# 1.3 Subtract Whole Numbers

### Learning Objectives

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

### Use Subtraction Notation

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.

### Model Subtraction of Whole Numbers

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.

### Subtract Whole Numbers

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.

### 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 1.3.

Table1.3

### 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.

1. 15−9
2. 18−16
3. 42−35
4. 83−64
5. 675−350
6. 790−525
Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

1. 5−2
2. 8−4
3. 6−3
4. 7−5
5. 18−5
6. 19−8
7. 17−8
8. 17−9
9. 35−13
10. 32−11
11. 61−47
12. 55−36
Subtract Whole Numbers

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

1. 9−4
2. 9−3
3. 8−0
4. 2−0
5. 38−16
6. 45−21
7. 85−52
8. 99−47
9. 493−370
10. 268−106
11. 5,946−4,625
12. 7,775−3,251
13. 75−47
14. 63−59
15. 461−239
16. 486−257
17. 525−179
18. 542−288
19. 6,318−2,799
20. 8,153−3,978
21. 2,150−964
22. 4,245−899
23. 43,650−8,982
24. 35,162−7,885
Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

1. The difference of 10 and 3
2. The difference of 12 and 8
3. The difference of 15 and 4
4. The difference of 18 and 7
5. Subtract 6 from 9
6. Subtract 8 from 9
7. Subtract 28 from 75
8. Subtract 59 from 81
9. 45 decreased by 20
10. 37 decreased by 24
11. 92 decreased by 67
12. 75 decreased by 49
13. 12 less than 16
14. 15 less than 19
15. 38 less than 61
16. 47 less than 62
Mixed Practice

In the following exercises, simplify.

1. 76−47
2. 91−53
3. 256−184
4. 305−262
5. 719+341
6. 647+528
7. 2,015−1,993
8. 2,020−1,984
In the following exercises, translate and simplify.
9. Seventy-five more than thirty-five
10. Sixty more than ninety-three
11. 13 less than 41
12. 28 less than 36
13. The difference of 100 and 76
14. The difference of 1,000 and 945

Subtract Whole Numbers in Applications

In the following exercises, solve.

1. 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?
2. 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?
3. 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?
4. 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?
5. 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?
6. 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?
7. 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?
8. Banking Mason had \$1,125 in his checking account. He spent \$892. How much money does he have left?
Everyday Math
9. 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?
10. 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
11. Explain how subtraction and addition are related.