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Prealgebra 2e

1.3 Subtract Whole Numbers

Prealgebra 2e1.3 Subtract Whole Numbers
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

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.

Manipulative Mathematics

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

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.

159159

142.

18161816

143.

42354235

144.

83648364

145.

675350675350

146.

790525790525

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

147.

5252

148.

8484

149.

6363

150.

7575

151.

185185

152.

198198

153.

178178

154.

179179

155.

35133513

156.

32113211

157.

61476147

158.

55365536

Subtract Whole Numbers

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

159.

9494

160.

9393

161.

8080

162.

2020

163.

38163816

164.

45214521

165.

85528552

166.

99479947

167.

493370493370

168.

268106268106

169.

5,9464,6255,9464,625

170.

7,7753,2517,7753,251

171.

75477547

172.

63596359

173.

461239461239

174.

486257486257

175.

525179525179

176.

542288542288

177.

6,3182,7996,3182,799

178.

8,1533,9788,1533,978

179.

2,1509642,150964

180.

4,2458994,245899

181.

43,6508,98243,6508,982

182.

35,1627,88535,1627,885

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.

76477647

200.

91539153

201.

256184256184

202.

305262305262

203.

719+341719+341

204.

647+528647+528

205.

2,0151,9932,0151,993

206.

2,0201,9842,0201,984

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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