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Prealgebra 2e

Chapter 4

Prealgebra 2eChapter 4

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Table of contents
  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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. 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

Be Prepared

4.1

11 11

4.2

2 > 5 2 > 5

4.3

2 2 2 2 3 2 2 2 2 3

4.5

Answers may vary. Acceptable answers include 1012,1518,5060,1012,1518,5060, etc.

4.6

3 3

4.7

1 12 1 12

4.8

13 5 13 5

4.9

5 x + 5 5 x + 5

4.11

5 6 5 6

4.12

10 12 , 15 18 10 12 , 15 18

4.13

2 2

4.15

2 3 4 2 3 4

4.16

7 2 7 2

4.17

1 1

4.18

y = 6 y = 6

4.19

- 6 - 6

Try It

4.1
  1. 3838
  2. 4949
4.2
  1. 3535
  2. 3434
4.9

5 3 = 1 2 3 5 3 = 1 2 3

4.10

13 8 = 1 5 8 13 8 = 1 5 8

4.13

1 2 7 1 2 7

4.14

1 3 4 1 3 4

4.15

11 8 11 8

4.16

11 6 11 6

4.17

1 6 7 . 1 6 7 .

4.18

1 5 9 1 5 9

4.19

3 2 7 3 2 7

4.20

4 4 11 4 4 11

4.21

26 7 26 7

4.22

23 8 23 8

4.23

50 11 50 11

4.24

34 3 34 3

4.25

2

4.26

3

4.27

Correct answers include 610,915,610,915, and 1220.1220.

4.28

Correct answers include 810,1215,810,1215, and 1620.1620.

4.29

18 21 18 21

4.30

30 100 30 100

4.35
  1. >
  2. >
  3. <
  4. <
4.36
  1. >
  2. <
  3. >
  4. <
4.37

2 3 2 3

4.38

3 4 3 4

4.39

3 4 3 4

4.40

2 3 2 3

4.41

9 7 9 7

4.42

9 5 9 5

4.43

23 40 23 40

4.44

5 8 5 8

4.45

x y x y

4.46

a b a b

4.47

3 10 3 10

A rectangle is shown, divided vertically into five equal pieces. Three of the pieces are shaded. The first three pieces of the rectangle are divided by a horizontal line, creating six equal pieces. Three of the six pieces are darkly shaded.
4.48

5 12 5 12

A rectangle is shown, divided vertically into six equal pieces. Five of the pieces are shaded.
4.49

2 15 2 15

4.50

21 40 21 40

4.51

5 14 5 14

4.52

14 27 14 27

4.53

4 21 4 21

4.54

3 16 3 16

4.55
  1. 9
  2. −33a
4.56
  1. 2424
  2. 44x344x3
4.57
  1. 7575
  2. −8−8
  3. 411411
  4. 114114
4.58
  1. 7373
  2. 1212
  3. 914914
  4. 121121
4.61

2


A rectangle is shown, labeled as one third. Below it is an identical rectangle split into two equal pieces, each labeled as one sixth.
4.62

2


A rectangle is shown, labeled as one half. Below it is an identical rectangle split into two equal pieces, each labeled as one fourth.
4.63

6


Two rectangles are shown, each labeled as 1. Below it are two identical rectangle, each split into three pieces. Each of the six pieces is labeled as one third.
4.64

6


Three rectangles are shown, each labeled as 1. Below are three identical rectangles, each split into 2 equal pieces. Each of these six pieces is labeled as one half.
4.65

9 14 9 14

4.66

10 21 10 21

4.67

21 5 p 21 5 p

4.68

15 8 q 15 8 q

4.69

4 5 4 5

4.70

5 4 5 4

4.71

4 15 4 15

4.72

2 3 2 3

4.73

2

4.74

9 4 9 4

4.75

−15

4.76

85 6 85 6

4.77

5 8 5 8

4.78

7 8 7 8

4.79

2

4.80

5 2 5 2

4.81

9 s 14 9 s 14

4.82

5 y 6 5 y 6

4.83

a b c d a b c d

4.84

p + q r p + q r

4.85

4 5 4 5

4.86

11 14 11 14

4.87

2 7 2 7

4.88

10 3 10 3

4.89

3 4 b 3 4 b

4.90

4 q 4 q

4.91

25 49 . 25 49 .

4.92

1 2 1 2

4.93

3 5 , 3 −5 3 5 , 3 −5

4.94

−2 7 , 2 −7 −2 7 , 2 −7

4.95

10 9 10 9

4.96

1 2 1 2

4.97

−3 4 −3 4

4.98

2 3 2 3

4.99

2 9 2 9

4.100

8 5 8 5

4.103

5 8 5 8

A circle divided into 8 sections, 5 of which are shaded.
4.104

5 6 5 6

A circle divided into 6 sections, 5 of which are shaded.
4.105

5 6 5 6

4.107

x + 3 4 x + 3 4

4.108

y + 5 8 y + 5 8

4.109

1 d 1 d

4.110

3 m 3 m

4.111

9 p 8 9 p 8

4.112

9 q 5 9 q 5

4.113

2 3 2 3

4.114

2 3 2 3

4.115

3838, models may differ.

4.116

1616, models may differ

4.117

3 7 3 7

4.118

1 2 1 2

4.119

x 2 7 x 2 7

4.120

y 13 14 y 13 14

4.121

16 x 16 x

4.122

22 a 22 a

4.123

−1

4.124

2 3 2 3

4.125

60

4.126

15

4.127

96

4.128

224

4.129

9 12 , 10 12 9 12 , 10 12

4.130

35 60 , 44 60 35 60 , 44 60

4.131

52 96 , 51 96 52 96 , 51 96

4.132

72 224 , 189 224 72 224 , 189 224

4.133

7 12 7 12

4.134

7 10 7 10

4.135

5 8 5 8

4.136

1 2 1 2

4.137

79 60 79 60

4.138

103 60 103 60

4.139

1 96 1 96

4.140

75 224 75 224

4.141

37 210 37 210

4.142

25 96 25 96

4.143

3 y + 14 18 3 y + 14 18

4.144

5 x + 14 30 5 x + 14 30

4.145
  1. 11121112
  2. 1818
4.146
  1. 103103
  2. 13121312
4.147
  1. (27a32)36(27a32)36
  2. 2a32a3
4.148
  1. (24k+25)30(24k+25)30
  2. 24k2524k25
4.149

1 90 1 90

4.150

272

4.152

2 7 2 7

4.153
  1. −1−1
  2. 1212
4.154
  1. 7676
  2. 1414
4.155

3 4 3 4

4.156

23 8 23 8

4.157

1 2 1 2

4.158

2 3 2 3

4.159

5 2 5 2

4.160

3 2 3 2

4.163

423423

The figure shows five circles. The last two are divided into six equal sections. Two sections of the last circle are white.
4.164

312312

The figure shows four circles. The last two are divided into eight equal sections. Four sections of the last circle are white.
4.165

5 6 7 5 6 7

4.166

7 9 11 7 9 11

4.167

16 1 2 16 1 2

4.168

15 1 3 15 1 3

4.169

9 1 3 9 1 3

4.170

6 3 5 6 3 5

4.171

3434

No alt text
4.172

4545

No alt text
4.173

9595

No alt text
4.174

5353

No alt text
4.175

2323

No alt text
4.176

3434

No alt text
4.177

2323

A circle divided into three sections, two of which are shaded.
4.178

2525

A circle divided into 5 sections, 2 of which are shaded.
4.179

2 2 3 2 2 3

4.180

1 5 7 1 5 7

4.181

2 2 3 2 2 3

4.182

1 5 7 1 5 7

4.183

6 7 12 6 7 12

4.184

12 3 10 12 3 10

4.185

4 7 10 4 7 10

4.186

2 11 12 2 11 12

4.187

41 8 41 8

4.188

757 63 757 63

4.189
  1. no
  2. yes
  3. no
4.190
  1. no
  2. no
  3. yes
4.191

1 2 1 2

4.192

4 15 4 15

4.193

−1

4.194

6 7 6 7

4.195

19 3 19 3

4.196

23 2 23 2

4.197

−125

4.198

−243

4.199

245

4.200

132

4.201

−48

4.202

23

4.203

35

4.204

18

4.205

−91

4.206

−108

4.207

n 7 = −21 ; n = −147 n 7 = −21 ; n = −147

4.208

n 8 = −56 ; n = −448 n 8 = −56 ; n = −448

4.209

q −8 = 72 ; q = −576 q −8 = 72 ; q = −576

4.210

p −9 = 81 ; p = −729 p −9 = 81 ; p = −729

4.211

2 5 f = 16 ; f = 40 2 5 f = 16 ; f = 40

4.212

3 4 f = 21 ; f = 28 3 4 f = 21 ; f = 28

4.213

n 2 3 = 5 12 ; n = 5 18 n 2 3 = 5 12 ; n = 5 18

4.214

c 3 8 = 4 9 ; c = 1 6 c 3 8 = 4 9 ; c = 1 6

4.215

5 8 + x = 1 4 ; x = 3 8 5 8 + x = 1 4 ; x = 3 8

4.216

1 3 4 x = 5 6 ; x = 11 12 1 3 4 x = 5 6 ; x = 11 12

Section 4.1 Exercises

1.
  1. 1414
  2. 3434
  3. 3838
  4. 5858
3.


A circle is shown. It is divided into 2 equal pieces. 1 piece is shaded.
5.


A circle is shown. It is divided into 4 equal pieces. 3 pieces are shaded.
7.


A circle is shown. It is divided into 6 equal pieces. 5 pieces are shaded.
9.


A circle is shown. It is divided into 8 equal pieces. 5 pieces are shaded.
11.


A circle is shown. It is divided into 3 equal pieces. All 3 pieces are shaded.
13.


Two circles are shown. Each is divided into 6 equal pieces. All 6 pieces are shaded in the circle on the left. 1 piece is shaded in the circle on the right.
15.


Two circles are shown. Each is divided into 5 equal pieces. All 5 pieces are shaded in the circle on the left. 2 pieces are shaded in the circle on the right.
17.
  1. 54=11454=114
  2. 74=13474=134
  3. 118=138118=138
19.
  1. 114=234114=234
  2. 198=238198=238
21.


A circle is shown. It is divided into 4 equal pieces. All 4 pieces are shaded.
23.


Two circles are shown. Each is divided into 3 equal pieces. All 3 pieces are shaded in the circle on the left. 2 pieces are shaded in the circle on the right.
25.


Two circles are shown. Each is divided into 8 equal pieces. All 8 pieces are shaded in the circle on the left. 5 pieces are shaded in the circle on the right.
27.


Three circles are shown. Each is divided into 4 equal pieces. All 4 pieces are shaded in the two circles on the left. 1 piece is shaded in the circle on the right.
29.

1 2 3 1 2 3

31.

2 3 5 2 3 5

33.

3 1 9 3 1 9

35.

3 2 15 3 2 15

37.

7 5 7 5

39.

17 6 17 6

41.

19 7 19 7

43.

32 9 32 9

45.

4

47.

9

49.

9

51.

Answers may vary. Correct answers include 26,39,412.26,39,412.

53.

Answers may vary. Correct answers include 1012,1518,2024.1012,1518,2024.

55.

Answers may vary. Correct answers include 1018,1527,2036.1018,1527,2036.

57.


A number line is shown. The numbers 0, 1, 2, 3, 4, 5, and 6 are labeled. Between 0 and 1, 1 third is labeled and shown with a red dot. Between 1 and 2, 7 fourths is labeled and shown with a red dot. Between 2 and 3, 13 fifths is labeled and shown with a red dot.
59.


A number line is shown. The numbers 0, 1, 2, 3, 4, 5, and 6 are labeled. Between 0 and 1, 7 tenths is labeled and shown with a red dot. Between 1 and 2, 13 eighths is labeled and shown with a red dot. Between 2 and 3, 5 halves is labeled and shown with a red dot. 3 is labeled and shown with a red dot.
61.


A number line is shown. The numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4 are labeled. Between negative 3 and negative 2, negative 2 and 1 third is labeled and shown with a red dot. Between 2 and 3, 2 and 1 third is labeled and shown with a red dot.
63.


A number line is shown. The numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4 are labeled. Between negative 3 and negative 2, negative 8 thirds is labeled and shown with a red dot. Between negative 2 and negative 1, negative 1 and 3 fourths is labeled and shown with a red dot. Between negative 1 and 0, negative 2 fifths is labeled and shown with a red dot. Between 0 and 1, 2 fifths is labeled and shown with a red dot. Between 1 and 2, 1 and 3 fourths is labeled and shown with a red dot. Between 2 and 3, 8 thirds is labeled and shown with a red dot.
65.

<

67.

>

69.

<

71.

<

73.
  1. 2
  2. 614614
75.

Answers will vary.

Section 4.2 Exercises

77.

1 3 1 3

79.

3 4 3 4

81.

5 11 5 11

83.

12 7 12 7

85.

10 21 10 21

87.

7 8 7 8

89.

x y x y

91.

x 4 y x 4 y

93.

2 x 2 3 y 2 x 2 3 y

95.

1313

No alt text
97.

518518

No alt text
99.

2 15 2 15

101.

27 40 27 40

103.

1 4 1 4

105.

1 6 1 6

107.

2 9 2 9

109.

21 50 21 50

111.

11 30 11 30

113.

20 11 20 11

115.

9n

117.

7p

119.

−34

121.

3 8 3 8

123.

8 27 8 27

125.

1296 625 1296 625

127.

4 3 4 3

129.

17 5 17 5

131.

8 11 8 11

133.

1 19 1 19

135.

1

136.


No alt text
137.


A table is shown with four columns and five rows. The first row reads Number, Opposite, Absolute Value, and Reciprocal. The second row reads negative three thirteenths, three thirteenths, three thirteenths, negative thirteen thirds. The third row reads nine fourteenths, negative nine fourteenths, nine fourteenths, and fourteen ninths. The fourth row reads fifteen sevenths, negative fifteen sevenths, fifteen sevenths, and seven fifteenths. The last row reads negative nine, nine, nine, negative one ninth.
139.

4

No alt text
141.

12

No alt text
143.

4

145.

16 15 16 15

147.

5 4 5 4

149.

1

151.

18 5 y 18 5 y

153.

25 2 c 25 2 c

155.

3 4 3 4

157.

2 9 2 9

159.

14 r 15 s 14 r 15 s

161.

−12

163.

1 25 1 25

165.

9

167.

8 7 8 7

169.
  • 4·234·23 cups=83=83 cups=223=223 cups
  • Answers will vary.
171.

1818 yard

173.

Answers will vary.

175.

Answers will vary.

Section 4.3 Exercises

177.

44 21 44 21

179.

35 8 35 8

181.

16 3 16 3

183.

63 16 63 16

185.

3 2 3 2

187.

4 3 4 3

189.

2

191.

5

193.

7 v 13 7 v 13

195.

a b a b

197.

A 3 B A 3 B

199.

3 2 3 2

201.

15 22 15 22

203.

3 10 3 10

205.

1 6 1 6

207.

3 r 5 s 3 r 5 s

209.

9 2 y 9 2 y

211.

28

213.

1 18 1 18

215.

−4 9 , 4 9 −4 9 , 4 9

217.

13 −6 , −13 6 13 −6 , −13 6

219.

12 7 12 7

221.

5 2 5 2

223.

23 4 23 4

225.

1 3 1 3

227.

4 5 4 5

229.

1 2 1 2

231.

2

233.

5 6 5 6

235.

26 25 26 25

237.

11 6 11 6

239.

5 2 5 2

241.

−10

243.

−2

245.

51 20 51 20

247.

18 7 18 7

249.
  1. 43=11343=113 cups
  2. 803=2623803=2623 cups
251.

Answers will vary.

253.

Answers will vary.

Section 4.4 Exercises

255.


A circle is divided into 10 equal pieces. 7 of the pieces are shaded.


710710

257.


A circle is divided into 8 equal pieces. 6 of the pieces are shaded.


3434

259.

7 9 7 9

261.

16 15 16 15

263.

y + 2 3 y + 2 3

265.

14 q 14 q

267.

9 a 7 9 a 7

269.

−4 x 5 −4 x 5

271.

3 4 3 4

273.

7 8 7 8

275.

8 19 8 19

277.

13 12 13 12

279.


A circle is divided into eight sections, three of which are shaded.


1212

281.

1 5 1 5

283.

5 13 5 13

285.

1 6 1 6

287.

8 3 8 3

289.

x 8 19 x 8 19

291.

11 z 8 13 11 z 8 13

293.

14 c 14 c

295.

55 v 55 v

297.

3 d 11 3 d 11

299.

14 s 3 14 s 3

301.

2 7 2 7

303.

3 11 3 11

305.

1 8 1 8

307.

6 s 11 6 s 11

309.

2 9 2 9

311.

49 27 49 27

313.

1414 cup

315.

No, adding up the number of pieces gives 13121312, which is greater than 1. (Answers may vary.)

Section 4.5 Exercises

317.

20

319.

48

321.

240

323.

245

325.

60

327.

5 20 , 4 20 5 20 , 4 20

329.

14 24 , 15 24 14 24 , 15 24

331.

33 48 , 20 48 33 48 , 20 48

333.

20 60 , 45 60 , 36 60 20 60 , 45 60 , 36 60

335.

9 20 9 20

337.

11 24 11 24

339.

3 8 3 8

341.

2 3 2 3

343.

23 20 23 20

345.

19 24 19 24

347.

1 48 1 48

349.

1 24 1 24

351.

1 12 1 12

353.

7 60 7 60

355.

53 80 53 80

357.

291 245 291 245

359.

1 20 1 20

361.

11 40 11 40

363.

11 6 11 6

365.

7 10 7 10

367.

3 y + 4 6 3 y + 4 6

369.

4 x 5 20 4 x 5 20

371.
  1. 5656
  2. 44
373.
  1. 37403740
  2. 110110
375.
  1. 9a149a14
  2. 9a14249a1424
377.
  1. 4q274q27
  2. 1225q451225q45
381.

11 24 11 24

383.

7 18 7 18

385.

2 15 2 15

387.

−33 8 x 88 −33 8 x 88

389.

16 39 16 39

391.

1 81 1 81

393.

32

395.

36 25 36 25

397.

60 7 60 7

399.

15 2 15 2

401.

3 13 3 13

403.

19 30 19 30

405.

−9

407.

91 60 91 60

409.

11 40 11 40

411.

5 6 5 6

413.

1

415.

22 7 22 7

417.
  1. 1212
  2. −1−1
419.
  1. 0 0
  2. 1616
421.
  1. 1313
  2. −1−1
423.
  1. 1616
  2. 2323
425.

4 15 4 15

427.

9 16 9 16

429.

−2

431.

3

433.

She needs 238238 cups

435.

Answers will vary.

Section 4.6 Exercises

437.


Four circles are shown. The first three are shaded. The last circle is divided into 3 equal parts. 2 parts are shaded.


323323

439.


Four circles are shown. The first three are shaded. The last circle is divided into 3 equal parts. 2 parts are shaded.


323323

441.

7 5 9 7 5 9

443.

11

445.

11 1 3 11 1 3

447.

11 1 3 11 1 3

449.


A circle is shown. It is divided into 8 equal pieces. 4 pieces are shaded.


1212

451.

1 1 6 1 1 6

453.

6 2 5 6 2 5

455.

1 7 9 1 7 9

457.

5 6 5 6

459.

7 11 12 7 11 12

461.

16 1 6 16 1 6

463.

5 11 20 5 11 20

465.

−1 11 24 −1 11 24

467.

6 17 18 6 17 18

469.

7 9 7 9

471.

23

473.

8 3 4 8 3 4

475.

4 15 4 15

477.

5 3 5 5 3 5

479.

1 16 1 16

481.

13 1 13 13 1 13

483.

7 1 30 7 1 30

485.

10 27 10 27

487.

2 7 45 2 7 45

489.

17 24 17 24

491.

712712 yards

493.

13141314 inches

495.

Answers will vary.

497.

Answers will vary.

Section 4.7 Exercises

499.
  1. no
  2. yes
  3. no
501.
  1. no
  2. yes
  3. no
503.

m = 1 2 m = 1 2

505.

h = 2 3 h = 2 3

507.

c = −1

509.

z = −1

511.

p = 37 40 p = 37 40

513.

k = 7 15 k = 7 15

515.

k = 18 7 k = 18 7

517.

v = 11 3 v = 11 3

519.

b = −27

521.

x = −256

523.

q = 160

525.

s = 45

527.

y = −42

529.

k = 17 20 k = 17 20

531.

p = 100

533.

m = −16

535.

b = −21

537.

v = 36

539.

y = 0

541.

g = 1 9 g = 1 9

543.

q = 3 4 q = 3 4

545.

n = 14 5 n = 14 5

547.

y = 25 24 y = 25 24

549.

d = 8 15 d = 8 15

551.

n 6 = −24 ; n = −144 n 6 = −24 ; n = −144

553.

m −7 = −8 ; m = 56 m −7 = −8 ; m = 56

555.

f −4 = −20 ; f = 80 f −4 = −20 ; f = 80

557.

g 9 = 14 ; g = 126 g 9 = 14 ; g = 126

559.

2 5 q = 20 ; q = 50 2 5 q = 20 ; q = 50

561.

4 9 p = −28 ; p = −63 4 9 p = −28 ; p = −63

563.

h 2 = 43 ; h = 86 h 2 = 43 ; h = 86

565.

a 2 3 = 3 4 ; a = 1 2 a 2 3 = 3 4 ; a = 1 2

567.

3 4 + x = 1 8 ; x = 5 8 3 4 + x = 1 8 ; x = 5 8

569.

y 1 3 = 1 6 ; y = 1 6 y 1 3 = 1 6 ; y = 1 6

571.

30 inches

573.

Answers will vary.

Review Exercises

575.

5 9 5 9

577.

3 2 = 1 1 2 3 2 = 1 1 2

579.

5 8 11 5 8 11

581.

49 5 49 5

583.

Answers may vary.

585.


A number line is shown. Integers from negative 4 to 4 are labeled. Between negative 4 and negative 3, negative 7 halves is labeled and marked with a red dot. Between negative 2 and negative 1, negative 1 and 1 third is labeled and marked with a red dot. Between negative 1 and 0, negative 1 fourth is labeled and marked with a red dot. Between 0 and 1, 1 fourth is labeled and marked with a red dot. Between 1 and 2, 1 and 1 third is labeled and marked with a red dot. Between 3 and 4, 7 halves is labeled and marked with a red dot.
587.

>

589.

3 4 3 4

591.

x y x y

593.

4 7 4 7

595.

24 m 11 24 m 11

597.

6

599.

4 15 4 15

601.

−4

603.

4

605.

4 15 4 15

607.

5 2 b 5 2 b

609.

268 11 268 11

611.

8

613.

V h 6 V h 6

615.

2 9 2 9

617.

22

619.

7 36 7 36

621.

5 8 5 8

623.

3 5 3 5

625.

x + 7 10 x + 7 10

627.

1 2 1 2

629.

19 15 19 15

631.

8 15 8 15

633.

15

635.

60

637.

924924 and 20242024

639.

2060,45602060,4560 and 48604860

641.

1 4 1 4

643.

77 90 77 90

645.

3 y 10 30 3 y 10 30

647.

14 d 11 14 d 11

649.

256 225 256 225

651.
  1. 8585
  2. 11201120
653.

13 2 3 13 2 3

655.

8 1 11 8 1 11

657.

5 1 10 5 1 10

659.

1 1 3 1 1 3

661.
  1. no
  2. yes
  3. no
663.

n = 5 11 n = 5 11

665.

h = 51 40 h = 51 40

667.

z = −23

669.

q 1 10 = 1 2 ; q = 3 5 q 1 10 = 1 2 ; q = 3 5

671.

3 8 y = 24 ; y = 64 3 8 y = 24 ; y = 64

Practice Test

673.

23 7 23 7

675.

1 4 1 4

677.

1 4 1 4

679.

16u

681.

−2

683.

12 25 12 25

685.

5

687.

5 p 2 q 5 p 2 q

689.

13

691.

7 13 7 13

693.

−1

695.

9 4 x 9 4 x

697.

3

699.

y = 4 5 y = 4 5

701.

f = 13 12 f = 13 12

703.

c = −27

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