# 1.3: Subtract Whole Numbers (Part 2)

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### Translate Word Phrases to Math Notation

As with addition, word phrases can tell us to operate on two numbers using subtraction. To translate from a word phrase to math notation, we look for key words that indicate subtraction. Some of the words that indicate subtraction are listed in Table 1.34.

#### Table 1.34

Operation | Word Phrase | Example | Expression |
---|---|---|---|

Subtraction | minus | 5 minus 1 | 5 - 1 |

difference | the difference of 9 and 4 | 9 - 4 | |

decreased by | 7 decreased by 3 | 7 - 3 | |

less than | 5 less than 8 | 8 - 5 | |

subtracted from | 1 subtracted from 6 | 6 - 1 |

Translate and then simplify: (a) the difference of 13 and 8 (b) subtract 24 from 43

##### Solution

(a) The word *difference *tells us to subtract the two numbers. The numbers stay in the same order as in the phrase.

the difference of 13 and 8 | |

Translate. | 13 - 8 |

Simplify. | 5 |

(b) The words subtract from tells us to take the second number away from the first. We must be careful to get the order correct.

subtract 24 from 43 | |

Translate. | 43 - 24 |

Simplify. | 19 |

Exercise 1.71:

Translate and simplify: (a) the difference of 14 and 9 (b) subtract 21 from 37.

Exercise 1.72:

Translate and simplify: (a) 11 decreased by 6 (b) 18 less than 67.

### Subtract Whole Numbers in Applications

To solve applications with subtraction, we will use the same plan that we used with addition. First, we need to determine what we are asked to find. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question, using the appropriate units.

Example 1.37:

The temperature in Chicago one morning was 73 degrees Fahrenheit. A cold front arrived and by noon the temperature was 27 degrees Fahrenheit. What was the difference between the temperature in the morning and the temperature at noon?

##### Solution

We are asked to find the difference between the morning temperature and the noon temperature.

Write a phrase. | the difference of 73 and 27 |

Translate to math notation. Difference tells us to subtract. |
73 - 27 |

Then we do the subtraction. | |

Write a sentence to answer the question. | The difference in temperatures was 46 degrees Fahrenheit. |

Exercise 1.73:

The high temperature on June 1st in Boston was 77 degrees Fahrenheit, and the low temperature was 58 degrees Fahrenheit. What was the difference between the high and low temperatures?

Exercise 1.74:

The weather forecast for June 2 in St Louis predicts a high temperature of 90 degrees Fahrenheit and a low of 73 degrees Fahrenheit. What is the difference between the predicted high and low temperatures?

Example 1.38:

A washing machine is on sale for $399. Its regular price is $588. What is the difference between the regular price and the sale price?

##### Solution

We are asked to find the difference between the regular price and the sale price.

Write a phrase. | the difference between 588 and 399 |

Translate to math notation. | 588 - 399 |

Subtract. | |

Write a sentence to answer the question. | The difference between the regular price and the sale price is $189. |

Exercise 1.75:

A television set is on sale for $499. Its regular price is $648. What is the difference between the regular price and the sale price?

Exercise 1.76:

A patio set is on sale for $149. Its regular price is $285. What is the difference between the regular price and the sale price?

ACCESS ADDITIONAL ONLINE RESOURCES

Model subtraction of two-digit whole numbers

### Practice Makes Perfect

#### Use Subtraction Notation

In the following exercises, translate from math notation to words.

- 15 - 9
- 18 - 16
- 42 - 35
- 83 - 64
- 675 - 350
- 790 - 525

#### Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

- 5 - 2
- 8 - 4
- 6 - 3
- 7 - 5
- 18 - 5
- 19 - 8
- 17 - 8
- 17 - 9
- 35 - 13
- 32 - 11
- 61 - 47
- 55 - 36

#### Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

- 9 - 4
- 9 - 3
- 8 - 0
- 2 - 0
- 38 - 16
- 45 - 21
- 85 - 52
- 99 - 47
- 493 - 370
- 268 - 106
- 5,946 - 4,625
- 7,775 - 3,251
- 75 - 47
- 63 - 59
- 461 - 239
- 486 - 257
- 525 - 179
- 542 - 288
- 6,318 - 2,799
- 8,153 - 3,978
- 2,150 - 964
- 4,245 - 899
- 43,650 - 8,982
- 35,162 - 7,885

#### Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

- The difference of 10 and 3
- The difference of 12 and 8
- The difference of 15 and 4
- The difference of 18 and 7
- Subtract 6 from 9
- Subtract 8 from 9
- Subtract 28 from 75
- Subtract 59 from 81
- 45 decreased by 20
- 37 decreased by 24
- 92 decreased by 67
- 75 decreased by 49
- 12 less than 16
- 15 less than 19
- 38 less than 61
- 47 less than 62

#### Mixed Practice

In the following exercises, simplify.

- 76−47
- 91 − 53
- 256 − 184
- 305 − 262
- 719 + 341
- 647 + 528
- 2,015 − 1,993
- 2,020 − 1,984

In the following exercises, translate and simplify.

- Seventy more than thirty-five
- Sixty more than ninety-three
- 13 less than 41
- 28 less than 36
- The difference of 100 and 76
- The difference of 1,000 and 945

#### Subtract Whole Numbers in Applications

In the following exercises, solve.

**Temperature**The high temperature on June 2 in Las Vegas was 80 degrees and the low temperature was 63 degrees. What was the difference between the high and low temperatures?**Temperature**The high temperature on June 1 in Phoenix was 97 degrees and the low was 73 degrees. What was the difference between the high and low temperatures?**Class size**Olivia’s third grade class has 35 children. Last year, her second grade class had 22 children. What is the difference between the number of children in Olivia’s third grade class and her second grade class?**Class size**There are 82 students in the school band and 46 in the school orchestra. What is the difference between the number of students in the band and the orchestra?**Shopping**A mountain bike is on sale for $399. Its regular price is $650. What is the difference between the regular price and the sale price?**Shopping**A mattress set is on sale for $755. Its regular price is $1,600. What is the difference between the regular price and the sale price?**Savings**John wants to buy a laptop that costs $840. He has $685 in his savings account. How much more does he need to save in order to buy the laptop?**Banking**Mason had $1,125 in his checking account. He spent $892. How much money does he have left?

### Everyday Math

**Road trip**Noah was driving from Philadelphia to Cincinnati, a distance of 502 miles. He drove 115 miles, stopped for gas, and then drove another 230 miles before lunch. How many more miles did he have to travel?**Test Scores**Sara needs 350 points to pass her course. She scored 75, 50, 70, and 80 on her first four tests. How many more points does Sara need to pass the course?

### Writing Exercises

- Explain how subtraction and addition are related.
- How does knowing addition facts help you to subtract numbers?

### Self Check

(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section

(b) What does this checklist tell you about your mastery of this section? What steps will you take to improve?