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# Recognizing Quantities and Relationships in Word Problems Help

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By McGraw-Hill Professional
Updated on Sep 27, 2011

## Introduction to Recognizing Quantities and Relationships in Word Problems

Success in solving word problems depends on the mastery of three skills— “translating” English into mathematics, setting the variable equal to an appropriate unknown quantity, and using knowledge of mathematics to solve the equation or inequality. This book will help you develop the first two skills and some attention will be given to the third.

 English Mathematical Symbol “Is,” “are,” “will be” (any form of the verb “to be”) mean “equal” = “More than,” “increased by,” “sum of” mean “add” + “Less than,” “decreased by,” “di.erence of” mean “subtract” - “Of ” means “multiply” × “Per” means “divide” % “More than” and “greater than” both mean the relation “greater than” although “more than” can mean “add” > “Less than,” means the relation “less than” although it can also mean “subtract” < “At least,” and “no less than,” mean the relation “greater than or equal to” ≥ “No more than,” and “at most,” mean the relation “less than or equal to” ≤

We will ease into the topic of word problems by translating English sentences into mathematical sentences. We will not solve word problems until later in the book.

## Recognizing Quantities and Relationships in Word Problems Practice Problems

#### Practice

Translate the English sentence into a mathematical sentence.

1. Fifteen less four is eleven.

2. Seven decreased by two is five.

3. Six increased by one is seven.

4. The sum of two and three is five.

5. Nine more than four is thirteen.

6. One-third of twelve is four.

7. One-third of twelve is greater than two.

8. Half of sixteen is eight.

9. The car gets 350 miles per eleven gallons.

10. Ten is less than twelve.

11. Ten is no more than twelve.

12. Three-fourths of sixteen is twelve.

13. Twice fifteen is thirty.

14. The difference of fourteen and five is nine.

15. Nine is more than six.

16. Nine is at least six.

#### Solutions

1. 15 – 4 = 11

2. 7 – 2 = 5

3. 6 + 1 = 7

4. 2 + 3 = 5

5. 9 + 4 = 13

9. 350 ÷ 11 (miles per gallon)

10. 10 < 12

11. 10 ≤ 12

13. 2 × 15 = 30

14. 14 – 5 = 9

15. 9 > 6

16. 9 ≥ 6

Practice problems for this concept can be found at: Algebra Fractions Practice Test.

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