’06 BA (Spanish, Portuguese), Project Manager at Squarespace

Tailor Each Cover Letter to the Position You Are Applying

Be sure to research the role and customize your cover letter for each position, relating your experience to the particular role you are applying for. Personalization is key—research who you are sending the cover letter to and address the letter to them directly. End your letter with a call to action, stating you will follow up by phone or email if you haven’t heard from anyone. Follow ups are very important! 

Jessica Rosenzweig, ’15 BSBA (Business Management), Account Manager at PeopleWare Staffing

Communicate Bankability and Personality 

Your cover letter answers two crucial questions; are you bankable and are you someone the company will enjoy working with? Communicate bankability with your knowledge of the company, industry and why your skills, capabilities and interests are a great fit. Share your passion for their mission, culture, brand—whatever excites you about becoming a member of their team.  

When conveyed through a concise, well-formulated, well-worded cover letter, you demonstrate the ability to write an effective business case—communicating that you are a ready professional and worthy teammate who will hit the ground running.

Theresa L Garcia, ’83 BSBA (Human Resources), Senior Change Management and Organization Capability Consultant at Boeing

Keep it Concise but Compelling

A cover letter is your chance to speak directly to the hiring team and tell them why you are not only the best match for the position for which you are applying but also give them additional insight into yourself as an individual that is less visible from your experience.

A great cover letter should be attention grabbing and touch upon the qualities that make you stand out from others in the applicant pool, highlight both your recent and most distinguished accomplishments and drive home why you are the right person for the job. Professionalism is always important, but don’t be hesitant to put your voice into the letter to let your personality shine through. Research the company, understand where they currently are, where they are going and show why you are the right person to get them from point A to point B. Recruiters spend a lot of time reviewing applicants and making yourself stand apart from the crowd is key. Keep it concise but compelling!

Matt Reineberg, ’14 BSBA (Marketing), Senior Talent Acquisition Sourcer at Cox Enterprises

Highlight the “Why”

Why are you applying to this company? Why do you want this position? Your cover letter should aim to answer the why behind applying for the job. Conveying an interest and excitement for working specifically for this job at this company, rather than a desire to get any job anywhere that will give you money, can go a long way. Show the company that they should hire you and your passion over someone that might have the skills needed for the job, but doesn’t care about the work as much as you do. 

Ryan Nouis, Trupath 

Ready to Learn More?

Using numerical data in your cover letter can show a hiring manager evidence of your skills. When you describe your previous sales experience, include data that shows your success in the role. This data can emphasize the value you might bring to the organization. 2. Relate your skills to the position and company values.

4. Sales cover letter template. Finally, here's a sales cover letter template that you can easily copy and paste into Microsoft Word or Google Docs: Today's Date. Hiring Manager's Name. 123 Company Address. Company's City, State, Zip Code. (xxx) xxx-xxxx. [email protected] .

Let's check out two salesperson cover letter examples to start things off: 1. Sales Cover Letter Examples. Let's have a look at Melvin. Melvin's the oldest of the Rios siblings, 5-foot-9, and an expectant father. But—the lead-in to capture the director of sales' attention needs more.

Use this Sales cover letter example to finish your application and get hired fast - no frustration, no guesswork. This cover letter example is specifically designed for Sales positions in 2024. Take advantage of our sample sentences + expert guides to download the perfect cover letter in just minutes. 4.2.

Top ↑ Sales Cover Letter Example 5 Steps for the Perfect Sales Cover Letter #1. Put Contact Information in the Header #2. Address the Hiring Manager #3. Write an Eye-Catching Opening Statement #4. Use the Cover Letter Body for the Details #5. Wrap It Up and Sign It 3 Essential Business Cover Letter Tips #1.

7 Sales Cover Letter. Examples & Writing Guide for 2024. Stephen Greet February 23, 2024. Sales are the lifeblood of business. Whether selling products or services, you take care of customers as they invest in your company. Sales mean selling well, and that makes all the difference in keeping clients happy and hungry for what you've got.

Use this Sales Representative cover letter example to finish your application and get hired fast - no frustration, no guesswork. This cover letter example is specifically designed for Sales Representative positions in 2024. Take advantage of our sample sentences + expert guides to download the perfect cover letter in just minutes.

A good sales representative cover letter should make your readers curious enough to learn more about you as a sales professional that they will want to ask you about yourself in person. Let's take a look at how to make them do just that, in five easy steps. 1. The Header. Think of yourself as a sales hiring manager.

Here's a sales cover letter example from an account executive applicant: Awarded Top Sales Consultant in the territory for two straight quarters and numerous other recognition for helping drive the business, with over $70,000 worth of merchandise sold in the top-performing quarter at Best Buy.

To write an effective cover letter for a sales job, start by addressing the hiring manager by name if possible. Introduce yourself and express your interest in the position. Highlight your relevant skills and experiences, emphasizing how they align with the requirements of the job.

a closing paragraph, sign-off statement and your name, a postscript (P.S.). That's our recommendation on what to put in the perfect sales cover letter. It's kind of like the BANT framework, but to get the sales job. Make sure the related resume for sales positions is in tip-top shape, as well: Sales Associate Resume.

Place your contact details at the top, adhering to the standard business letter format. Aim for a length of 3-5 paragraphs totaling, at the most, 400 words. Choose a professional, easy-to-read font such as Arial or Calibri. Stick to a font size between 10 and 12 for maximum readability.

A good cover letter for a sales position can land you an interview opportunity. Countless people graduate from business school and are competing on the same racing road, let's shine yourself with a powerful sales cover letter. ... Thank you for your time reviewing my cover letter and resume. I genuinely believe that my experience would make ...

6. The unique cover letter. This sales cover letter is one of the best examples we've seen of how to mix creativity with professionalism: Just like this cover letter, sales is one part skill and two parts confidence. Why this is a good cover letter example. In an industry as competitive as sales, you need your application to be convincing and ...

Sales management skills. It is good to provide evidence of your sales manager skills when writing your cover letter, as companies closely evaluate these skills when considering a candidate. ... A compelling cover letter and a sleek resume are a sales manager's way of communicating their sales experience to employers. You must have these ...

A professional sales associate cover letter should include information that highlights the applicant's relevant skills and experience to the position. It should also demonstrate the applicant's enthusiasm for the role and express their interest in the company. The cover letter should start with a brief introduction and provide a brief ...

Consultant Cover Letter Example #10. Digital Marketing Cover Letter Example #11. Graphic Designer Cover Letter Example #12. Administrative Assistant Cover Letter Example #13. Front Desk Cover Letter Example #14. Human Resources Cover Letter Example #15. Sales Agent Cover Letter Example #16.

Employer name. Company Name. Street address. City, State. Salutation. Dear [Hiring Manager's Name], Opening Paragraph (Introduction) Your cover letter opening should contain a self-introduction. Write about who you are, where your expertise lies, where you found the job posting, and why you want to apply for the job.

This sales manager cover letter has set a good pace for you by expertly combining tools, competencies, and quantifiable achievements to make a strong case. Notice how Zoho Analytics and Hive have been leveraged to highlight the candidate's past achievements. ... Unlike your resume, your sales management cover letter shouldn't use bullet ...

That Landed Jobs in 2024. Stephen Greet January 22, 2024. Sales are the lifeblood of any growing company. Without sales, companies grow stagnant—or worse, fail. But with a good sales department, a company can truly thrive. You know how to care for customers, present solutions to problems, and adapt to any situation.

If you think you need to open the letter with something creative or catchy, I am here to tell you that you don't. Just be simple and straightforward: • "I'm writing to apply for your X ...

Tell Your Story. A cover letter is your opportunity to tell your story—tying your experience and personal interests into why you want a position and why you are the best candidate for it. Paint the picture of your journey and what about the position excites you personally and professionally. Similar to your resume, keep it short and sweet.

Many job seekers think a good resume and cover letter are enough to land interviews and stand out. In today's competitive market, you need a lot more than…

27 adjectives to describe your conscientiousness. Highlighting your work ethic, organizational skills, and problem solving abilities is a great way to show hiring managers that you'd be a dedicated employee: Diligent. Attentive. Responsible. Enthusiastic. Industrious. Keen. Observant.

Write your contact information. The first step is to put your contact details at the top of the resume. Include your full name in bold text on the first line. Write your phone number, email address, city and state or union territory below it in standard text. Place this information in the top left corner of the document.

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How to Solve Integers and Their Properties

Last Updated: June 30, 2018

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An integer is a set of natural numbers, their negatives, and zero. However, some integers are natural numbers, including 1, 2, 3, and so on. Their negative values are, -1, -2, -3, and so on. So integers are the set of numbers including (…-3, -2, -1, 0, 1, 2, 3,…). An integer is never a fraction, decimal, or percentage, it can only be a whole number. To solve integers and use their properties, learn to use addition and subtraction properties and use multiplication properties.

Using Addition and Subtraction Properties

• a + b = c (where both a and b are positive numbers the sum c is also positive)
• For example: 2 + 2 = 4

• -a + -b = -c (where both a and b are negative, you get the absolute value of the numbers then you proceed to add, and use the negative sign for the sum)
• For example: -2+ (-2)=-4

• a + (-b) = c (when your terms are of different signs, determine the larger number's value, then get the absolute value of both terms and subtract the lesser value from the larger value. Use the sign of the larger number for the answer.)
• For example: 5 + (-1) = 4

• -a +b = c (get the absolute value of the numbers and again, proceed to subtract the lesser value from the larger value and assume the sign of the larger value)
• For example: -5 + 2 = -3

• An example of the additive identity is: a + 0 = a
• Mathematically, the additive identity looks like: 2 + 0 = 2 or 6 + 0 = 6

• The additive inverse is when a number is added to the negative equivalent of itself.
• For example: a + (-b) = 0, where b is equal to a
• Mathematically, the additive inverse looks like: 5 + -5 = 0

• For example: (5+3) +1 = 9 has the same sum as 5+ (3+1) = 9

Using Multiplication Properties

• When a and b are positive numbers and not equal to zero: +a * + b = +c
• When a and b are both negative numbers and not equal to zero: -a*-b = +c

• However, understand that any number multiplied by zero, equals zero.

• For example: a(b+c) = ab + ac
• Mathematically, this looks like: 5(2+3) = 5(2) + 5(3)
• Note that there is no inverse property for multiplication because the inverse of a whole number is a fraction, and fractions are not an element of integer.

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Integers Worksheets

Welcome to the integers worksheets page at Math-Drills.com where you may have a negative experience, but in the world of integers, that's a good thing! This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers.

If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand. Banks like you to keep negative balances in your accounts, so they can charge you loads of interest. Deep sea divers spend all sorts of time in negative integer territory. There are many reasons why a knowledge of integers is helpful even if you are not going to pursue an accounting or deep sea diving career. One hugely important reason is that there are many high school mathematics topics that will rely on a strong knowledge of integers and the rules associated with them.

We've included a few hundred integers worksheets on this page to help support your students in their pursuit of knowledge. You may also want to get one of those giant integer number lines to post if you are a teacher, or print off a few of our integer number lines. You can also project them on your whiteboard or make an overhead transparency. For homeschoolers or those with only one or a few students, the paper versions should do. The other thing that we highly recommend are integer chips a.k.a. two-color counters. Read more about them below.

Most Popular Integers Worksheets this Week

Integer Resources

Coordinate graph paper can be very useful when studying integers. Coordinate geometry is a practical application of integers and can give students practice with using integers while learning another related skill. Coordinate graph paper can be found on the Graph Paper page:

Coordinate Graph Paper

Integer number lines can be used for various math activities including operations with integers, counting, comparing, ordering, etc.

• Integer Number Lines Integers Number Lines from -10 to 10 Integers Number Lines from -15 to 15 Integers Number Lines from -20 to 20 Integers Number Lines from -25 to 25 OLD Integer Number Lines

Comparing and Ordering Integers

For students who are just starting with integers, it is very helpful if they can use an integer number line to compare integers and to see how the placement of integers works. They should quickly realize that negative numbers are counter-intuitive because they are probably quite used to larger absolute values meaning larger numbers. The reverse is the case, of course, with negative numbers. Students should be able to recognize easily that a positive number is always greater than a negative number and that between two negative integers, the one with the lesser absolute value is actually the greater number. Have students practice with these integers worksheets and follow up with the close proximity comparing integers worksheets.

• Comparing Integers Worksheets Comparing Positive and Negative Integers (-9 to +9) Comparing Positive and Negative Integers (-15 to +15) Comparing Positive and Negative Integers (-25 to +25) Comparing Positive and Negative Integers (-50 to +50) Comparing Positive and Negative Integers (-99 to +99) Comparing Negative Integers (-15 to -1)

By close proximity, we mean that the integers being compared differ very little in value. Depending on the range, we have allowed various differences between the two integers being compared. In the first set where the range is -9 to 9, the difference between the two numbers is always 1. With the largest range, a difference of up to 5 is allowed. These worksheets will help students further hone their ability to visualize and conceptualize the idea of negative numbers and will serve as a foundation for all the other worksheets on this page.

• Comparing Integers in Close Proximity Comparing Positive and Negative Integers (-9 to +9) in Close Proximity Comparing Positive and Negative Integers (-15 to +15) in Close Proximity Comparing Positive and Negative Integers (-25 to +25) in Close Proximity Comparing Positive and Negative Integers (-50 to +50) in Close Proximity Comparing Positive and Negative Integers (-99 to +99) in Close Proximity
• Ordering Integers Worksheets Ordering Integers on a Number Line Ordering Integers (range -9 to 9) Ordering Integers (range -20 to 20) Ordering Integers (range -50 to 50) Ordering Integers (range -99 to 99) Ordering Integers (range -999 to 999) Ordering Negative Integers (range -9 to -1) Ordering Negative Integers (range -99 to -10) Ordering Negative Integers (range -999 to -100)

Adding and Subtracting Integers

Two-color counters are fantastic manipulatives for teaching and learning about integer addition. Two-color counters are usually plastic chips that come with yellow on one side and red on the other side. They might be available in other colors, so you'll have to substitute your own colors in the following description.

Adding with two-color counters is actually quite easy. You model the first number with a pile of chips flipped to the correct side and you also model the second number with a pile of chips flipped to the correct side; then you mash them all together, take out the zeros (if any) and behold, you have your answer! Need further elaboration? Read on!

The correct side means using red to model negative numbers and yellow to model positive numbers. You would model —5 with five red chips and 7 with seven yellow chips. Mashing them together should be straight forward although, you'll want to caution your students to be less exuberant than usual, so none of the chips get flipped. Taking out the zeros means removing as many pairs of yellow and red chips as you can. You can do this because —1 and 1 when added together equals zero (this is called the zero principle). If you remove the zeros, you don't affect the answer. The benefit of removing the zeros, however, is that you always end up with only one color and as a consequence, the answer to the integer question. If you have no chips left at the end, the answer is zero!

• Adding Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (75 Questions) ✎ Adding Integers from -12 to 12 (75 Questions) ✎ Adding Integers from -15 to 15 (75 Questions) ✎ Adding Integers from -20 to 20 (75 Questions) ✎ Adding Integers from -25 to 25 (75 Questions) ✎ Adding Integers from -50 to 50 (75 Questions) ✎ Adding Integers from -99 to 99 (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (50 Questions) ✎ Adding Integers from -12 to 12 (50 Questions) ✎ Adding Integers from -15 to 15 (50 Questions) ✎ Adding Integers from -20 to 20 (50 Questions) ✎ Adding Integers from -25 to 25 (50 Questions) ✎ Adding Integers from -50 to 50 (50 Questions) ✎ Adding Integers from -99 to 99 (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Addition Worksheets 3-Digit Integer Addition (Vertically Arranged) 3-Digit Positive Plus a Negative Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Positive Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Negative Integer Addition (Vertically Arranged)

Subtracting with integer chips is a little different. Integer subtraction can be thought of as removing. To subtract with integer chips, begin by modeling the first number (the minuend) with integer chips. Next, remove the chips that would represent the second number from your pile and you will have your answer. Unfortunately, that isn't all there is to it. This works beautifully if you have enough of the right color chip to remove, but often times you don't. For example, 5 - (-5), would require five yellow chips to start and would also require the removal of five red chips, but there aren't any red chips! Thank goodness, we have the zero principle. Adding or subtracting zero (a red chip and a yellow chip) has no effect on the original number, so we could add as many zeros as we wanted to the pile, and the number would still be the same. All that is needed then is to add as many zeros (pairs of red and yellow chips) as needed until there are enough of the correct color chip to remove. In our example 5 - (-5), you would add 5 zeros, so that you could remove five red chips. You would then be left with 10 yellow chips (or +10) which is the answer to the question.

• Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (75 Questions) ✎ Subtracting Integers from -12 to 12 (75 Questions) ✎ Subtracting Integers from -15 to 15 (75 Questions) ✎ Subtracting Integers from -20 to 20 (75 Questions) ✎ Subtracting Integers from -25 to 25 (75 Questions) ✎ Subtracting Integers from -50 to 50 (75 Questions) ✎ Subtracting Integers from -99 to 99 (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (50 Questions) ✎ Subtracting Integers from -12 to 12 (50 Questions) ✎ Subtracting Integers from -15 to 15 (50 Questions) ✎ Subtracting Integers from -20 to 20 (50 Questions) ✎ Subtracting Integers from -25 to 25 (50 Questions) ✎ Subtracting Integers from -50 to 50 (50 Questions) ✎ Subtracting Integers from -99 to 99 (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Subtraction Worksheets 3-Digit Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Negative Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Negative Integer Subtraction (Vertically Arranged)

The worksheets in this section include addition and subtraction on the same page. Students will have to pay close attention to the signs and apply their knowledge of integer addition and subtraction to each question. The use of counters or number lines could be helpful to some students.

• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (75 Questions) ✎ Adding & Subtracting Integers from -10 to 10 (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-5) to (+5) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding & Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎

These worksheets include groups of questions that all result in positive or negative sums or differences. They can be used to help students see more clearly how certain integer questions end up with positive and negative results. In the case of addition of negative and positive integers, some people suggest looking for the "heavier" value to determine whether the sum will be positive of negative. More technically, it would be the integer with the greater absolute value. For example, in the question (−2) + 5, the absolute value of the positive integer is greater, so the sum will be positive.

In subtraction questions, the focus is on the subtrahend (the value being subtracted). In positive minus positive questions, if the subtrahend is greater than the minuend, the answer will be negative. In negative minus negative questions, if the subtrahend has a greater absolute value, the answer will be positive. Vice-versa for both situations. Alternatively, students can always convert subtraction questions to addition questions by changing the signs (e.g. (−5) − (−7) is the same as (−5) + 7; 3 − 5 is the same as 3 + (−5)).

• Scaffolded Integer Addition and Subtraction Positive Plus Negative Integer Addition (Scaffolded) ✎ Negative Plus Positive Integer Addition (Scaffolded) ✎ Mixed Integer Addition (Scaffolded) ✎ Positive Minus Positive Integer Subtraction (Scaffolded) ✎ Negative Minus Negative Integer Subtraction (Scaffolded) ✎

Multiplying and Dividing Integers

Multiplying integers is very similar to multiplication facts except students need to learn the rules for the negative and positive signs. In short, they are:

In words, multiplying two positives or two negatives together results in a positive product, and multiplying a negative and a positive in either order results in a negative product. So, -8 × 8, 8 × (-8), -8 × (-8) and 8 × 8 all result in an absolute value of 64, but in two cases, the answer is positive (64) and in two cases the answer is negative (-64).

Should you wish to develop some "real-world" examples of integer multiplication, it might be a stretch due to the abstract nature of negative numbers. Sure, you could come up with some scenario about owing a debt and removing the debt in previous months, but this may only result in confusion. For now students can learn the rules of multiplying integers and worry about the analogies later!

• Multiplying Integers with 100 Questions Per Page Multiplying Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Mixed Integers from -20 to 20 (100 Questions) ✎ Multiplying Mixed Integers from -50 to 50 (100 Questions) ✎
• Multiplying Integers with 50 Questions Per Page Multiplying Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying Integers with 25 Large Print Questions Per Page Multiplying Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

Luckily (for your students), the rules of dividing integers are the same as the rules for multiplying:

Dividing a positive by a positive integer or a negative by a negative integer will result in a positive integer. Dividing a negative by a positive integer or a positive by a negative integer will result in a negative integer. A good grasp of division facts and a knowledge of the rules for multiplying and dividing integers will go a long way in helping your students master integer division. Use the worksheets in this section to guide students along.

• Dividing Integers with 100 Questions Per Page Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (100 Questions) ✎
• Dividing Integers with 50 Questions Per Page Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Dividing Integers with 25 Large Print Questions Per Page Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

This section includes worksheets with both multiplying and dividing integers on the same page. As long as students know their facts and the integer rules for multiplying and dividing, their sole worry will be to pay attention to the operation signs.

• Multiplying and Dividing Integers with 100 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (100 Questions) ✎
• Multiplying and Dividing Integers with 75 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (75 Questions) ✎
• Multiplying and Dividing Integers with 50 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying and Dividing Integers with 25 Large Print Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

All Operations with Integers

In this section, the integers math worksheets include all of the operations. Students will need to pay attention to the operations and the signs and use mental math or another strategy to arrive at the correct answers. It should go without saying that students need to know their basic addition, subtraction, multiplication and division facts and rules regarding operations with integers before they should complete any of these worksheets independently. Of course, the worksheets can be used as a source of questions for lessons, tests or other learning activities.

• All Operations with Integers with 50 Questions Per Page (Some Parentheses) All operations with integers from -9 to 9 (50 Questions) ✎ All operations with integers from -12 to 12 (50 Questions) ✎ All operations with integers from -15 to 15 (50 Questions) ✎ All operations with integers from -20 to 20 (50 Questions) ✎ All operations with integers from -25 to 25 (50 Questions) ✎ All operations with integers from -50 to 50 (50 Questions) ✎ All operations with integers from -99 to 99 (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (All Parentheses) All operations with integers from (-9) to (+9) All Parentheses (50 Questions) ✎ All operations with integers from (-12) to (+12) All Parentheses (50 Questions) ✎ All operations with integers from (-15) to (+15) All Parentheses (50 Questions) ✎ All operations with integers from (-20) to (+20) All Parentheses (50 Questions) ✎ All operations with integers from (-25) to (+25) All Parentheses (50 Questions) ✎ All operations with integers from (-50) to (+50) All Parentheses (50 Questions) ✎ All operations with integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (No Parentheses) All operations with integers from -9 to 9 No Parentheses (50 Questions) ✎ All operations with integers from -12 to 12 No Parentheses (50 Questions) ✎ All operations with integers from -15 to 15 No Parentheses (50 Questions) ✎ All operations with integers from -20 to 20 No Parentheses (50 Questions) ✎ All operations with integers from -25 to 25 No Parentheses (50 Questions) ✎ All operations with integers from -50 to 50 No Parentheses (50 Questions) ✎ All operations with integers from -99 to 99 No Parentheses (50 Questions) ✎

Order of operations with integers can be found on the Order of Operations page:

Order of Operations with Integers

Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.

Integer Word Problems Worksheets

An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses. Integers are closed under the operations of addition and multiplication . Integer word problems worksheets provide a variety of word problems associated with the use and properties of integers. 

Benefits of Integers Word Problems Worksheets

We use integers in our day-to-day life like measuring temperature, sea level, and speed limit. Translating verbal descriptions into expressions is an essential initial step in solving word problems. Deposits are normally represented by a positive sign and withdrawals are denoted by a negative sign. Negative numbers are used in weather forecasting to show the temperature of a region. Solving these integers word problems will help us relate the concept with practical applications.

Download Integers Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

☛ Check Grade wise Integers Word Problems Worksheets

• 6th Grade Integers Worksheets
• Integers Worksheets for Grade 7
• 8th Grade Integers Worksheets

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1.3: Integers

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By the end of this section, you will be able to:

• Simplify expressions with absolute value
• Add and subtract integers
• Multiply and divide integers
• Simplify expressions with integers
• Evaluate variable expressions with integers
• Translate phrases to expressions with integers
• Use integers in applications

A more thorough introduction to the topics covered in this section can be found in the Elementary Algebra chapter, Foundations.

Simplify Expressions with Absolute Value

A negative number is a number less than 0. The negative numbers are to the left of zero on the number line ( Figure \(\PageIndex{1}\)).

You may have noticed that, on the number line, the negative numbers are a mirror image of the positive numbers, with zero in the middle. Because the numbers \(2\) and \(−2\) are the same distance from zero, each one is called the opposite of the other. The opposite of \(2\) is \(−2\), and the opposite of \(−2\) is \(2\).

The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.

Figure \(\PageIndex{2}\) illustrates the definition.

OPPOSITE NOTATION

\[\begin{align} & -a \text{ means the opposite of the number }a \\ & \text{The notation} -a \text{ is read as “the opposite of }a \text{.”} \end{align} \]

We saw that numbers such as 3 and −3 are opposites because they are the same distance from 0 on the number line. They are both three units from 0. The distance between 0 and any number on the number line is called the absolute value of that number.

Definition: ABSOLUTE VALUE

The absolute value of a number is its distance from 0 on the number line.

The absolute value of a number \(n\) is written as \(|n|\) and \(|n|≥0\) for all numbers.

Absolute values are always greater than or equal to zero.

For example,

\[\begin{align} & -5 \text{ is } 5 \text{ units away from 0, so } |-5|=5. \\ & 5 \text{ is }5\text{ units away from 0, so }|5|=5. \end{align}\]

Figure \(\PageIndex{3}\) illustrates this idea.

The absolute value of a number is never negative because distance cannot be negative. The only number with absolute value equal to zero is the number zero itself because the distance from 0 to 0 on the number line is zero units.

In the next example, we’ll order expressions with absolute values.

EXAMPLE \(\PageIndex{1}\)

Fill in \(<,\,>,\) or \(=\) for each of the following pairs of numbers:

• \(\mathrm{|−5|}\_\_\mathrm{−|−5|}\_\_\mathrm{−|5|}\)
• \(\text{8__−|−8|}\)
• \(\text{−9__−|−9|}\)
• (\text{−(−16)__|−16|}\).

\(\begin{array}{lrcc} { \text{ } \\ \text{Simplify.} \\ \text{Order.} \\ \text{ } } & {|−5| \\ 5 \\ 5 \\ |−5|} & {\_\_ \\ \_\_ \\ > \\ >} & {−|−5| \\ −5 \\ −5 \\ −|−5|} \end{array}\)

\(\begin{array}{llcc} { \text{ } \\ \text{Simplify.} \\ \text{Order.} \\ \text{ } } & {8 \\ 8 \\ 8 \\ 8} & {\_\_ \\ \_\_ \\ > \\ >} & {−|−8| \\ −8 \\ −8 \\ −|−8|} \end{array}\)

\(\begin{array}{lrcc} { \text{ } \\ \text{Simplify.} \\ \text{Order.} \\ \text{ } } & {−9 \\ −9 \\ −9 \\ −9} & {\_\_ \\ \_\_ \\ = \\ =} & {−|−9| \\ −9 \\ −9 \\ −|−9|} \end{array}\)

\(\begin{array}{lrcc} { \text{ } \\ \text{Simplify.} \\ \text{Order.} \\ \text{ } } & {−(−16) \\ 16 \\ 16 \\ −(−16)} & {\_\_ \\ \_\_ \\ = \\ =} & {−|−16| \\ 16 \\ 16 \\ |−16|} \end{array}\)

EXAMPLE \(\PageIndex{2}\)

ⓐ \(−9 \_\_−|−9|\) ⓑ \(2 \_\_−|−2|\) ⓒ \(−8 \_\_|−8|\) ⓓ \(−(−9) \_\_|−9|.\)

ⓐ \(>\) ⓑ \(>\) ⓒ \(<\)

ⓓ \(=\)

EXAMPLE \(\PageIndex{3}\)

Fill in \(<,>,\) or \(=\) for each of the following pairs of numbers:

• \(7 \_\_ −|−7|\)
• \(−(−10) \_ \_|−10|\)
• \(|−4| \_\_ −|−4|\)
• \(−1 \_\_ |−1|.\)

ⓐ \(>\) ⓑ \(=\) ⓒ \(>\)

ⓓ \(<\)

We now add absolute value bars to our list of grouping symbols. When we use the order of operations, first we simplify inside the absolute value bars as much as possible, then we take the absolute value of the resulting number.

GROUPING SYMBOLS

• \[\begin{array}{lclc} \text{Parentheses} & () & \text{Braces} & \{ \} \\ \text{Brackets} & [] & \text{Absolute value} & ||\end{array}\]

In the next example, we simplify the expressions inside absolute value bars first just like we do with parentheses.

EXAMPLE \(\PageIndex{4}\)

Simplify: \(\mathrm{24−|19−3(6−2)|}\).

\(\begin{array}{lc} \text{} & 24−|19−3(6−2)| \\ \text{Work inside parentheses first:} & \text{} \\ \text{subtract 2 from 6.} & 24−|19−3(4)| \\ \text{Multiply 3(4).} & 24−|19−12| \\ \text{Subtract inside the absolute value bars.} & 24−|7| \\ \text{Take the absolute value.} & 24−7 \\ \text{Subtract.} & 17 \end{array}\)

EXAMPLE \(\PageIndex{5}\)

Simplify: \(19−|11−4(3−1)|\).

EXAMPLE \(\PageIndex{6}\)

Simplify: \(9−|8−4(7−5)|\).

Add and Subtract Integers

So far in our examples, we have only used the counting numbers and the whole numbers.

\[\begin{array}{ll} \text{Counting numbers} & 1,2,3… \\ \text{Whole numbers} 0,1,2,3…. \end{array}\]

Our work with opposites gives us a way to define the integers . The whole numbers and their opposites are called the integers. The integers are the numbers \(…−3,−2,−1,0,1,2,3…\)

Definition: INTEGERS

The whole numbers and their opposites are called the integers .

The integers are the numbers

\[…-3,-2,-1,0,1,2,3…,\]

Most students are comfortable with the addition and subtraction facts for positive numbers. But doing addition or subtraction with both positive and negative numbers may be more challenging.

We will use two color counters to model addition and subtraction of negatives so that you can visualize the procedures instead of memorizing the rules.

We let one color (blue) represent positive. The other color (red) will represent the negatives.

If we have one positive counter and one negative counter, the value of the pair is zero. They form a neutral pair. The value of this neutral pair is zero.

We will use the counters to show how to add:

\[5+3 \; \; \; \; \; \; −5+(−3) \; \; \; \; \; \; −5+3 \; \; \; \; \; \; \; 5+(−3)\]

The first example, \(5+3,\) adds 5 positives and 3 positives—both positives.

The second example, \(−5+(−3),\) adds 5 negatives and 3 negatives—both negatives.

When the signs are the same, the counters are all the same color, and so we add them. In each case we get 8—either 8 positives or 8 negatives.

So what happens when the signs are different? Let’s add \(−5+3\) and \(5+(−3)\).

When we use counters to model addition of positive and negative integers, it is easy to see whether there are more positive or more negative counters. So we know whether the sum will be positive or negative.

EXAMPLE \(\PageIndex{7}\)

Add: ⓐ \(−1+(−4)\) ⓑ \(−1+5\) ⓒ \(1+(−5)\).

EXAMPLE \(\PageIndex{8}\)

Add: ⓐ \(−2+(−4)\) ⓑ \(−2+4\) ⓒ \(2+(−4)\).

ⓐ \(−6\) ⓑ \(2\) ⓒ \(−2\)

EXAMPLE \(\PageIndex{9}\)

Add: ⓐ \(−2+(−5)\) ⓑ \(−2+5\) ⓒ \(2+(−5)\).

ⓐ \(−7\) ⓑ \(3\) ⓒ \(−3\)

We will continue to use counters to model the subtraction. Perhaps when you were younger, you read \(“5−3”\) as “5 take away 3.” When you use counters, you can think of subtraction the same way!

We will use the counters to show to subtract:

\[5−3 \; \; \; \; \; \; −5−(−3) \; \; \; \; \; \; −5−3 \; \; \; \; \; \; 5−(−3) \]

The first example, \(5−3\), we subtract 3 positives from 5 positives and end up with 2 positives.

In the second example, \(−5−(−3),\) we subtract 3 negatives from 5 negatives and end up with 2 negatives.

Each example used counters of only one color, and the “take away” model of subtraction was easy to apply.

What happens when we have to subtract one positive and one negative number? We’ll need to use both blue and red counters as well as some neutral pairs. If we don’t have the number of counters needed to take away, we add neutral pairs. Adding a neutral pair does not change the value. It is like changing quarters to nickels—the value is the same, but it looks different.

Let’s look at \(−5−3\) and \(5−(−3)\).

EXAMPLE \(\PageIndex{10}\)

Subtract: ⓐ \(3−1\) ⓑ \(−3−(−1)\) ⓒ \(−3−1\) ⓓ \(3−(−1)\).

EXAMPLE \(\PageIndex{11}\)

Subtract: ⓐ \(6−4\) ⓑ \(−6−(−4)\) ⓒ \(−6−4\) ⓓ \(6−(−4)\).

ⓐ \(2\) ⓑ \(−2\) ⓒ \(−10\) ⓓ \(10\)

EXAMPLE \(\PageIndex{12}\)

Subtract: ⓐ \(7−4\) ⓑ \(−7−(−4)\) ⓒ \(−7−4\) ⓓ \(7−(−4)\).

ⓐ \(3\) ⓑ \(−3\) ⓒ \(−11\) ⓓ \(11\)

Have you noticed that subtraction of signed numbers can be done by adding the opposite ? In the last example, \(−3−1\) is the same as \(−3+(−1)\) and \(3−(−1)\) is the same as \(3+1\). You will often see this idea, the Subtraction Property, written as follows:

Definition: SUBTRACTION PROPERTY

\[a−b=a+(−b)\]

Subtracting a number is the same as adding its opposite.

EXAMPLE \(\PageIndex{13}\)

Simplify: ⓐ \(13−8\) and \(13+(−8)\) ⓑ \(−17−9\) and \(−17+(−9)\) ⓒ \(9−(−15)\) and \(9+15\) ⓓ \(−7−(−4)\) and \(−7+4\).

\(\begin{array}{lccc} \text{} & −17−9 & \text{and} & −17+(−9) \\ \text{Subtract.} & −26 & \text{} & −26 \end{array}\)

\(\begin{array}{lccc} \text{} & 9−(−15) & \text{and} & 9+15 \\ \text{Subtract.} & 24 & \text{} & 24 \end{array}\)

\(\begin{array}{lccc} \text{} & −7−(−4) & \text{and} & −7+4 \\ \text{Subtract.} & −3 & \text{} & −3 \end{array}\)

EXAMPLE \(\PageIndex{14}\)

Simplify: ⓐ \(21−13\) and \(21+(−13)\) ⓑ \(−11−7\) and \(−11+(−7)\) ⓒ \(6−(−13)\) and \(6+13\) ⓓ \(−5−(−1)\) and \(−5+1\).

ⓐ \(8,8\) ⓑ \(−18,−18\)

ⓒ \(19,19\) ⓓ \(−4,−4\)

EXAMPLE \(\PageIndex{15}\)

Simplify: ⓐ \(15−7\) and \(15+(−7)\) ⓑ \(−14−8\) and \(−14+(−8)\) ⓒ \(4−(−19)\) and \(4+19\) ⓓ \(−4−(−7)\) and \(−4+7\).

ⓐ \(8,8\) ⓑ \(−22,−22\)

ⓒ \(23,23\) ⓓ \(3,3\)

What happens when there are more than three integers? We just use the order of operations as usual.

EXAMPLE \(\PageIndex{16}\)

Simplify: \(7−(−4−3)−9.\)

\(\begin{array}{lc} \text{} & 7−(−4−3)−9 \\ \text{Simplify inside the parentheses first.} & 7−(−7)−9 \\ \text{Subtract left to right.} & 14−9 \\ \text{Subtract.} & 5 \end{array}\)

Simplify: \(8−(−3−1)−9.\)

EXAMPLE \(\PageIndex{18}\)

Simplify: \(12−(−9−6)−14.\)

Multiply and Divide Integers

Since multiplication is mathematical shorthand for repeated addition, our model can easily be applied to show multiplication of integers. Let’s look at this concrete model to see what patterns we notice. We will use the same examples that we used for addition and subtraction. Here, we are using the model just to help us discover the pattern.

We remember that a⋅ba·b means add a , b times .

The next two examples are more interesting. What does it mean to multiply 5 by −3? It means subtract 5,3 times. Looking at subtraction as “taking away”, it means to take away 5, 3 times. But there is nothing to take away, so we start by adding neutral pairs on the workspace.

In summary:

\[\begin{array}{ll} 5·3=15 & −5(3)=−15 \\ 5(−3)=−15 & (−5)(−3)=15 \end{array}\]

Notice that for multiplication of two signed numbers, when the

\[ \text{signs are the } \textbf{same} \text{, the product is } \textbf{positive.} \\ \text{signs are } \textbf{different} \text{, the product is } \textbf{negative.} \]

What about division? Division is the inverse operation of multiplication. So, \(15÷3=5\) because \(15·3=15\). In words, this expression says that 15 can be divided into 3 groups of 5 each because adding five three times gives 15. If you look at some examples of multiplying integers, you might figure out the rules for dividing integers.

\[\begin{array}{lclrccl} 5·3=15 & \text{so} & 15÷3=5 & \text{ } −5(3)=−15 & \text{so} & −15÷3=−5 \\ (−5)(−3)=15 & \text{so} & 15÷(−3)=−5 & \text{ } 5(−3)=−15 & \text{so} & −15÷(−3)=5 \end{array}\]

Division follows the same rules as multiplication with regard to signs.

MULTIPLICATION AND DIVISION OF SIGNED NUMBERS

For multiplication and division of two signed numbers:

If the signs are the same, the result is positive.

If the signs are different, the result is negative.

EXAMPLE \(\PageIndex{19}\)

Multiply or divide: ⓐ \(−100÷(−4)\) ⓑ \(7⋅6\) ⓒ \(4(−8)\) ⓓ \(−27÷3.\)

\(\begin{array}{lc} \text{} & −100÷(−4) \\ \text{Divide, with signs that are} \\ \text{the same the quotient is positive.} & 25 \end{array}\)

\(\begin{array} {lc} \text{} & 7·6 \\ \text{Multiply, with same signs.} & 42 \end{array}\)

\(\begin{array} {lc} \text{} & 4(−8) \\ \text{Multiply, with different signs.} & −32 \end{array}\)

\(\begin{array}{lc} \text{} & −27÷3 \\ \text{Divide, with different signs,} \\ \text{the quotient is negative.} & −9 \end{array}\)

EXAMPLE \(\PageIndex{20}\)

Multiply or divide: ⓐ \(−115÷(−5)\) ⓑ \(5⋅12\) ⓒ \(9(−7)\) ⓓ\(−63÷7.\)

ⓐ 23 ⓑ 60 ⓒ −63 ⓓ −9

Multiply or divide: ⓐ \(−117÷(−3)\) ⓑ \(3⋅13\) ⓒ \(7(−4)\) ⓓ\(−42÷6\).

ⓐ 39 ⓑ 39 ⓒ −28 ⓓ −7

When we multiply a number by 1, the result is the same number. Each time we multiply a number by −1, we get its opposite!

MULTIPLICATION BY −1

\[−1a=−a\]

Multiplying a number by \(−1\) gives its opposite.

Simplify Expressions with Integers

What happens when there are more than two numbers in an expression? The order of operations still applies when negatives are included. Remember Please Excuse My Dear Aunt Sally?

Let’s try some examples. We’ll simplify expressions that use all four operations with integers—addition, subtraction, multiplication, and division. Remember to follow the order of operations.

EXAMPLE \(\PageIndex{22}\)

Simplify: ⓐ \((−2)^4\) ⓑ \(−2^4\).

Notice the difference in parts (a) and (b). In part (a), the exponent means to raise what is in the parentheses, the −2 to the 4 th power. In part (b), the exponent means to raise just the 2 to the 4 th power and then take the opposite.

\(\begin{array}{lc} \text{} & −2^4 \\ \text{Write in expanded form.} & −(2·2·2·2) \\ \text{We are asked to find} & \text{} \\ \text{the opposite of }24. & \text{} \\ \text{Multiply.} & −(4·2·2) \\ \text{Multiply.} & −(8·2) \\ \text{Multiply.} & −16 \end{array}\)

Simplify: ⓐ \((−3)^4\) ⓑ \(−3^4\).

ⓐ 81 ⓑ −81

EXAMPLE \(\PageIndex{24}\)

Simplify: ⓐ \((−7)^2\) ⓑ \(−7^2\).

ⓐ 49 ⓑ −49

The last example showed us the difference between \((−2)^4\) and \(−2^4\). This distinction is important to prevent future errors. The next example reminds us to multiply and divide in order left to right.

EXAMPLE \(\PageIndex{25}\)

Simplify: ⓐ \(8(−9)÷(−2)^3\) ⓑ \(−30÷2+(−3)(−7)\).

\(\begin{array}{lc} \text{} & 8(−9)÷(−2)^3 \\ \text{Exponents first.} & 8(−9)÷(−8) \\ \text{Multiply.} & −72÷(−8) \\ \text{Divide.} & 9 \end{array}\)

\(\begin{array}{lc} \text{} & −30÷2+(−3)(−7) \\ \text{Multiply and divide} \\ \text{left to right, so divide first.} & −15+(−3)(−7) \\ \text{Multiply.} & −15+21 \\ \text{Add.} & 6 \end{array}\)

Simplify: ⓐ \(12(−9)÷(−3)^3\) ⓑ \(−27÷3+(−5)(−6).\)

ⓐ 4 ⓑ 21

EXAMPLE \(\PageIndex{27}\)

Simplify: ⓐ \(18(−4)÷(−2)^3\) ⓑ \(−32÷4+(−2)(−7).\)

ⓐ 9 ⓑ 6

Evaluate Variable Expressions with Integers

Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers.

EXAMPLE \(\PageIndex{28}\)

Evaluate \(4x^2−2xy+3y^2\) when \(x=2,y=−1\).

EXAMPLE \(\PageIndex{29}\)

Evaluate: \(3x^2−2xy+6y^2\) when \(x=1,y=−2\).

EXAMPLE \(\PageIndex{30}\)

Evaluate: \(4x^2−xy+5y^2\) when \(x=−2,y=3\).

Translate Phrases to Expressions with Integers

Our earlier work translating English to algebra also applies to phrases that include both positive and negative numbers.

EXAMPLE \(\PageIndex{31}\)

Translate and simplify: the sum of 8 and −12, increased by 3.

\(\begin{array}{lc} \text{} & \text{the } \textbf{sum } \underline{\text{of}} \; –8 \; \underline{\text{and}} −12 \text{ increased by } 3 \\ \text{Translate.} & [8+(−12)]+3 \\ \text{Simplify. Be careful not to confuse the} \; \; \; \; \; \; \; \; \; \; & (−4)+3 \\ \text{brackets with an absolute value sign.} \\ \text{Add.} & −1 \end{array}\)

EXAMPLE \(\PageIndex{32}\)

Translate and simplify the sum of 9 and −16, increased by 4.

\((9+(−16))+4;−3\)

EXAMPLE \(\PageIndex{33}\)

Translate and simplify the sum of −8 and −12, increased by 7.

\((−8+(−12))+7;−13\)

Use Integers in Applications

We’ll outline a plan to solve applications. It’s hard to find something if we don’t know what we’re looking for or what to call it! So when we solve an application, we first need to determine what the problem is asking us to find. Then we’ll write a phrase that gives the information to find it. We’ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.

EXAMPLE \(\PageIndex{34}\): How to Solve Application Problems Using Integers

The temperature in Kendallville, Indiana one morning was 11 degrees. By mid-afternoon, the temperature had dropped to −9−9degrees. What was the difference in the morning and afternoon temperatures?

EXAMPLE \(\PageIndex{35}\)

The temperature in Anchorage, Alaska one morning was 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?

The difference in temperatures was 45 degrees Fahrenheit.

EXAMPLE \(\PageIndex{36}\)

The temperature in Denver was −6 degrees at lunchtime. By sunset the temperature had dropped to −15 degrees. What was the difference in the lunchtime and sunset temperatures?

The difference in temperatures was 9 degrees.

USE INTEGERS IN APPLICATIONS.

• Read the problem. Make sure all the words and ideas are understood.
• Identify what we are asked to find.
• Write a phrase that gives the information to find it.
• Translate the phrase to an expression.
• Simplify the expression.
• Answer the question with a complete sentence.

Access this online resource for additional instruction and practice with integers.

• Subtracting Integers with Counters

Key Concepts

• \[\begin{align} & −a \text{ means the opposite of the number }a \\ & \text{The notation} −a \text{ is read as “the opposite of }a \text{.”} \end{align} \]

The absolute value of a number n is written as \(|n|\) and \(|n|≥0\) for all numbers.

• Subtraction Property \(a−b=a+(−b)\) Subtracting a number is the same as adding its opposite.

\(−1a=−a\)

• Read the problem. Make sure all the words and ideas are understood

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• Jovan Fonte
• Matin Naseri
• Sharky Kesa
• Anuj Shikarkhane

An integer is a number that does not have a fractional part. The set of integers is

\[\mathbb{Z}=\{\cdots -4, -3, -2, -1, 0, 1, 2, 3, 4 \dots\}. \]

The notation \(\mathbb{Z}\) for the set of integers comes from the German word Zahlen , which means "numbers". Integers strictly larger than zero are positive integers and integers strictly less than zero are negative integers .

For example, \(2\), \(67\), \(0\), and \(-13\) are all integers (2 and 67 are positive integers and -13 is a negative integer). The values \(\frac{4}{7}\), \(10.7\), \(\frac{34}{7}\), \(\sqrt{2}\), and \(\pi\) are not integers.

Properties of Integers

Integers - problem solving.

The following are the properties of integers:

• The set of integers is closed under the operation of addition: if \(a, b \in \mathbb{Z}\), then \(a+b \in \mathbb{Z}\).
• The set of integers is closed under the operation of multiplication: if \(a, b \in \mathbb{Z}\), then \(ab\in \mathbb{Z}\).
• For any integer \(a\), the additive inverse \(-a\) is an integer.
• If \(a\) and \(b\) are integers such that \(a \cdot b = 0\), then \(a=0\) or \(b=0\).
• The set of integers is infinite and has no smallest element and no largest element.

\((\in\) means "belongs to", as \(a \in Z\) means \(a\) is an element of the set \(Z\) or \(a\) belongs to the set \(Z.)\)

Note that the set of integers is not closed under the operation of division. As an example, \(a=3\) and \(b=4\) are integers, but \(\frac{a}{b} = \frac{3}{4} \) is not an integer.

Which of the following are integers? \[\begin{array} &\frac{4}{2}, &-8, &0. 2, &12-4, &\frac{10}{4} \end{array}\] Since \(\frac{4}{2} = 2\), \(12-4 = 8,\) and \(2 < \frac{10}{4} < 3\), the integers in the list are \( \frac{4}{2}, -8 \), and \( 12-4.\) \(_\square\)

What is the smallest integer that is larger than \(\frac{10}{3}?\) Since \( 3< \frac{10}{3} < 4,\) the smallest integer that is larger than \(\frac{10}{3}\) is \(4\). \(_\square\)

What is the largest integer that is smaller than \(\frac{10}{3}?\) Since \( 3< \frac{10}{3} < 4,\) the largest integer that is smaller than \(\frac{10}{3}\) is \(3\). \(_\square\)

Using the properties of integers above, show that set of integers is closed under the operation of subtraction. Consider any two integers \(a\) and \(b\). We would like to show \(a-b\) is also an integer. By property \(3,\) the additive inverse of \(b\) is \(-b\), which is an integer. Then \[ a-b = a + (-b)\] is an integer by Property \(1.\) Therefore, the set of integers is closed under the operation of subtraction. \(_\square\)

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Integer Word Problems

In these lessons, we will look at Integer Word Problems that have more than two unknowns.

In another set of lessons, we have some examples of Integer Word Problems that involve two unknowns .

Related Pages Consecutive Integer Word Problems Consecutive Integers 1 Consecutive Integers 2 More Algebra Word Problems

Integer Problems With More Than Two Unknowns

Integer Problems with three unknowns are not necessarily more difficult than integer word problems with two unknowns . You just have to be careful when relating the different unknowns.

Example: Jane and her friends were selling cookies. They sold 4 more boxes the second week than they did the first. On the third week, they doubled the sale of their second week. Altogether, they sold a total of 352 boxes. How many boxes did they sell in the third week?

Solution: Step 1: Sentence: They sold 4 more boxes the second week than they did the first. On the third week, they doubled the sale of their second week.

Assign variables :

Example: The sum of three numbers is 12. The first is five times the second and the sum of the first and third is 9. Find the numbers.

Advanced Consecutive Integer Problems Example: (1) Find three consecutive positive integers such that the sum of the two smaller integers exceed the largest integer by 5.

(2) The sum of a number and three times its additive inverse is 16. Find the number.

Example: The largest of five consecutive even integers is 2 less than twice the smallest. Which of the following is the largest integer?

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1.2 Integers

Learning objectives.

Be Prepared 1.2

A more thorough introduction to the topics covered in this section can be found in the Elementary Algebra 2e chapter, Foundations.

A negative number is a number less than 0. The negative numbers are to the left of zero on the number line. See Figure 1.2 .

You may have noticed that, on the number line, the negative numbers are a mirror image of the positive numbers, with zero in the middle. Because the numbers 2 2 and −2 −2 are the same distance from zero, each one is called the opposite of the other. The opposite of 2 2 is −2 , −2 , and the opposite of −2 −2 is 2 . 2 .

Figure 1.3 illustrates the definition.

Opposite Notation

We saw that numbers such as 3 and −3 −3 are opposites because they are the same distance from 0 on the number line. They are both three units from 0. The distance between 0 and any number on the number line is called the absolute value of that number.

Absolute Value

The absolute value of a number n n is written as | n | | n | and | n | ≥ 0 | n | ≥ 0 for all numbers.

Figure 1.4 illustrates this idea.

In the next example, we’ll order expressions with absolute values.

Example 1.12

Fill in < , > , < , > , or = = for each of the following pairs of numbers:

ⓐ | −5 | __ − | −5 | | −5 | __ − | −5 | ⓑ 8 __ − | −8 | 8 __ − | −8 | ⓒ −9 __ − | −9 | −9 __ − | −9 | ⓓ − ( −16 ) __ | −16 | . − ( −16 ) __ | −16 | .

Try It 1.23

ⓐ −9 __ − | −9 | −9 __ − | −9 | ⓑ 2 __ − | −2 | 2 __ − | −2 | ⓒ −8 __ | −8 | −8 __ | −8 | ⓓ − ( −9 ) __ | −9 | . − ( −9 ) __ | −9 | .

Try It 1.24

ⓐ 7 __ − | −7 | 7 __ − | −7 | ⓑ − ( −10 ) __ | −10 | − ( −10 ) __ | −10 | ⓒ | −4 | __ − | −4 | | −4 | __ − | −4 | ⓓ −1 __ | −1 | . −1 __ | −1 | .

Grouping Symbols

In the next example, we simplify the expressions inside absolute value bars first just as we do with parentheses.

Example 1.13

Simplify: 24 − | 19 − 3 ( 6 − 2 ) | . 24 − | 19 − 3 ( 6 − 2 ) | .

Try It 1.25

Simplify: 19 − | 11 − 4 ( 3 − 1 ) | . 19 − | 11 − 4 ( 3 − 1 ) | .

Try It 1.26

Simplify: 9 − | 8 − 4 ( 7 − 5 ) | . 9 − | 8 − 4 ( 7 − 5 ) | .

So far, we have only used the counting numbers and the whole numbers.

Our work with opposites gives us a way to define the integers . The whole numbers and their opposites are called the integers. The integers are the numbers … −3 , −2 , −1 , 0 , 1 , 2 , 3 … … −3 , −2 , −1 , 0 , 1 , 2 , 3 …

The first example, 5 + 3 , 5 + 3 , adds 5 positives and 3 positives—both positives.

The second example, −5 + ( −3 ) , −5 + ( −3 ) , adds 5 negatives and 3 negatives—both negatives.

When the signs are the same, the counters are all the same color, and so we add them. In each case we get 8—either 8 positives or 8 negatives.

So what happens when the signs are different? Let’s add −5 + 3 −5 + 3 and 5 + ( −3 ) . 5 + ( −3 ) .

Example 1.14

Add: ⓐ −1 + ( −4 ) −1 + ( −4 ) ⓑ −1 + 5 −1 + 5 ⓒ 1 + ( −5 ) . 1 + ( −5 ) .

Try It 1.27

Add: ⓐ −2 + ( −4 ) −2 + ( −4 ) ⓑ −2 + 4 −2 + 4 ⓒ 2 + ( −4 ) . 2 + ( −4 ) .

Try It 1.28

Add: ⓐ −2 + ( −5 ) −2 + ( −5 ) ⓑ −2 + 5 −2 + 5 ⓒ 2 + ( −5 ) . 2 + ( −5 ) .

We will continue to use counters to model the subtraction. Perhaps when you were younger, you read “ 5 − 3 ” “ 5 − 3 ” as “5 take away 3.” When you use counters, you can think of subtraction the same way!

The first example, 5 − 3 , 5 − 3 , we subtract 3 positives from 5 positives and end up with 2 positives.

In the second example, −5 − ( −3 ) , −5 − ( −3 ) , we subtract 3 negatives from 5 negatives and end up with 2 negatives.

Each example used counters of only one color, and the “take away” model of subtraction was easy to apply.

What happens when we have to subtract one positive and one negative number? We’ll need to use both blue and red counters as well as some neutral pairs. If we don’t have the number of counters needed to take away, we add neutral pairs. Adding a neutral pair does not change the value. It is like changing quarters to nickels—the value is the same, but it looks different.

Let’s look at −5 − 3 −5 − 3 and 5 − ( −3 ) . 5 − ( −3 ) .

Example 1.15

Subtract: ⓐ 3 − 1 3 − 1 ⓑ −3 − ( −1 ) −3 − ( −1 ) ⓒ −3 − 1 −3 − 1 ⓓ 3 − ( −1 ) . 3 − ( −1 ) .

Try It 1.29

Subtract: ⓐ 6 − 4 6 − 4 ⓑ −6 − ( −4 ) −6 − ( −4 ) ⓒ −6 − 4 −6 − 4 ⓓ 6 − ( −4 ) . 6 − ( −4 ) .

Try It 1.30

Subtract: ⓐ 7 − 4 7 − 4 ⓑ −7 − ( −4 ) −7 − ( −4 ) ⓒ −7 − 4 −7 − 4 ⓓ 7 − ( −4 ) . 7 − ( −4 ) .

Have you noticed that subtraction of signed numbers can be done by adding the opposite ? In the last example, −3 − 1 −3 − 1 is the same as −3 + ( −1 ) −3 + ( −1 ) and 3 − ( −1 ) 3 − ( −1 ) is the same as 3 + 1 . 3 + 1 . You will often see this idea, the Subtraction Property, written as follows:

Subtraction Property

Example 1.16.

Simplify: ⓐ 13 − 8 13 − 8 and 13 + ( −8 ) 13 + ( −8 ) ⓑ −17 − 9 −17 − 9 and −17 + ( −9 ) −17 + ( −9 ) ⓒ 9 − ( −15 ) 9 − ( −15 ) and 9 + 15 9 + 15 ⓓ −7 − ( −4 ) −7 − ( −4 ) and −7 + 4 . −7 + 4 .

Try It 1.31

Simplify: ⓐ 21 − 13 21 − 13 and 21 + ( −13 ) 21 + ( −13 ) ⓑ −11 − 7 −11 − 7 and −11 + ( −7 ) −11 + ( −7 ) ⓒ 6 − ( −13 ) 6 − ( −13 ) and 6 + 13 6 + 13 ⓓ −5 − ( −1 ) −5 − ( −1 ) and −5 + 1 . −5 + 1 .

Try It 1.32

Simplify: ⓐ 15 − 7 15 − 7 and 15 + ( −7 ) 15 + ( −7 ) ⓑ −14 − 8 −14 − 8 and −14 + ( −8 ) −14 + ( −8 ) ⓒ 4 − ( −19 ) 4 − ( −19 ) and 4 + 19 4 + 19 ⓓ −4 − ( −7 ) −4 − ( −7 ) and −4 + 7 . −4 + 7 .

Example 1.17

Simplify: 7 − ( −4 − 3 ) − 9 . 7 − ( −4 − 3 ) − 9 .

Try It 1.33

Simplify: 8 − ( −3 − 1 ) − 9 . 8 − ( −3 − 1 ) − 9 .

Try It 1.34

Simplify: 12 − ( −9 − 6 ) − 14 . 12 − ( −9 − 6 ) − 14 .

Since multiplication is mathematical shorthand for repeated addition, our model can easily be applied to show multiplication of integers. Let’s look at this concrete model to see what patterns we notice. We will use the same examples that we used for addition and subtraction. Here, we are using the model just to help us discover the pattern.

We remember that a · b a · b means add a , b times .

The next two examples are more interesting. What does it mean to multiply 5 by −3 ? −3 ? It means subtract 5 , 3 5 , 3 times. Looking at subtraction as “taking away”, it means to take away 5, 3 times. But there is nothing to take away, so we start by adding neutral pairs on the workspace.

What about division? Division is the inverse operation of multiplication. So, 15 ÷ 3 = 5 15 ÷ 3 = 5 because 5 · 3 = 15 . 5 · 3 = 15 . In words, this expression says that 15 can be divided into 3 groups of 5 each because adding five three times gives 15. If you look at some examples of multiplying integers, you might figure out the rules for dividing integers.

Multiplication and Division of Signed Numbers

Example 1.18.

Multiply or divide: ⓐ −100 ÷ ( −4 ) −100 ÷ ( −4 ) ⓑ 7 · 6 7 · 6 ⓒ 4 ( −8 ) 4 ( −8 ) ⓓ −27 ÷ 3 . −27 ÷ 3 .

Try It 1.35

Multiply or divide: ⓐ −115 ÷ ( −5 ) −115 ÷ ( −5 ) ⓑ 5 · 12 5 · 12 ⓒ 9 ( −7 ) 9 ( −7 ) ⓓ −63 ÷ 7 . −63 ÷ 7 .

Try It 1.36

Multiply or divide: ⓐ −117 ÷ ( −3 ) −117 ÷ ( −3 ) ⓑ 3 · 13 3 · 13 ⓒ 7 ( −4 ) 7 ( −4 ) ⓓ −42 ÷ 6 . −42 ÷ 6 .

When we multiply a number by 1, the result is the same number. Each time we multiply a number by −1 , −1 , we get its opposite!

Multiplication by −1 −1

Multiplying a number by −1 −1 gives its opposite.

Let’s try some examples. We’ll simplify expressions that use all four operations with integers—addition, subtraction, multiplication, and division. Remember to follow the order of operations.

Example 1.19

Simplify: ⓐ ( −2 ) 4 ( −2 ) 4 ⓑ − 2 4 . − 2 4 .

Notice the difference in parts (a) and (b). In part (a), the exponent means to raise what is in the parentheses, the −2 −2 to the 4 th power. In part (b), the exponent means to raise just the 2 to the 4 th power and then take the opposite.

Try It 1.37

Simplify: ⓐ ( −3 ) 4 ( −3 ) 4 ⓑ − 3 4 . − 3 4 .

Try It 1.38

Simplify: ⓐ ( −7 ) 2 ( −7 ) 2 ⓑ − 7 2 . − 7 2 .

The last example showed us the difference between ( −2 ) 4 ( −2 ) 4 and − 2 4 . − 2 4 . This distinction is important to prevent future errors. The next example reminds us to multiply and divide in order left to right.

Example 1.20

Simplify: ⓐ 8 ( −9 ) ÷ ( −2 ) 3 8 ( −9 ) ÷ ( −2 ) 3 ⓑ −30 ÷ 2 + ( −3 ) ( −7 ) . −30 ÷ 2 + ( −3 ) ( −7 ) .

Try It 1.39

Simplify: ⓐ 12 ( −9 ) ÷ ( −3 ) 3 12 ( −9 ) ÷ ( −3 ) 3 ⓑ −27 ÷ 3 + ( −5 ) ( −6 ) . −27 ÷ 3 + ( −5 ) ( −6 ) .

Try It 1.40

Simplify: ⓐ 18 ( −4 ) ÷ ( −2 ) 3 18 ( −4 ) ÷ ( −2 ) 3 ⓑ −32 ÷ 4 + ( −2 ) ( −7 ) . −32 ÷ 4 + ( −2 ) ( −7 ) .

Example 1.21

Evaluate 4 x 2 − 2 x y + 3 y 2 4 x 2 − 2 x y + 3 y 2 when x = 2 , y = −1 . x = 2 , y = −1 .

Try It 1.41

Evaluate: 3 x 2 − 2 x y + 6 y 2 3 x 2 − 2 x y + 6 y 2 when x = 1 , y = −2 . x = 1 , y = −2 .

Try It 1.42

Evaluate: 4 x 2 − x y + 5 y 2 4 x 2 − x y + 5 y 2 when x = −2 , y = 3 . x = −2 , y = 3 .

Example 1.22

Translate and simplify: the sum of 8 and −12 , −12 , increased by 3 . 3 .

Try It 1.43

Translate and simplify the sum of 9 and −16 , −16 , increased by 4.

Try It 1.44

Translate and simplify the sum of −8 −8 and −12 , −12 , increased by 7.

We’ll outline a plan to solve applications. It’s hard to find something if we don’t know what we’re looking for or what to call it! So when we solve an application, we first need to determine what the problem is asking us to find. Then we’ll write a phrase that gives the information to find it. We’ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.

Example 1.23

How to solve application problems using integers.

In the morning, the temperature in Kendallville, Indiana was 11 degrees. By mid-afternoon, the temperature had dropped to −9 −9 degrees. What was the difference in the morning and afternoon temperatures?

Try It 1.45

In the morning, the temperature in Anchorage, Alaska was 15 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?

Try It 1.46

The temperature in Denver was −6 −6 degrees at lunchtime. By sunset the temperature had dropped to −15 −15 degrees. What was the difference in the lunchtime and sunset temperatures?

Use Integers in Applications.

• Step 1. Read the problem. Make sure all the words and ideas are understood.
• Step 2. Identify what we are asked to find.
• Step 3. Write a phrase that gives the information to find it.
• Step 4. Translate the phrase to an expression.
• Step 5. Simplify the expression.
• Step 6. Answer the question with a complete sentence.

Section 1.2 Exercises

Practice makes perfect.

In the following exercises, fill in < , > , < , > , or = = for each of the following pairs of numbers.

ⓐ | −7 | ___ − | −7 | | −7 | ___ − | −7 | ⓑ 6 ___ − | −6 | 6 ___ − | −6 | ⓒ | −11 | ___ − 11 | −11 | ___ − 11 ⓓ − ( −13 ) ___ − | −13 | − ( −13 ) ___ − | −13 |

ⓐ − | −9 | ___ | −9 | − | −9 | ___ | −9 | ⓑ −8 ___ | −8 | −8 ___ | −8 | ⓒ | −1 | ___ − 1 | −1 | ___ − 1 ⓓ − ( −14 ) ___ − | −14 | − ( −14 ) ___ − | −14 |

ⓐ − | 2 | ___ − | −2 | − | 2 | ___ − | −2 | ⓑ −12 ___ − | −12 | −12 ___ − | −12 | ⓒ | −3 | ___ − 3 | −3 | ___ − 3 ⓓ | −19 | ___ − ( −19 ) | −19 | ___ − ( −19 )

ⓐ − | −4 | ___ − | 4 | − | −4 | ___ − | 4 | ⓑ 5 ___ − | −5 | 5 ___ − | −5 | ⓒ − | −10 | ___ − 10 − | −10 | ___ − 10 ⓓ − | −0 | ___ − ( −0 ) − | −0 | ___ − ( −0 )

In the following exercises, simplify.

| 15 − 7 | − | 14 − 6 | | 15 − 7 | − | 14 − 6 |

| 17 − 8 | − | 13 − 4 | | 17 − 8 | − | 13 − 4 |

18 − | 2 ( 8 − 3 ) | 18 − | 2 ( 8 − 3 ) |

15 − | 3 ( 8 − 5 ) | 15 − | 3 ( 8 − 5 ) |

18 − | 12 − 4 ( 4 − 1 ) + 3 | 18 − | 12 − 4 ( 4 − 1 ) + 3 |

27 − | 19 + 4 ( 3 − 1 ) − 7 | 27 − | 19 + 4 ( 3 − 1 ) − 7 |

10 − 3 | 9 − 3 ( 3 − 1 ) | 10 − 3 | 9 − 3 ( 3 − 1 ) |

13 − 2 | 11 − 2 ( 5 − 2 ) | 13 − 2 | 11 − 2 ( 5 − 2 ) |

In the following exercises, simplify each expression.

ⓐ −7 + ( −4 ) −7 + ( −4 ) ⓑ −7 + 4 −7 + 4 ⓒ 7 + ( −4 ) . 7 + ( −4 ) .

ⓐ −5 + ( −9 ) −5 + ( −9 ) ⓑ −5 + 9 −5 + 9 ⓒ 5 + ( −9 ) 5 + ( −9 )

48 + ( −16 ) 48 + ( −16 )

34 + ( −19 ) 34 + ( −19 )

−14 + ( −12 ) + 4 −14 + ( −12 ) + 4

−17 + ( −18 ) + 6 −17 + ( −18 ) + 6

19 + 2 ( −3 + 8 ) 19 + 2 ( −3 + 8 )

24 + 3 ( −5 + 9 ) 24 + 3 ( −5 + 9 )

ⓐ 13 − 7 13 − 7 ⓑ −13 − ( −7 ) −13 − ( −7 ) ⓒ −13 − 7 −13 − 7 ⓓ 13 − ( −7 ) 13 − ( −7 )

ⓐ 15 − 8 15 − 8 ⓑ −15 − ( −8 ) −15 − ( −8 ) ⓒ −15 − 8 −15 − 8 ⓓ 15 − ( −8 ) 15 − ( −8 )

−17 − 42 −17 − 42

−58 − ( −67 ) −58 − ( −67 )

−14 − ( −27 ) + 9 −14 − ( −27 ) + 9

64 + ( −17 ) − 9 64 + ( −17 ) − 9

ⓐ 44 − 28 44 − 28 ⓑ 44 + ( −28 ) 44 + ( −28 )

ⓐ 35 − 16 35 − 16 ⓑ 35 + ( −16 ) 35 + ( −16 )

ⓐ 27 − ( −18 ) 27 − ( −18 ) ⓑ 27 + 18 27 + 18

ⓐ 46 − ( −37 ) 46 − ( −37 ) ⓑ 46 + 37 46 + 37

( 2 − 7 ) − ( 3 − 8 ) ( 2 − 7 ) − ( 3 − 8 )

( 1 − 8 ) − ( 2 − 9 ) ( 1 − 8 ) − ( 2 − 9 )

− ( 6 − 8 ) − ( 2 − 4 ) − ( 6 − 8 ) − ( 2 − 4 )

− ( 4 − 5 ) − ( 7 − 8 ) − ( 4 − 5 ) − ( 7 − 8 )

25 − [ 10 − ( 3 − 12 ) ] 25 − [ 10 − ( 3 − 12 ) ]

32 − [ 5 − ( 15 − 20 ) ] 32 − [ 5 − ( 15 − 20 ) ]

In the following exercises, multiply or divide.

ⓐ −4 · 8 −4 · 8 ⓑ 13 ( −5 ) 13 ( −5 ) ⓒ −24 ÷ 6 −24 ÷ 6 ⓓ −52 ÷ ( −4 ) −52 ÷ ( −4 )

ⓐ −3 · 9 −3 · 9 ⓑ 9 ( −7 ) 9 ( −7 ) ⓒ 35 ÷ ( −7 ) 35 ÷ ( −7 ) ⓓ −84 ÷ ( −6 ) −84 ÷ ( −6 )

ⓐ −28 ÷ 7 −28 ÷ 7 ⓑ −180 ÷ 15 −180 ÷ 15 ⓒ 3 ( −13 ) 3 ( −13 ) ⓓ −1 ( −14 ) −1 ( −14 )

ⓐ −36 ÷ 4 −36 ÷ 4 ⓑ −192 ÷ 12 −192 ÷ 12 ⓒ 9 ( −7 ) 9 ( −7 ) ⓓ −1 ( −19 ) −1 ( −19 )

Simplify and Evaluate Expressions with Integers

ⓐ ( −2 ) 6 ( −2 ) 6 ⓑ − 2 6 − 2 6

ⓐ ( −3 ) 5 ( −3 ) 5 ⓑ − 3 5 − 3 5

5 ( −6 ) + 7 ( −2 ) − 3 5 ( −6 ) + 7 ( −2 ) − 3

8 ( −4 ) + 5 ( −4 ) − 6 8 ( −4 ) + 5 ( −4 ) − 6

−3 ( −5 ) ( 6 ) −3 ( −5 ) ( 6 )

−4 ( −6 ) ( 3 ) −4 ( −6 ) ( 3 )

( 8 − 11 ) ( 9 − 12 ) ( 8 − 11 ) ( 9 − 12 )

( 6 − 11 ) ( 8 − 13 ) ( 6 − 11 ) ( 8 − 13 )

26 − 3 ( 2 − 7 ) 26 − 3 ( 2 − 7 )

23 − 2 ( 4 − 6 ) 23 − 2 ( 4 − 6 )

65 ÷ ( −5 ) + ( −28 ) ÷ ( −7 ) 65 ÷ ( −5 ) + ( −28 ) ÷ ( −7 )

52 ÷ ( −4 ) + ( −32 ) ÷ ( −8 ) 52 ÷ ( −4 ) + ( −32 ) ÷ ( −8 )

9 − 2 [ 3 − 8 ( −2 ) ] 9 − 2 [ 3 − 8 ( −2 ) ]

11 − 3 [ 7 − 4 ( −2 ) ] 11 − 3 [ 7 − 4 ( −2 ) ]

8 − | 2 − 4 ( 4 − 1 ) + 3 | 8 − | 2 − 4 ( 4 − 1 ) + 3 |

7 − | 5 − 3 ( 4 − 1 ) − 6 | 7 − | 5 − 3 ( 4 − 1 ) − 6 |

9 − 3 | 2 ( 2 − 6 ) − ( 3 − 7 ) | 9 − 3 | 2 ( 2 − 6 ) − ( 3 − 7 ) |

5 − 2 | 2 ( 1 − 4 ) − ( 2 − 5 ) | 5 − 2 | 2 ( 1 − 4 ) − ( 2 − 5 ) |

( −3 ) 2 − 24 ÷ ( 8 − 2 ) ( −3 ) 2 − 24 ÷ ( 8 − 2 )

( −4 ) 2 − 32 ÷ ( 12 − 4 ) ( −4 ) 2 − 32 ÷ ( 12 − 4 )

In the following exercises, evaluate each expression.

y + ( −14 ) y + ( −14 ) when ⓐ y = −33 y = −33 ⓑ y = 30 y = 30

x + ( −21 ) x + ( −21 ) when ⓐ x = −27 x = −27 ⓑ x = 44 x = 44

( x + y ) 2 ( x + y ) 2 when x = −3 , y = 14 x = −3 , y = 14

( y + z ) 2 ( y + z ) 2 when y = −3 , z = 15 y = −3 , z = 15

9 a − 2 b − 8 9 a − 2 b − 8 when a = −6 a = −6 and b = −3 b = −3

7 m − 4 n − 2 7 m − 4 n − 2 when m = −4 m = −4 and n = −9 n = −9

3 x 2 − 4 x y + 2 y 2 3 x 2 − 4 x y + 2 y 2 when x = −2 , y = −3 x = −2 , y = −3

4 x 2 − x y + 3 y 2 4 x 2 − x y + 3 y 2 when x = −3 , y = −2 x = −3 , y = −2

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the sum of 3 and −15 , −15 , increased by 7

the sum of −8 −8 and −9 , −9 , increased by 23 23

ⓐ the difference of 10 10 and −18 −18 ⓑ subtract 11 11 from −25 −25

ⓐ the difference of −5 −5 and −30 −30 ⓑ subtract −6 −6 from −13 −13

the quotient of −6 −6 and the sum of a a and b b

the product of −13 −13 and the difference of c c and d d

In the following exercises, solve.

Temperature On January 15, the high temperature in Anaheim, California, was 84°. That same day, the high temperature in Embarrass, Minnesota, was − 12 ° . − 12 ° . What was the difference between the temperature in Anaheim and the temperature in Embarrass?

Temperature On January 21, the high temperature in Palm Springs, California, was 89 ° , 89 ° , and the high temperature in Whitefield, New Hampshire, was − 31 ° . − 31 ° . What was the difference between the temperature in Palm Springs and the temperature in Whitefield?

Football On the first down, the Chargers had the ball on their 25-yard line. They lost 6 yards on the first-down play, gained 10 yards on the second-down play, and lost 8 yards on the third-down play. What was the yard line at the end of the third-down play?

Football On first down, the Steelers had the ball on their 30-yard line. They gained 9 yards on the first-down play, lost 14 yards on the second-down play, and lost 2 yards on the third-down play. What was the yard line at the end of the third-down play?

Checking Account Mayra has $124 in her checking account. She writes a check for $152. What is the new balance in her checking account?

Checking Account Reymonte has a balance of − $ 49 − $ 49 in his checking account. He deposits $281 to the account. What is the new balance?

Writing Exercises

Explain why the sum of −8 −8 and 2 is negative, but the sum of 8 and −2 −2 is positive.

Give an example from your life experience of adding two negative numbers.

In your own words, state the rules for multiplying and dividing integers.

Why is − 4 3 = ( −4 ) 3 ? − 4 3 = ( −4 ) 3 ?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

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• Book title: Intermediate Algebra 2e
• Publication date: May 6, 2020
• Location: Houston, Texas
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• Section URL: https://openstax.org/books/intermediate-algebra-2e/pages/1-2-integers

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• Math Article
• Word Problems On Integers

Integers: Word Problems On Integers

An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, subtraction, multiplication and division. Arithmetic operations are applicable to different types of numbers including integers.

Integers are a special group of numbers that do not have a fractional or a decimal part. It includes positive numbers, negative numbers and zero.  Arithmetic operations on integers are similar to that of whole numbers. Since integers can be positive or negative numbers i.e. as these numbers are preceded either by a positive (+) or a negative sign (-), it makes them a little confusing concept. Therefore, they are different from whole numbers . Let us now see how various arithmetical operations can be performed on integers with the help of a few word problems. Solve the following word problems using various rules of operations of integers.

Word problems on integers Examples:

Example 1: Shyak has overdrawn his checking account by Rs.38.  The bank debited him Rs.20 for an overdraft fee.  Later, he deposited Rs.150.  What is his current balance?

Solution:  Given,

Total amount deposited= Rs. 150

Amount overdrew by Shyak= Rs. 38

Amount charged by bank= Rs. 20

⇒ Debit amount= -20

Total amount debited = (-38) + (-20) = -58

Current balance= Total deposit +Total Debit

Hence, the current balance is Rs. 92.

Example 2: Anna is a microbiology student. She was doing research on optimum temperature for the survival of different strains of bacteria. Studies showed that bacteria X need optimum temperature of -31˚C while bacteria Y need optimum temperature of -56˚C. What is the temperature difference?

Solution: Given,

Optimum temperature for bacteria X = -31˚C

Optimum temperature for bacteria Y= -56˚C

Temperature difference= Optimum temperature for bacteria X – Optimum temperature for bacteria Y

⇒ (-31) – (-56)

Hence, temperature difference is 25˚C.

Example 3: A submarine submerges at the rate of 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?

Initial position = 20 m    (above sea level)

Final position = 250 m    (below sea level)

Total depth it submerged = (250+20) = 270 m

Thus, the submarine travelled 270 m below sea level.

Time taken to submerge 1 meter = 1/5 minutes

Time taken to submerge 270 m = 270 (1/5) = 54 min

Hence, the submarine will reach 250 m below sea level in 54 minutes.

To solve more problems on the topic, download BYJU’S – The Learning App and watch interactive videos. Also, take free tests to practice for exams.

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Fun teaching resources & tips to help you teach math with confidence

{FREE} Add & Subtract Integers: Real Life Lesson

There are so many ways we see and use integers in the real world. We even add and subtract integers all the time, though we might not realize it. So even though teaching how to add & subtract integers might sound scary to both teacher and student, there are actually ways to introduce this in real and meaningful ways . This post includes a real life lesson you can use to add & subtract integers and help kids see the “rules” before you actually teach integer rules.

* Please Note : This post contains affiliate links which support the work of this site. Read our full disclosure here .*

Teaching Integer Operations Through Problem Solving

To begin introducing integers, I prefer to start with real world examples . This can include common things like temperature, being above or below sea level, or other ideas that may or may not be familiar to students such as golf scores (above or below par).

In this lesson, the focus is on money , and balancing your budget . In this example, kids will add & subtract integers as money is earned (through working) or lost (by buying things).

What’s great about this lesson is that kids will actually use integers in a meaningful context and will see integer rules play out ( such as when you have a negative and subtract a positive you end up with a bigger negative ).

In addition, kids will see the commutative property , so that no matter what order they include the transactions in their ledger, they will always end up with the same amount of money in the bank.

How to Add & Subtract Integers

When you’re ready to set up this lesson, begin by printing a tracking page for each student. You will want to print this front and back so that students have enough space to keep track of each line item in the budget.

Students will then need a set of word problem cards .

I suggest putting students in small groups, and having them go through the cards in a different order . In this case, you can print just one set per group .

Just be sure students are careful not to mix the cards up or lose track of what items they’ve already calculated.

You want them to see that at the end, they all end up with the same final balance .

You could also assign this work individually , which means each student will need a page of word problems .

Then they could go through them in order , without cutting the cards out.

If you do it this way, every student s hould have the same answers all the way through the assignment.

This might be helpful if you’d rather everyone complete it in the same order so you can discuss various steps and compare how they worked them out and how they wrote their equations.

Finally, you will need to give everyone a starting balance .

If the starting balance is $0, they will end the assignment with $277 in the bank .

If you start with money already, however, you will end with: (starting value) + $277 . For instance, if the starting balance is $500, you will end with $777.

I hope this lesson provides a fun, real life math lesson for your students, and begins to build a foundation for how to work with integers.

Need more practice and visuals to teaching addition & subtraction with integers? Grab this complete lesson and games collection: Add & Subtract Integers Lessons & Games .

Extension and Follow Up Questions

To follow up, you’ll want to discuss why all students ended up with the same final total (if they didn’t, have them go back through their work to check first).

You could also discuss this specific situation and ask, “How could Bob have saved more money?” or “What was the best/worst choice he made with his money?”

You could also challenge kids to compare specific problems that are similar and estimate which is better. For example, what is better for Bob, working 5 hours at $15 an hour or working 10 hours for $10 an hour?

After discussing ideas, estimations and strategies, work out each problem.

Finally, you can then discuss what they noticed about integers and as them to explain in their own words how to add negative numbers , or how to subtract negative numbers .

When you’re ready to explore the integer rules more specifically, you might like this lesson to add & subtract integers .

This shows what happens as you add & subtract integers using +/- tables.

Find more helpful pre-algebra lessons in this post .

{Click HERE to go to my shop and grab the FREE Add & Subtract Integers in Real Life Lesson}

Looking for another fun and engaging way to work with integers? Try playing the game Absolute Zero ! This game is a great introduction to adding and subtracting integers, and there are tons of fun variations as well.

>> Learn more and grab Absolute Zero on Amazon HERE .

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Class 7 (Old)

Course: class 7 (old)   >   unit 1.

• Unit test Integers
• Our Mission

11 Real World Math Activities That Engage Students

Bridging the gap between abstract math concepts and real life experiences can make the subject accessible and relevant for kids.

During a unit on slope, José Vilson’s students just weren’t getting it, and their frustration was growing. The former middle school math teacher began brainstorming creative ways to illustrate the concept. “I kept thinking, ‘My students already understand how this works—they just don’t know that they know,’” Vilson writes in a recent article for Teacher2Teacher . “How can I activate knowledge they don’t believe they have?”

Then he thought about a hill a couple of blocks from school that his students “walk up every day to get to the subway.” He tacked up paper and began sketching stick figures on the hill. “One was at the top of the hill, one was halfway up, one was near the bottom skating on flat ground, and one was on a cliff,” writes Vilson, now the executive director of EduColor. “Which of these figures will go faster and why?” he asked his students. “That got my kids laughing because, of course, my stick figures weren’t going to hang in the MoMA.” Still, his sketch got them thinking and talking, and it provided a simple stepping stone that “gave that math relevance and belonging in their own lives,” Vilson concludes. 

“It’s not unusual for students to walk into our classrooms thinking that math belongs to people who are smarter, who are older, or who aren’t in their immediate circle,” Vilson writes. “But every time I teach math in a way that’s accessible and real for my students, I’m teaching them: ‘The math is yours.’”

To build on Vilson’s idea, we posted on our social channels asking teachers to share their favorite strategies for connecting math to students’ experiences and lives outside of school. We received hundreds of responses from math educators across grade levels. Here are 11 teacher-tested ideas that get students seeing and interacting with the math that surrounds them each day.

Hunt for clues

Coordinate systems can feel abstract to some students—but using coordinates to navigate a familiar space can solidify the concept in a relevant and fun way. “Before starting a unit on coordinates, I make gridded maps of the school—I make them look old using tea staining —and send my students off on a treasure hunt using the grid references to locate clues,” says Kolbe Burgoyne, an educator in Australia. “It’s meaningful, it’s fun, and definitely gets them engaged.”

Budget a trip

Students enjoy planning and budgeting for imaginary trips, teachers tell us, offering ample opportunities to practice adding, subtracting, and multiplying large numbers. In Miranda Henry’s resource classroom, for example, students are assigned a budget for a fictional spring break trip; then they find flights, hotels, food, and whatever else they’ll need, while staying within budget.

Math teacher Alicia Wimberley has her Texas students plan and budget a hypothetical trip to the Grand Canyon. “They love the real world context of it and start to see the relevance of the digits after the decimal—including how the .00 at the end of a price was relevant when adding.” One of Wimberley’s students, she writes, mixed up his decimals and nearly planned a $25,000 trip, but found his mistake and dialed back his expenses to under $3,000.

Tap into pizza love

Educators in our audience are big fans of “pizza math”—that is, any kind of math problem that involves pizza. “Pizza math was always a favorite when teaching area of a circle,” notes Shane Capps. If a store is selling a 10-inch pizza, for example, and we know that’s referring to its diameter, what is its total area? “Pizza math is a great tool for addition, subtraction, multiplication, word problems, fractions, and geometry,” another educator writes on our Instagram. There are endless pizza-based word problems online. Here’s a simple one to start, from Jump2Math : “The medium pizza had six slices. Mom and Dad each ate one slice. How much pizza is left?”

Break out the measuring cups

Lindsey Allan has her third-grade students break into pairs, find a recipe they like online, and use multiplication to calculate how much of each ingredient they’d need in order to feed the whole class. The class then votes on a favorite recipe, and they write up a shopping list—“which involves more math, because we have to decide, ‘OK, if we need this much butter for the doubled recipe, will we need three or four sticks, and then how much will be left over?’” Allan writes. “And then it turns out students were also doing division without even realizing!” 

Sometimes, a cooking mistake teaches students about proportions the hard way. “Nobody wants a sad chocolate chip cookie where you doubled the dough but not the chocolate chips,” adds teacher Holly Satter.

Heading outdoors is good for kids’ bodies , of course, but it can also be a rich mathematical experience. In second grade, kids can head out to measure perimeters, teacher Jenna McCann suggests—perhaps of the flower boxes in the school garden. If outdoors isn’t an option, there’s plenty of math to be found by walking around inside school—like measuring the perimeter of the tables in the cafeteria or the diameters of circles taped off on the gym floor.

In Maricris Lamigo’s eighth-grade geometry class, “I let [students] roam around the school and take photos of things where congruent triangles were applied,” says Lamigo. “I have students find distances in our indoor courtyard between two stickers that I place on the floor using the Pythagorean theorem,” adds Christopher Morrone, another eighth-grade teacher. In trigonometry, Cathee Cullison sends students outside “with tape measures and homemade clinometers to find heights, lengths, and areas using learned formulas for right and non-right triangles.” Students can make their own clinometers , devices that measure angles of elevation, using protractors and a few other household items.

Plan for adult life

To keep her math lessons both rigorous and engaging, Pamela Kranz runs a monthlong project-based learning activity where her middle school students choose an occupation and receive a salary based on government data. Then they have to budget their earnings to “pay rent, figure out transportation, buy groceries,” and navigate any number of unexpected financial dilemmas, such as medical expenses or car repairs. While learning about personal finance, they develop their mathematical understanding of fractions, decimals, and percents, Kranz writes.

Dig into sports stats

To help students learn how to draw conclusions from data and boost their comfort with decimals and percentages, fourth-grade teacher Kyle Pisselmyer has his students compare the win-loss ratio of the local sports team to that of Pisselmyer’s hometown team. While students can struggle to grasp the relevance of decimals—or to care about how 0.3 differs from 0.305—the details snap into place when they look at baseball players’ stats, educator Maggierose Bennion says.

March Madness is a great source of real world data for students to analyze in math class, says sixth-grade math teacher Jeff Norris. Last March, Norris decorated his classroom like a basketball court, then had his students do basic statistical analysis—like calculating mean, median, and mode—using March Madness data, including individual game scores and the total win rate of each team. “We also did some data collection through our own basketball stations to make it personally relevant,” Norris says; students lined up in teams to shoot paper balls into a basket in a set amount of time, recorded their scores in a worksheet, and then examined the scoring data of the entire class to answer questions about mean, median, mode, range, and outliers.

Go on a (pretend) shopping spree

“My students love any activities that include SHOPPING!” says Jessie, a sixth-grade teacher who creates shopping-related problems using fake (or sometimes real) store ads and receipts. Her students practice solving percentage problems, and the exercise includes opportunities to work with fractions and decimals.

To get students more engaged with the work, math educator Rachel Aleo-Cha zeroes in on objects she knows students are excited about. “I make questions that incorporate items like AirPods, Nike shoes, makeup, etc.,” Aleo-Cha says. She also has students calculate sales tax and prompts them to figure out “what a 50% off plus 20% off discount is—it’s not 70% off.”

Capture math on the fly

Math is everywhere, and whipping out a smartphone when opportunities arise can lead to excellent content for math class. At the foot of Mount Elbert in Colorado, for example, math teacher Ryan Walker recorded a short word problem for his fourth- and fifth-grade students. In the video, he revealed that it was 4:42 a.m., and it would probably take him 249 minutes to reach the summit. What time would he reach the summit, he asked his students—and, assuming it took two-thirds as long to descend, what time would he get back down?

Everyday examples can be especially relatable. At the gas station, “I record a video that tells the size of my gas tank, shows the current price of gas per gallon, and shows how empty my gas tank is,” says Walker. “Students then use a variety of skills (estimation, division, multiplying fractions, multiplying decimals, etc.) to make their estimate on how much money it will cost to fill my tank.”

Connect to social issues

It can be a powerful exercise to connect math to compelling social issues that students care about. In a unit on ratios and proportions, middle school teacher Jennifer Schmerler starts by having students design the “most unfair and unjust city”—where resources and public services like fire departments are distributed extremely unevenly. Using tables and graphs that reflect the distribution of the city’s population and the distribution of its resources, students then design a more equitable city.

Play entrepreneur

Each year, educator Karen Hanson has her fourth- and fifth-grade students brainstorm a list of potential business ideas and survey the school about which venture is most popular. Then the math begins: “We graph the survey results and explore all sorts of questions,” Hanson writes, like whether student preferences vary with age. Winning ideas in the past included selling T-shirts and wallets made of duct tape.

Next, students develop a resource list for the business, research prices, and tally everything up. They calculate a fair price point for the good they’re selling and the sales quantity needed to turn a profit. As a wrap-up, they generate financial statements examining how their profits stack up against the sales figures they had projected.

HELP OTHER TEACHERS OUT!

We’d love this article to be an evolving document of lesson ideas that make math relevant to kids. So, teachers, please tell us about your go-to activities that connect math to kids’ real world experiences.

Solution to Problem 1: Let x and x + 1 (consecutive integers differ by 1) be the two numbers. Use the fact that their sum is equal to 129 to write the equation. x + (x + 1) = 129. Solve for x to obtain. x = 64. The two numbers are. x = 64 and x + 1 = 65. We can see that the sum of the two numbers is 129.

For example: 5 + (-1) = 4. 4. Use the commutative property when a is negative and b is positive. Do the addition as follows: -a +b = c (get the absolute value of the numbers and again, proceed to subtract the lesser value from the larger value and assume the sign of the larger value) For example: -5 + 2 = -3. 5.

In the following exercises, evaluate. 35 − a when a = −4. (−2r) 2 when r = 3. 3m − 2n when m = 6, n = −8. −|−y| when y = 17. In the following exercises, translate each phrase into an algebraic expression and then simplify, if possible. the difference of −7 and −4. the quotient of 25 and the sum of m and n.

This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers. If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand.

Integer Word Problems Worksheets. An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses.

12. The temperature was -3o C last night. It is now -4o C. What was the change in temperature? 13. While watching a football game, Lin Chow decided to list yardage gained as positive integers and yardage lost as negative integers. After these plays, Lin recorded 14, -7, and 9.

The first example, \ (5+3,\) adds 5 positives and 3 positives—both positives. The second example, \ (−5+ (−3),\) adds 5 negatives and 3 negatives—both negatives. When the signs are the same, the counters are all the same color, and so we add them. In each case we get 8—either 8 positives or 8 negatives.

Using the properties of integers above, show that set of integers is closed under the operation of subtraction. Consider any two integers \(a\) and \(b\). We would like to show \(a-b\) is also an integer.

If we were to take the rules for multiplication and change the multiplication signs to division signs, we would have an accurate set of rules for division. Here are three examples: Example 1: -9 ÷ 3 = -3. Example 2: 20 ÷ (-4) = -5. Example 3: -18 ÷ (-3) = 6. uizmaster: Dividing Integers.

The first is five times the second and the sum of the first and third is 9. Find the numbers. Advanced Consecutive Integer Problems. Example: (1) Find three consecutive positive integers such that the sum of the two smaller integers exceed the largest integer by 5. (2) The sum of a number and three times its additive inverse is 16.

We could solve the problem above using Integers, the set of whole numbers and their opposites. The number line below is used to represent them. Definitions. The number line goes on forever in both directions. This is indicated by the arrows. Whole numbers greater than zero are called positive integers (+). These numbers are to the right of zero ...

Learn how to use integers to represent positive and negative numbers, and how to perform operations with them. This unit covers the concepts of addition, subtraction, multiplication, and division of integers, as well as the properties of these operations. You will also practice solving word problems involving integers and applying them to real-world situations.

4. Plot the integers from -10 to +10 on the number line. To learn about the properties of integers and to solve problems on the topic, download BYJU'S - The Learning App from Google Play Store and watch interactive videos.

Does it make sense for the problem? When subtracting integers, be sure to subtract the smaller integer from the larger integer. The smaller integer is farther to the left on the number line. 1. Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level ...

See Figure 1.2. Figure 1.2 The number line shows the location of positive and negative numbers. You may have noticed that, on the number line, the negative numbers are a mirror image of the positive numbers, with zero in the middle. Because the numbers 2 and −2 are the same distance from zero, each one is called the opposite of the other.

Integer. An integer is one of the numbers obtained in counting the natural numbers ( ), zero ( ), or the negatives of the natural numbers ( ). If and are integers, then their sum , their difference , and their product are all integers (that is, the integers are closed under addition and multiplication), but their quotient may or may not be an ...

Let us now see how various arithmetical operations can be performed on integers with the help of a few word problems. Solve the following word problems using various rules of operations of integers. Word problems on integers Examples: Example 1: Shyak has overdrawn his checking account by Rs.38. The bank debited him Rs.20 for an overdraft fee.

How to Add & Subtract Integers. When you're ready to set up this lesson, begin by printing a tracking page for each student. You will want to print this front and back so that students have enough space to keep track of each line item in the budget. Students will then need a set of word problem cards. I suggest putting students in small ...

http://www.greenemath.com/In this video, we practice solving integer word problems. These applied problems that deal with integers are very basic in nature.

Unit test Integers. Class 7 (Old) Integers. Unit test. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

Integers In Word Problems - Sample Math Practice Problems The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are ...

Since the temperatures are given as integers, a number line will help us solve this problem. As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value. Solution: The cities in order from least to greatest according to their temperatures are listed below.

Integers are "whole numbers" that are either positive or negative, which means we're not including fractions or decimals. ... How to solve consecutive integer problems in Algebra ... Learn math Krista King March 1, 2021 math, learn online, online course, online math, linear algebra, orthonormal basis, ...

Her students practice solving percentage problems, and the exercise includes opportunities to work with fractions and decimals. To get students more engaged with the work, math educator Rachel Aleo-Cha zeroes in on objects she knows students are excited about. "I make questions that incorporate items like AirPods, Nike shoes, makeup, etc ...

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