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

- Use subtraction notation
- Model subtraction of whole numbers
- Subtract whole numbers
- Translate word phrases to math notation
- Subtract whole numbers in applications

Suppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference. The notation we use to subtract 3 from 7 is

7−3

We read 7−3 as seven minus three and the result is the difference of seven and three.

A model can help us visualize the process of subtraction much as it did with addition. Again, we will use base-10base-10 blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, 7−3.

We start by modeling the first number, 7. | |

Now take away the second number, 3. We’ll circle 3 blocks to show that we are taking them away. | |

Count the number of blocks remaining. | |

There are 4 ones blocks left. | We have shown that 7−3=4 |

Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition.

We know 7−3=4 because 4+3=7. Knowing all the addition number facts will help with subtraction. Then we can check subtraction by adding. In the examples above, our subtractions can be checked by addition.

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 1.3.

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

Subtraction | minus | 55 minus 11 | 5−1 |

difference | the difference of 99 and 44 | 9−4 | |

decreased by | 77 decreased by 33 | 7−3 | |

less than | 55 less than 88 | 8−5 | |

subtracted from | 11 subtracted from 66 | 6−1 |

**Table1.3**

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.

- 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-five 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,and80 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?

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

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

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