By LearningExpress Editors

Updated on Aug 24, 2011

To review these concepts, go to: The Keywords of Word Problems Study Guide.

### Practice

**Directions:** For each problem, underline the keywords and choose the operation needed to solve the problem. Then, find the solution to the problem.

- Find the product of 15 and 9.
- Aimee has 19 more jelly beans than Andrea. If Aimee has 33 jelly beans, how many jelly beans does Andrea have?
- Twenty students share 220 books evenly. How many books does each student receive?
- The bull's-eye of Matt's dartboard is worth 45 points for every time it is hit. If Matt hits the bull's-eye 14 times, how many points will he score?
- If 26 is increased by 37, what is the new value?
- A group of 12 skiers pays $420 for lift tickets. What is the cost of a ticket per person?
- A store receives a shipment of 55 snow shovels. If 38 of the shovels are sold, how many remain in stock?
- What is the quotient of 126 and 42?
- Maurice and Steve play hockey for the Blizzards. If Maurice scored 37 goals, and Steve scored 24 goals, how many goals did they score altogether?
- Natila brings 75 euros to France. If she spends 59 euros, how many euros does she have left?

**Directions: **For each problem, decide whether to use division or multiplication using fact families or the situation described in the problem. Then, find the answer to the problem.

- Every student in Mr. Barry's class must perform eight experiments in order to complete a lab assignment. If there are 27 students in his class, how many experiments will be performed?
- The cost of a field trip to the zoo is $9 per person. If there are 54 people going on the trip, how much will the trip cost?
- Robert sells 250 raffle tickets to his cousins. If he sells 50 raffle tickets to each cousin, how many cousins does Robert have?
- It takes a website 400 milliseconds to load for every ad on a webpage. If a webpage contains four ads, how long will it take the website to display those ads?
- Alex has 72 minutes to play golf. If he spends eight minutes per hole, how many holes of golf can he play?

### Solutions

- The keyword
*product*signals multiplication: 15 × 9 = 135. - The problem contains the keyword phrase
*more than*(even though*jelly beans*is in between the words*more*and*than*). Since Aimee has 19 more jelly beans than Andrea, we must subtract 19 from the number of jelly beans Aimee has (33) to find the number of jelly beans Andrea has: 33 – 19 = 14 jelly beans. - The keywords in this problem are
*share*and*each. Each*can signal multiplication or division, but the keyword*share*always signals division. Since 20 students are sharing 220 books, each student will receive fewer than 220 books. We must divide 220 ÷ 20 to find how many books each student will receive: 220 ÷ 20 = 11 books. - The keyword
*every*signals multiplication. If one bull's-eye hit is 45 points, then two bull's-eye hits will be more than 45 points—two times more. Multiply the value of a bull's-eye hit by the number of times Matt hits the bull's-eye: 45 × 14 = 630 points. - The keyword
*increased*signals addition. To increase 25 by 37, we must add 37 to 25: 25 + 37 = 62. - The keyword
*per*can signal multiplication or division. In this problem, we are given a number of skiers and how much they all paid for lift tickets. The cost of a ticket per person will be less than $420, so we are looking for an operation that can be performed on $420 to make that value smaller. We must divide $420 by 12 to find the cost of a ticket per person: $420 ÷ 12 = $35. Each skier paid $35. - The keyword
*remain*signals subtraction. The store had 55 snow shovels, but has fewer now that it has sold some of them. To find how many snow shovels remain, we must subtract the number of shovels sold from the original number of shovels: 55 – 38 = 17 shovels. - The keyword
*quotient*signals division. Divide 126 by 42: 126 ÷ 42 = 3. - The keyword
*altogether*signals addition. Add the number of goals scored by Maurice to the number of goals scored by Steve to find how many goals they scored combined: 37 + 24 = 61 goals. - The keyword
*left*signals subtraction. Natila's original total of 75 euros decreases after she spends 59 euros. Subtract 59 from 75: 75 – 59 = 16 euros. - 8 × 27 = 216 experiments and 27 ÷ 8 = experiments. Which answer makes more sense? Every student must complete eight assignments. If there were only one student in the class, then the class would need to complete eight assignments. If there were more than one student in the class, then the class would need to complete more than eight assignments. We are looking for an operation than makes eight greater. Multiply the number of assignments by the number of students in the class: 8 × 27 = 216 experiments.
- 54 ÷ 9 = $6 and 54 × 9 = $486. Which answer makes more sense? The cost of one person is $9, which means that the cost of two people will be more than $9. We are looking for an operation that makes $9 greater. Multiply the number of people on the trip by the cost per person: 54 × 9 = $486.
- 250 ÷ 50 = 5 tickets and 250 × 50 = 12,500 tickets. Which answer makes more sense? Robert sells 250 raffle tickets to his cousins. If he had one cousin, he would have sold all 250 tickets to that cousin. If he has more than one cousin, then he would have sold fewer than 250 tickets to each cousin. The tickets are split evenly among the number of cousins, which means that we need to divide: 250 ÷ 50 = 5 tickets.
- 400 ÷ 4 = 100 milliseconds and 400 × 4 = 1,600 milliseconds. Which answer makes more sense? If a website takes 400 milliseconds to load one ad on a page, then it takes the website more than 400 milliseconds to load more than one ad on a page. We are looking for an operation that makes 400 greater. Multiply the time it takes one ad to load by the number of ads: 400 × 4 = 1,600 milliseconds.
- 72 ÷ 8 = 9 holes and 72 × 8 = 576 holes. Which makes more sense? If Alex spends only one minute playing a hole, he could play 72 holes The Keywords of Word Problems 35 of golf. Since he spends eight minutes per hole, he will play less than 72 holes of golf. We are given a total number of minutes, so we are looking for an operation that makes 72 smaller. Divide the total number of minutes Alex has by the amount of time it takes him to play one hole: 72 ÷ 8 = 9 holes.

From Express Review Guides: Math Word Problems. Copyright © 2008 by LearningExpress, LLC. All Rights Reserved.

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