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Subtract Whole Numbers

Module by: First Last. E-mail the author

Summary: 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

Note: You are viewing an old style version of this document. The new style version is available here.

Note:

Before you get started, take this readiness quiz.

  1. 1) Model 3+43+4 using base-ten blocks.
    If you missed this problem, review (Reference).
  2. 2) Add: 324+586.324+586.
    If you missed this problem, review (Reference).

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 33 from 77 is

7373

We read 7373 as seven minus three and the result is the difference of seven and three.

Note: Subtraction Notation:

To describe subtraction, we can use symbols and words.

Operation Notation Expression Read as Result
Subtraction 7373 seven minus three the difference of 77 and 33

Example 1

Problem 1

Translate from math notation to words: 8181 26142614.

Solution: Solution
  • We read this as eight minus one. The result is the difference of eight and one.
  • We read this as twenty-six minus fourteen. The resuilt is the difference of twenty-six and fourteen.

Note:

Translate from math notation to words:

Exercise 1

  1. 124124
  2. 29112911
Solution
  1. twelve minus four; the difference of twelve and four
  2. twenty-nine minus eleven; the difference of twenty-nine and eleven

Note:

Translate from math notation to words:

Exercise 2

  1. 112112
  2. 29122912
Solution
  1. eleven minus two; the difference of eleven and two
  2. twenty-nine minus twelve; the difference of twenty-nine and twelve

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, 73.73.

We start by modeling the first number, 7. CNX_BMath_Figure_01_03_018_img-02.png
Now take away the second number, 3. We'll circle 3 blocks to show that we are taking them away. CNX_BMath_Figure_01_03_018_img-03.png
Count the number of blocks remaining. CNX_BMath_Figure_01_03_018_img-04.png
There are 4 ones blocks left. We have shown that 73=473=4.

Note:

Doing the Manipulative Mathematics activity Model Subtraction of Whole Numbers will help you develop a better understanding of subtracting whole numbers.

Example 2

Problem 1

Model the subtraction: 82.82.

Solution: Solution
8282 means the difference of 8 and 2.  
Model the first, 8. CNX_BMath_Figure_01_03_019_img-02.png
Take away the second number, 2. CNX_BMath_Figure_01_03_019_img-03.png
Count the number of blocks remaining. CNX_BMath_Figure_01_03_019_img-04.png
There are 6 ones blocks left. We have shown that 82=682=6.

Note:

Exercise 3

Model: 96.96.

Solution


No Alt Text

Note:

Exercise 4

Model: 61.61.

Solution


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Example 3

Problem 1

Model the subtraction: 138.138.

Solution: Solution
Model the first number, 13. We use 1 ten and 3 ones. CNX_BMath_Figure_01_03_020_img-02.png
Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones. CNX_BMath_Figure_01_03_020_img-03.png
Now we can take away 8 ones. CNX_BMath_Figure_01_03_020_img-04.png
Count the blocks remaining. CNX_BMath_Figure_01_03_020_img-05.png
There are five ones left. We have shown that 138=5138=5.

As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.

Note:

Exercise 5

Model the subtraction: 127.127.

Solution


No Alt Text

Note:

Exercise 6

Model the subtraction: 148.148.

Solution


No Alt Text

Example 4

Problem 1

Model the subtraction: 4326.4326.

Solution: Solution

Because 43264326 means 4343 take away 26,26, we begin by modeling the 43.43.
An image containing two items. The first item is 4 horizontal rods containing 10 blocks each. The second item is 3 individual blocks.

Now, we need to take away 26,26, which is 22 tens and 66 ones. We cannot take away 66 ones from 33 ones. So, we exchange 11 ten for 1010 ones.
This figure contains two groups. The first group on the left includes 3 rows of blue base 10 blocks and 1 red row of 10 blocks. This is labeled 4 tens. Alongside the first row of ten blocks are 3 individual blocks. This is labeled 3 ones. An arrow points to the right to the second group in which there are three rows of 10 base blocks labeled 3 tens. Next to this is a row of 3 blue individual blocks and two rows each with five individual blocks in red. This is labeled 13 ones.

Now we can take away 22 tens and 66 ones.
This image includes one row of base ten blocks at the top of the image; Next to it are seven individual blocks. Below this, is a group of two rows of base ten blocks, and two rows of 3 individual blocks with a circle around all. The arrow points to the right and shows one row of ten blocks and seven individual blocks underneath.

Count the number of blocks remaining. There is 11 ten and 77 ones, which is 17.17.

4326=174326=17

Note:

Exercise 7

Model the subtraction: 4227.4227.

Solution


No Alt Text

Note:

Exercise 8

Model the subtraction: 4529.4529.

Solution


No Alt Text

Subtract Whole Numbers

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

We know 73=473=4 because 4+3=7.4+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.

73=4because4+3=7138=5because5+8=134326=17because17+26=4373=4because4+3=7138=5because5+8=134326=17because17+26=43

Example 5

Problem 1

Subtract and then check by adding:

  1. 9797
  2. 83.83.

Solution: Solution
 
  9797
Subtract 7 from 9. 22
Check with addition.
2+7=92+7=9
 
 
  8383
Subtract 3 from 8. 55
Check with addition.
5+3=85+3=8
 

Note:

Exercise 9

Subtract and then check by adding:

7070

Solution

7 − 0 = 7; 7 + 0 = 7

Note:

Exercise 10

Subtract and then check by adding:

6262

Solution

6 − 2 = 4; 2 + 4 = 6

To subtract numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition. Align the digits by place value, and then subtract each column starting with the ones and then working to the left.

Example 6

Problem 1

Subtract and then check by adding: 8961.8961.

Solution: Solution
Table 7
Write the numbers so the ones and tens digits line up vertically. 89 61____ 89 61____
Subtract the digits in each place value.

Subtract the ones: 9-1=89-1=8
Subtract the tens: 8-6=28-6=2
89 61____ 28 89 61____ 28
Check using addition.
28 +61____ 89 28 +61____ 89
 

Our answer is correct.

Note:

Exercise 11

Subtract and then check by adding: 8654.8654.

Solution

86 − 54 = 32 because 54 + 32 = 86

Note:

Exercise 12

Subtract and then check by adding: 9974.9974.

Solution

99 − 74 = 25 because 74 + 25 = 99

When we modeled subtracting 2626 from 43,43, we exchanged 11 ten for 1010 ones. When we do this without the model, we say we borrow 11 from the tens place and add 1010 to the ones place.

Note: Find the difference of whole numbers.:

  1. Step 1. Write the numbers so each place value lines up vertically.
  2. Step 2. Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed.
  3. Step 3. Continue subtracting each place value from right to left, borrowing if needed.
  4. Step 4. Check by adding.

Example 7

Problem 1

Subtract: 4326.4326.

Solution: Solution
Write the numbers so each place value lines up vertically. ..
Subtract the ones. We cannot subtract 6 from 3, so we borrow 1 ten. This makes 3 tens and 13 ones. We write these numbers above each place and cross out the original digits. ..
Now we can subtract the ones. 136=7.136=7. We write the 7 in the ones place in the difference. ..
Now we subtract the tens. 32=1.32=1. We write the 1 in the tens place in the difference. ..
Check by adding.

..
Our answer is correct.
 

Note:

Exercise 13

Subtract and then check by adding: 9358.9358.

Solution

93 − 58 = 35 because 58 + 35 = 93

Note:

Exercise 14

Subtract and then check by adding: 8139.8139.

Solution

81 − 39 = 42 because 42 + 39 = 81

Example 8

Problem 1

Subtract and then check by adding: 20764.20764.

Solution: Solution
Write the numbers so each place value lines up vertically. ..
Subtract the ones. 74=3.74=3.
Write the 3 in the ones place in the difference. Write the 3 in the ones place in the difference.
..
Subtract the tens. We cannot subtract 6 from 0 so we borrow 1 hundred and add 10 tens to the 0 tens we had. This makes a total of 10 tens. We write 10 above the tens place and cross out the 0. Then we cross out the 2 in the hundreds place and write 1 above it. ..
Now we subtract the tens. 106=4.106=4. We write the 4 in the tens place in the difference. ..
Finally, subtract the hundreds. There is no digit in the hundreds place in the bottom number so we can imagine a 0 in that place. Since 10=1,10=1, we write 1 in the hundreds place in the difference...
Check by adding.
..
Our answer is correct.
 

Note:

Exercise 15

Subtract and then check by adding: 43952.43952.

Solution

439 − 52 = 387 because 387 + 52 = 439

Note:

Exercise 16

Subtract and then check by adding: 31875.31875.

Solution

318 − 75 = 243 because 243 + 75 = 318

Example 9

Problem 1

Subtract and then check by adding: 910586.910586.

Solution: Solution
Write the numbers so each place value lines up vertically. ..
Subtract the ones. We cannot subtract 6 from 0, so we borrow 1 ten and add 10 ones to the 10 ones we had. This makes 10 ones. We write a 0 above the tens place and cross out the 1. We write the 10 above the ones place and cross out the 0. Now we can subtract the ones. 106=4.106=4...
Write the 4 in the ones place of the difference. ..
Subtract the tens. We cannot subtract 8 from 0, so we borrow 1 hundred and add 10 tens to the 0 tens we had, which gives us 10 tens. Write 8 above the hundreds place and cross out the 9. Write 10 above the tens place. ..
Now we can subtract the tens. 108=2108=2. ..
Subtract the hundreds place. 85=385=3 Write the 3 in the hundreds place in the difference. ..
Check by adding.

...

Our answer is correct.
 

Note:

Exercise 17

Subtract and then check by adding: 832376.832376.

Solution

832 − 376 = 456 because 456 + 376 = 832

Note:

Exercise 18

Subtract and then check by adding: 847578.847578.

Solution

847 − 578 = 269 because 269 + 578 = 847

Example 10

Problem 1

Subtract and then check by adding: 2,162479.2,162479.

Solution: Solution
Write the numbers so each place values line up vertically. CNX_BMath_Figure_01_03_028_img-02.png
Subtract the ones. Since we cannot subtract 9 from 2, borrow 1 ten and add 10 ones to the 2 ones to make 12 ones. Write 5 above the tens place and cross out the 6. Write 12 above the ones place and cross out the 2. CNX_BMath_Figure_01_03_028_img-03.png
Now we can subtract the ones. 129=3129=3
Write 3 in the ones place in the difference. CNX_BMath_Figure_01_03_028_img-04.png
Subtract the tens. Since we cannot subtract 7 from 5, borrow 1 hundred and add 10 tens to the 5 tens to make 15 tens. Write 0 above the hundreds place and cross out the 1. Write 15 above the tens place.CNX_BMath_Figure_01_03_028_img-06.png
Now we can subtract the tens.157=8157=8
Write 8 in the tens place in the difference.CNX_BMath_Figure_01_03_028_img-05.png
Now we can subtract the hundreds.CNX_BMath_Figure_01_03_028_img-07.png
Write 6 in the hundreds place in the difference.CNX_BMath_Figure_01_03_028_img-08.png
Subtract the thousands. There is no digit in the thousands place of the bottom number, so we imagine a 0. 10=1.10=1. Write 1 in the thousands place of the difference.CNX_BMath_Figure_01_03_028_img-09.png
Check by adding.

11,61813+479______2,16211,61813+479______2,162
 

Our answer is correct.

Note:

Exercise 19

Subtract and then check by adding: 4,585697.4,585697.

Solution

4,585 − 697 = 3,888 because 3,888 + 697 = 4,585

Note:

Exercise 20

Subtract and then check by adding: 5,637899.5,637899.

Solution

5,637 − 899 = 4,738 because 4,738 + 899 = 5,637

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 12.

Table 12
Operation Word Phrase Example Expression
Subtraction minus 55 minus 11 5151
  difference the difference of 99 and 44 9494
  decreased by 77 decreased by 33 7373
  less than 55 less than 88 8585
  subtracted from 11 subtracted from 66 6161

Example 11

Problem 1

Translate and then simplify:

  1. the difference of 1313 and 88
  2. subtract 2424 from 4343
Solution: Solution
  • 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. 138138
    Simplify. 5
  • 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. 43244324
    Simplify. 19

Note:

Exercise 21

Translate and simplify:

  1. the difference of 1414 and 99
  2. subtract 2121 from 3737
Solution
  1. 14 − 9 = 5
  2. 37 − 21 = 16

Note:

Exercise 22

Translate and simplify:

  1. 1111 decreased by 66
  2. 1818 less than 6767
Solution
  1. 11 − 6 = 5
  2. 67 − 18 = 49

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 12

Problem 1

The temperature in Chicago one morning was 7373 degrees Fahrenheit. A cold front arrived and by noon the temperature was 2727 degrees Fahrenheit. What was the difference between the temperature in the morning and the temperature at noon?

Solution: 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. 73277327
Then we do the subtraction. ...
Write a sentence to answer the question. The difference in temperatures was 46 degrees Fahrenheit.

Note:

Exercise 23

The high temperature on June1stJune1st in Boston was 7777 degrees Fahrenheit, and the low temperature was 5858 degrees Fahrenheit. What was the difference between the high and low temperatures?

Solution

The difference is 19 degrees Fahrenheit.

Note:

Exercise 24

The weather forecast for June 22 in St Louis predicts a high temperature of 9090 degrees Fahrenheit and a low of 7373 degrees Fahrenheit. What is the difference between the predicted high and low temperatures?

Solution

The difference is 17 degrees Fahrenheit.

Example 13

Problem 1

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

Solution: 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. 588399588399
Subtract. ..
Write a sentence to answer the question. The difference between the regular price and the sale price is $189.

Note:

Exercise 25

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

Solution

The difference is $149.

Note:

Exercise 26

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

Solution

The difference is $136.

Key Concepts

Operation Notation Expression Read as Result
Subtraction 7373 seven minus three the difference of 77 and 33
  • Subtract whole numbers.
    1. Step 1. Write the numbers so each place value lines up vertically.
    2. Step 2. Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed.
    3. Step 3. Continue subtracting each place value from right to left, borrowing if needed.
    4. Step 4. Check by adding.

Practice Makes Perfect

Use Subtraction Notation

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

Exercise 27

159159

Solution

fifteen minus nine; the difference of fifteen and nine

Exercise 28

18161816

Exercise 29

42354235

Solution

forty-two minus thirty-five; the difference of forty-two and thirty-five

Exercise 30

83648364

Exercise 31

675350675350

Solution

hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty

Exercise 32

790525790525

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

Exercise 33

Exercise 34

8484

Exercise 35

Exercise 36

7575

Exercise 37

Exercise 38

198198

Exercise 39

Exercise 40

179179

Exercise 41

Exercise 42

32113211

Exercise 43

Exercise 44

55365536

Subtract Whole Numbers

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

Exercise 45

Exercise 46

9393

Exercise 47

Exercise 48

2020

Exercise 49

38163816

Solution

22

Exercise 50

45214521

Exercise 51

85528552

Solution

33

Exercise 52

99479947

Exercise 53

493370493370

Solution

123

Exercise 54

268106268106

Exercise 55

5,9464,6255,9464,625

Solution

1,321

Exercise 56

7,7753,2517,7753,251

Exercise 57

75477547

Solution

28

Exercise 58

63596359

Exercise 59

461239461239

Solution

222

Exercise 60

486257486257

Exercise 61

525179525179

Solution

346

Exercise 62

542288542288

Exercise 63

6,3182,7996,3182,799

Solution

3,519

Exercise 64

8,1533,9788,1533,978

Exercise 65

2,1509642,150964

Solution

1,186

Exercise 66

4,2458994,245899

Exercise 67

43,6508,98243,6508,982

Solution

34,668

Exercise 68

35,1627,88535,1627,885

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

Exercise 69

The difference of 1010 and 33

Solution

10 − 3; 7

Exercise 70

The difference of 1212 and 88

Exercise 71

The difference of 1515 and 44

Solution

15 − 4; 11

Exercise 72

The difference of 1818 and 77

Exercise 73

Subtract 66 from 99

Solution

9 − 6; 3

Exercise 74

Subtract 88 from 99

Exercise 75

Subtract 2828 from 7575

Solution

75 − 28; 47

Exercise 76

Subtract 5959 from 8181

Exercise 77

4545 decreased by 2020

Solution

45 − 20; 25

Exercise 78

3737 decreased by 2424

Exercise 79

9292 decreased by 6767

Solution

92 − 67; 25

Exercise 80

7575 decreased by 4949

Exercise 81

1212 less than 1616

Solution

16 − 12; 4

Exercise 82

1515 less than 1919

Exercise 83

3838 less than 6161

Solution

61 − 38; 23

Exercise 84

4747 less than 6262

Mixed Practice

In the following exercises, simplify.

Exercise 85

76477647

Solution

29

Exercise 86

91539153

Exercise 87

256184256184

Solution

72

Exercise 88

305262305262

Exercise 89

719+341719+341

Solution

1,060

Exercise 90

647+528647+528

Exercise 91

2,0151,9932,0151,993

Solution

22

Exercise 92

2,0201,9842,0201,984

In the following exercises, translate and simplify.

Exercise 93

Seventy more than thirty-five

Solution

75 + 35; 110

Exercise 94

Sixty more than ninety-three

Exercise 95

1313 less than 4141

Solution

41 − 13; 28

Exercise 96

2828 less than 3636

Exercise 97

The difference of 100100 and 7676

Solution

100 − 76; 24

Exercise 98

The difference of 1,0001,000 and 945945

Subtract Whole Numbers in Applications

In the following exercises, solve.

Exercise 99

Temperature The high temperature on June 22 in Las Vegas was 8080 degrees and the low temperature was 6363 degrees. What was the difference between the high and low temperatures?

Solution

The difference between the high and low temperature was 17 degrees

Exercise 100

Temperature The high temperature on June 11 in Phoenix was 9797 degrees and the low was 7373 degrees. What was the difference between the high and low temperatures?

Exercise 101

Class size Olivia’s third grade class has 3535 children. Last year, her second grade class had 2222 children. What is the difference between the number of children in Olivia’s third grade class and her second grade class?

Solution

The difference between the third grade and second grade was 13 children.

Exercise 102

Class size There are 8282 students in the school band and 4646 in the school orchestra. What is the difference between the number of students in the band and the orchestra?

Exercise 103

Shopping A mountain bike is on sale for $399.$399. Its regular price is $650.$650. What is the difference between the regular price and the sale price?

Solution

The difference between the regular price and sale price is $251.

Exercise 104

Shopping A mattress set is on sale for $755.$755. Its regular price is $1,600.$1,600. What is the difference between the regular price and the sale price?

Exercise 105

Savings John wants to buy a laptop that costs $840.$840. He has $685$685 in his savings account. How much more does he need to save in order to buy the laptop?

Solution

John needs to save $155 more.

Exercise 106

Banking Mason had $1,125$1,125 in his checking account. He spent $892.$892. How much money does he have left?

Everyday Math

Exercise 107

Road trip Noah was driving from Philadelphia to Cincinnati, a distance of 502502 miles. He drove 115115 miles, stopped for gas, and then drove another 230230 miles before lunch. How many more miles did he have to travel?

Solution

157 miles

Exercise 108

Test Scores Sara needs 350350 points to pass her course. She scored 75,50,70,and8075,50,70,and80 on her first four tests. How many more points does Sara need to pass the course?

Writing Exercises

Exercise 109

Explain how subtraction and addition are related.

Solution

Answers may vary.

Exercise 110

How does knowing addition facts help you to subtract numbers?

Self Check

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?

Glossary

difference:
The difference is the result of subtracting two or more numbers.

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