Skip to ContentGo to accessibility page
OpenStax Logo
Prealgebra

Chapter 5

PrealgebraChapter 5
  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

Try It

5.1
  1. six and seven tenths
  2. nineteen and fifty-eight hundredths
  3. eighteen thousandths
  4. negative two and fifty-three thousandths
5.2
  1. five and eight tenths three and fifty-seven hundredths
  2. three and fifty-seven hundredths
  3. five thousandths
  4. negative thirteen and four hundred sixty-one thousandths
5.3

13.68

5.4

5.894

5.5

0.058

5.6

0.067

5.7
  1. 5 3 10 5 3 10
  2. 6710067100
  3. 234 1000 234 1000
5.8
  1. 8 7 10 8 7 10
  2. 1 3 100 1 3 100
  3. 24 1000 24 1000
5.13
  1. >
  2. >
5.14
  1. <
  2. <
5.15

>

5.16

>

5.17

1.05

5.18

9.17

5.19
  1. 6.58
  2. 6.6
  3. 7
5.20
  1. 15.218
  2. 15.22
  3. 15.2
5.21

17.6

5.22

33.11

5.23

16.49

5.24

23.593

5.25

0.42

5.26

12.58

5.27

−1.53

5.28

−3.58

5.29

27.4815

5.30

87.6148

5.31

−13.427

5.32

38.122

5.33

0.00348

5.34

0.00603

5.35
  1. 25.8
  2. 258
  3. 2,580
5.36
  1. 142
  2. 1,420
  3. 14,200
5.37

0.07

5.38

0.08

5.39

$0.19

5.40

$0.42

5.41

−0.39

5.42

−0.4

5.43

587.3

5.44

34.25

5.45

200

5.46

350

5.47

$16.52

5.48

$65.97

5.49

$41.28

5.50

$48.75

5.51

$15.47

5.52

$14.25

5.53

$5.97

5.54

$43.00

5.55

0.25

5.56

0.375

5.57

−2.25

5.58

−5.5

5.59

2 . 45 2 . 45

5.60

2.3 18 2.3 18

5.61

5.275

5.62

6.35

5.63

>

5.64

<

5.65

<

5.66

>

5.67

4 5 , 0.82 , 7 8 4 5 , 0.82 , 7 8

5.68

3 4 , 13 16 , 0.835 3 4 , 13 16 , 0.835

5.69
  1. −183.2
  2. 4.5
5.70
  1. −776.25
  2. 2.2
5.71

11.16

5.72

1.51

5.73
  1. 314 in.
  2. 7850 sq. in.
5.74
  1. 628 ft.
  2. 31,400 sq. ft.
5.75
  1. 325.304 cm
  2. 8425.3736 sq. cm
5.76
  1. 165.792 m
  2. 2188.4544 sq. m
5.77
  1. 220 147 m 220 147 m
  2. 550 3087 sq. m 550 3087 sq. m
5.78
  1. 40 21 in. 40 21 in.
  2. 200 693 sq.in. 200 693 sq.in.
5.79
  1. no
  2. yes
  3. no
5.80
  1. yes
  2. no
  3. no
5.81

y = −8

5.82

y = −8.4

5.83

a = 1.07

5.84

n = 0.83

5.85

b = −12

5.86

c = −8

5.87

c = 11.7

5.88

b = 6.48

5.89

y − 4.9 = 2.8; y = 7.7

5.90

z − 5.7 = 3.4; z = 9.1

5.91

−4.3x = 12.04; x = −2.8

5.92

−3.1m = 26.66; m = −8.6

5.93

q −3.4 = 4.5 ; q = −15.3 q −3.4 = 4.5 ; q = −15.3

5.94

r −2.6 = 2.5 ; r = −6.5 r −2.6 = 2.5 ; r = −6.5

5.95

j + 3.8 = 2.6; j = −1.2

5.96

k + 4.7 = 0.3; k = −4.4

5.97

8.5

5.98

9

5.99

21.5 years years

5.100

10

5.101

$7.19

5.102

$39.62

5.103

43

5.104

30

5.105

8.5

5.106

20.5

5.109

21

5.111
  1. 1 10 1 10
  2. 0.1 0.1
5.112
  1. 1 20 1 20
  2. 0.05 0.05
5.113
  1. 5 8 5 8
  2. 0.625 0.625
5.114
  1. 2 8 2 8
  2. 0.25 0.25
5.115
  1. 3838
  2. 3232
5.116
  1. 3838
  2. 3232
5.117
  1. 2 5 2 5
  2. 10 3 10 3
5.118
  1. 2929
  2. 5151
5.119

2 3 2 3

5.120

9 22 9 22

5.121

37 8 37 8

5.122

102 19 102 19

5.123

8 3 8 3

5.124

2 9 2 9

5.125

123 miles 2 hours 123 miles 2 hours

5.126

121 miles 3 hours 121 miles 3 hours

5.127

$18.00/hour

5.128

$19.00/hour

5.129

23.5 mpg

5.130

28 mpg

5.131

$0.29/box

5.132

$0.53/bottle

5.133

Brand A costs $0.12 per bag. Brand B costs $0.13 per bag. Brand A is the better buy.

5.134

Brand C costs $0.07 per ounce. Brand D costs $0.09 per ounce. Brand C is the better buy.

5.135
  1. 689 mi/h hours
  2. y parents/22 students
  3. $d/9 min
5.136
  1. m mi/9 h
  2. x students/8 buses
  3. $y/40 h
5.137
  1. 6
  2. 13
5.138
  1. 4
  2. 14
5.139
  1. −2
  2. −15
5.140
  1. −9
  2. −8
5.141
  1. not a real number
  2. −9
5.142
  1. −7
  2. not a real number
5.143
  1. 7
  2. 5
5.144
  1. 17
  2. 23
5.145

6 < 38 < 7 6 < 38 < 7

5.146

9 < 84 < 10 9 < 84 < 10

5.147

≈ 3.32

5.148

≈ 3.61

5.151

8x

5.152

13y

5.153

−11y

5.154

−10p

5.155

10ab

5.156

15mn

5.157

19.2 feet

5.158

52 centimeters

5.159

9 seconds

5.160

3.5 seconds

5.161

42.7 mph

5.162

54.1 mph

Section 5.1 Exercises

1.

five and five tenths

3.

five and one hundredth

5.

eight and seventy-one hundredths

7.

two thousandths

9.

three hundred eighty-one thousandths

11.

negative seventeen and nine tenths

13.

8.03

15.

29.81

17.

0.7

19.

0.001

21.

0.029

23.

−11.0009

25.

13.0395

27.

1 99 100 1 99 100

29.

15 7 10 15 7 10

31.

239 1000 239 1000

33.

13 100 13 100

35.

11 1000 11 1000

37.

7 100000 7 100000

39.

6 2 5 6 2 5

41.

7 1 20 7 1 20

43.

4 3 500 4 3 500

45.

10 1 4 10 1 4

47.

1 81 250 1 81 250

49.

14 1 8 14 1 8

51.


There is a number line shown with integers from negative 4 to 4. There is a red dot between 0 and 1 labeled 0.8.
53.


There is a number line shown with integers from negative 4 to 4. There is a red dot between negative 1 and  0 labeled negative 0.2.
55.


This is an image of a number line. It spans from negative 5 on the left to 5 on the right. To the right of 0 are tick marks with the numbers 1, 2, 3, 4, 5 on the number line. To the left of the zero are tick marks with the numbers negative 1, negative 2, negative 3, negative 4, and negative 5. A point is plotted at 3.1.
57.


There is a number line shown with integers from negative 4 to 4. There is a red dot between negative 3 and negative 2 labeled negative 2.5.
59.

>

61.

<

63.

>

65.

>

67.

<

69.

<

71.

0.7

73.

2.8

75.

0.85

77.

5.79

79.

0.30

81.

4.10

83.
  1. 5.78
  2. 5.8
  3. 6
85.
  1. 63.48
  2. 63.5
  3. 63
87.
  1. $58,966
  2. $59,000
  3. $60,000
89.
  1. $142.19
  2. $142
91.

Answers will vary.

93.

Tim had the faster time. 12.3 is less than 12.32, so Tim had the faster time.

Section 5.2 Exercises

95.

24.48

97.

170.88

99.

−9.23

101.

49.73

103.

−40.91

105.

−7.22

107.

−13.5

109.

35.8

111.

−27.5

113.

15.73

115.

42.51

117.

102.212

119.

51.31

121.

−4.89

123.

0.12

125.

0.144

127.

42.008

129.

26.7528

131.

−11.653

133.

337.8914

135.

2.2302

137.

1.305

139.

92.4

141.

55,200

143.

0.03

145.

0.19

147.

$0.71

149.

$2.44

151.

3

153.

−4.8

155.

35

157.

2.08

159.

150

161.

20

163.

19.2

165.

12.09

167.

32.706

169.

$48.60

171.

20

173.

2

175.

$17.80

177.

$24.89

179.

$29.06

181.

$3.19

183.

181.7 pounds

185.

$15.00

187.

$296.00

189.

$12.75

191.
  1. $3
  2. $2
  3. $1.50
  4. $1.20
  5. $1
193.

$18.64

195.

$259.45

197.
  1. $243.57
  2. $79.35
199.

The difference: 0.03 seconds. Three hundredths of a second.

Section 5.3 Exercises

201.

0.4

203.

−0.375

205.

0.85

207.

2.75

209.

−12.4

211.

0 . 5 0 . 5

213.

1 . 36 1 . 36

215.

0 . 135 0 . 135

217.

7

219.

3.025

221.

10.58

223.

<

225.

>

227.

<

229.

<

231.

>

233.

>

235.

0.55 , 9 16 , 3 5 0.55 , 9 16 , 3 5

237.

5 8 , 13 20 , 0.702 5 8 , 13 20 , 0.702

239.

7 20 , 1 3 , 0.3 7 20 , 1 3 , 0.3

241.

7 9 , 3 4 , −0.7 7 9 , 3 4 , −0.7

243.

−187

245.

295.12

247.

6.15

249.

20.2

251.

107.11

253.

449

255.

9.14

257.

−0.23

259.

−3.25

261.

16.29

263.

632.045

265.

−5.742

267.
  1. 31.4 in
  2. 78.5 sq.in.
269.
  1. 56.52.ft.
  2. 254.34 sq.ft.
271.
  1. 288.88 cm
  2. 6644.24 sq.cm
273.
  1. 116.808 m
  2. 1086.3144 sq.m
275.
  1. 22 5 mile 22 5 mile
  2. 77 50 sq.mile 77 50 sq.mile
277.
  1. 33 14 yard 33 14 yard
  2. 99 224 sq.yard 99 224 sq.yard
279.
  1. 55 21 m 55 21 m
  2. 275 504 sq.m 275 504 sq.m
281.

$56.66

283.

Answers will vary.

Section 5.4 Exercises

285.
  1. no
  2. no
  3. yes
287.
  1. no
  2. yes
  3. no
289.

y = 2.8

291.

f = −0.85

293.

a = −7.9

295.

c = −4.65

297.

n = 4.4

299.

x = −3.5

301.

j = −4.68

303.

m = −1.42

305.

x = 7

307.

c = −5

309.

p = 3

311.

q = −80

313.

x = 20

315.

z = 2.7

317.

a = −8

319.

x = −0.28

321.

p = 8.25

323.

r = 7.2

325.

x = −6

327.

p = −10

329.

m = 8

331.

q = 3 4 q = 3 4

333.

m = 4 35 m = 4 35

335.

y = 25 24 y = 25 24

337.

f = 11 20 f = 11 20

339.

a = −0.8

341.

r = −1.45

343.

h = 24

345.

n 1.9 = 3.4 ; 5.3 n 1.9 = 3.4 ; 5.3

347.

−6.2x = −4.96; 0.8

349.

y 1.7 = −5 ; 8.5 y 1.7 = −5 ; 8.5

351.

n + (−7.3) = 2.4; 9.7

353.

$104

355.

Answers will vary.

Section 5.5 Exercises

357.

4

359.

35

361.

245.5

363.

11.65

365.

$18.84

367.

19.5 minutes

369.

0.329

371.

21

373.

45

375.

4.5

377.

99.65

379.

$6.50

381.

40.5 months

383.

2

385.

22

387.

2 children

389.

11 units

391.

1 20 , 0.05 1 20 , 0.05

393.

1 24 , 0.041 6 0.042 1 24 , 0.041 6 0.042

395.

4 10 , 0.4 4 10 , 0.4

397.

10 14 , 0 . 714285 ——— 0.714 10 14 , 0 . 714285 ——— 0.714

399.
  1. $285.47
  2. $275.63
  3. $236.25
401.

Answers will vary.

Section 5.6 Exercises

403.

5 9 5 9

405.

7 8 7 8

407.

7 3 7 3

409.

7 3 7 3

411.

1 5 1 5

413.

10 17 10 17

415.

5 4 5 4

417.

2 7 2 7

419.

11 4 11 4

421.

1 3 1 3

423.

6 23 6 23

425.

82 15 82 15

427.

35 9 35 9

429.

9 4 9 4

431.

35 calories 3 ounces 35 calories 3 ounces

433.

41 lbs 15 sq. in . 41 lbs 15 sq. in .

435.

488 miles 7 hours 488 miles 7 hours

437.

$119 8 hours $119 8 hours

439.

11.67 calories/ounce

441.

2.73 lbs./sq. in.

443.

69.71 mph

445.

$14.88/hour

447.

32 mpg

449.

2.69 lbs./week

451.

92 beats/minute

453.

8,000

455.

$1.09/bar

457.

$1.33/pair

459.

$0.48/pack

461.

$0.60/disc

463.

$1.29/box

465.

The 50.7-ounce size costs $0.138 per ounce. The 33.8-ounce size costs $0.142 per ounce. The 50.7-ounce size is the better buy.

467.

The 18-ounce size costs $0.222 per ounce. The 14-ounce size costs $0.235 per ounce. The 18-ounce size is a better buy.

469.

The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.

471.

The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.

473.

793 miles p hours 793 miles p hours

475.

$3 0.5 lbs . $3 0.5 lbs .

477.

105 calories x ounces 105 calories x ounces

479.

y 5 x y 5 x

481.

15.2 students per teacher

483.
  1. 72 calories/ounce
  2. 3.87 grams of fat/ounce
  3. 5.73 grams carbs/once
  4. 3.33 grams protein/ounce
485.

Answers will vary.

487.

Answers will vary.

Section 5.7 Exercises

489.

6

491.

8

493.

−2

495.

−1

497.

not a real number

499.

not a real number

501.

5

503.

7

505.

8 < 70 < 9 8 < 70 < 9

507.

14 < 200 < 15 14 < 200 < 15

509.

4.36

511.

7.28

513.

y

515.

7x

517.

−8a

519.

12xy

521.

8.7 feet

523.

8 seconds

525.

15.8 seconds

527.

72 mph

529.

53.0 mph

531.

45 inches

533.

Answers will vary. 92 reads: “nine squared” and means nine times itself. The expression 99 reads: “the square root of nine” which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.

Review Exercises

535.

three hundred seventy-five thousandths

537.

five and twenty-four hundredths

539.

negative four and nine hundredths

541.

0.09

543.

10.035

545.

−0.05

547.

33 40 33 40

549.

3 16 25 3 16 25

551.

<

553.

<

555.
  1. 12.53
  2. 12.5
  3. 13
557.
  1. 5.90
  2. 5.9
  3. 6
559.

24.67

561.

24.831

563.

−2.37

565.

−1.6

567.

15,400

569.

0.18

571.

4

573.

200

575.

$28.22

577.

$1.79

579.

0.875

581.

−5.25

583.

0 . 54 0 . 54

585.

>

587.

>

589.

>

591.

11 15 , 0.75 , 7 9 11 15 , 0.75 , 7 9

593.

6.03

595.

1.975

597.

−0.22

599.
  1. 21.98 ft.
  2. 38.465 sq.ft.
601.
  1. 34.54 cm
  2. 379.94 sq.cm
603.
  1. no
  2. yes
605.
  1. no
  2. yes
607.

h = −3.51

609.

p = 2.65

611.

j = 3.72

613.

x = −4

615.

a = −7.2

617.

s = 25

619.

−5.9x = −3.54; x = 0.6

621.

m + (−4.03) = 6.8; m = 0.83

623.

$269.10

625.

$40.94

627.

24.5

629.

16 clients

631.

2

633.

1 5 ; 0.2 1 5 ; 0.2

635.

7 4 7 4

637.

2 3 2 3

639.

4 9 4 9

641.

7 9 7 9

643.

90 pounds 7.5 square inches 90 pounds 7.5 square inches

645.

$612.50 35 hours $612.50 35 hours

647.

12 pounds/sq.in.

649.

$17.50/hour

651.

$0.42

653.

$1.65

655.

$0.11, $0.12; 60 tablets for $6.49

657.

a adults 45 children a adults 45 children

659.

19 3 + n 19 3 + n

661.

12

663.

−9

665.

not a real number

667.

17

669.

12 < 155 < 13 12 < 155 < 13

671.

7.55

673.

8b

675.

15mn

677.

7y

679.

11cd

681.

5.5 feet

683.

72 mph

Practice Test

685.

1 73 100 1 73 100

687.
  1. 16.7
  2. 16.75
  3. 17
689.

18.42

691.

0.192

693.

−0.08

695.

2

697.

200

699.

1.975

701.

−1.2

703.

8.8

705.

$26.45

707.
  1. 59
  2. 51.5
  3. 55
709.

64 ounces for $10.99 is the better buy

711.

12n

713.

15 feet

Do you know how you learn best?
Kinetic by OpenStax offers access to innovative study tools designed to help you maximize your learning potential.
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/prealgebra/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/prealgebra/pages/1-introduction
Citation information

© Feb 9, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.