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Prealgebra 2e

1.3 Subtract Whole Numbers

Prealgebra 2e1.3 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

Be Prepared 1.3

Before you get started, take this readiness quiz.

Model 3+43+4 using base-ten blocks.
If you missed this problem, review Example 1.12.

Be Prepared 1.4

Add: 324+586.324+586.
If you missed this problem, review Example 1.20.

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.

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 1.26

Translate from math notation to words: 8181 26142614.

Try It 1.51

Translate from math notation to words:

  1. 124124
  2. 29112911

Try It 1.52

Translate from math notation to words:

  1. 112112
  2. 29122912

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.

Example 1.27

Model the subtraction: 82.82.

Try It 1.53

Model: 96.96.

Try It 1.54

Model: 61.61.

Example 1.28

Model the subtraction: 138.138.

Try It 1.55

Model the subtraction: 127.127.

Try It 1.56

Model the subtraction: 148.148.

Example 1.29

Model the subtraction: 4326.4326.

Try It 1.57

Model the subtraction: 4227.4227.

Try It 1.58

Model the subtraction: 4529.4529.

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 1.30

Subtract and then check by adding:

  1. 9797
  2. 83.83.

Try It 1.59

Subtract and then check by adding:

7070

Try It 1.60

Subtract and then check by adding:

6262

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 1.31

Subtract and then check by adding: 8961.8961.

Try It 1.61

Subtract and then check by adding: 8654.8654.

Try It 1.62

Subtract and then check by adding: 9974.9974.

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.

How To

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 1.32

Subtract: 4326.4326.

Try It 1.63

Subtract and then check by adding: 9358.9358.

Try It 1.64

Subtract and then check by adding: 8139.8139.

Example 1.33

Subtract and then check by adding: 20764.20764.

Try It 1.65

Subtract and then check by adding: 43952.43952.

Try It 1.66

Subtract and then check by adding: 31875.31875.

Example 1.34

Subtract and then check by adding: 910586.910586.

Try It 1.67

Subtract and then check by adding: 832376.832376.

Try It 1.68

Subtract and then check by adding: 847578.847578.

Example 1.35

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

Try It 1.69

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

Try It 1.70

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

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.

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
Table 1.3

Example 1.36

Translate and then simplify:

  1. the difference of 1313 and 88
  2. subtract 2424 from 4343

Try It 1.71

Translate and simplify:

  1. the difference of 1414 and 99
  2. subtract 2121 from 3737

Try It 1.72

Translate and simplify:

  1. 1111 decreased by 66
  2. 1818 less than 6767

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 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?

Try It 1.73

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?

Try It 1.74

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?

Example 1.38

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?

Try It 1.75

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?

Try It 1.76

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?

Section 1.3 Exercises

Practice Makes Perfect

Use Subtraction Notation

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

141.

15 9 15 9

142.

18 16 18 16

143.

42 35 42 35

144.

83 64 83 64

145.

675 350 675 350

146.

790 525 790 525

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

147.

5 2 5 2

148.

8 4 8 4

149.

6 3 6 3

150.

7 5 7 5

151.

18 5 18 5

152.

19 8 19 8

153.

17 8 17 8

154.

17 9 17 9

155.

35 13 35 13

156.

32 11 32 11

157.

61 47 61 47

158.

55 36 55 36

Subtract Whole Numbers

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

159.

9 4 9 4

160.

9 3 9 3

161.

8 0 8 0

162.

2 0 2 0

163.

38 16 38 16

164.

45 21 45 21

165.

85 52 85 52

166.

99 47 99 47

167.

493 370 493 370

168.

268 106 268 106

169.

5,946 4,625 5,946 4,625

170.

7,775 3,251 7,775 3,251

171.

75 47 75 47

172.

63 59 63 59

173.

461 239 461 239

174.

486 257 486 257

175.

525 179 525 179

176.

542 288 542 288

177.

6,318 2,799 6,318 2,799

178.

8,153 3,978 8,153 3,978

179.

2,150 964 2,150 964

180.

4,245 899 4,245 899

181.

43,650 8,982 43,650 8,982

182.

35,162 7,885 35,162 7,885

Translate Word Phrases to Algebraic Expressions

In the following exercises, translate and simplify.

183.

The difference of 1010 and 33

184.

The difference of 1212 and 88

185.

The difference of 1515 and 44

186.

The difference of 1818 and 77

187.

Subtract 66 from 99

188.

Subtract 88 from 99

189.

Subtract 2828 from 7575

190.

Subtract 5959 from 8181

191.

4545 decreased by 2020

192.

3737 decreased by 2424

193.

9292 decreased by 6767

194.

7575 decreased by 4949

195.

1212 less than 1616

196.

1515 less than 1919

197.

3838 less than 6161

198.

4747 less than 6262

Mixed Practice

In the following exercises, simplify.

199.

76 47 76 47

200.

91 53 91 53

201.

256 184 256 184

202.

305 262 305 262

203.

719 + 341 719 + 341

204.

647 + 528 647 + 528

205.

2,015 1,993 2,015 1,993

206.

2,020 1,984 2,020 1,984

In the following exercises, translate and simplify.

207.

Seventy-five more than thirty-five

208.

Sixty more than ninety-three

209.

1313 less than 4141

210.

2828 less than 3636

211.

The difference of 100100 and 7676

212.

The difference of 1,0001,000 and 945945

Subtract Whole Numbers in Applications

In the following exercises, solve.

213.

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?

214.

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?

215.

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?

216.

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?

217.

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?

218.

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?

219.

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?

220.

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

Everyday Math

221.

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?

222.

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

223.

Explain how subtraction and addition are related.

224.

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?

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