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Prealgebra 2e

Chapter 5

Prealgebra 2eChapter 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. 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

Be Prepared

5.1

Four million, nine hundred twenty-six thousand, fifteen

5.2

750750

5.3

5.4

710710

5.5

2710027100

5.6

44

5.7

0.030.03

5.8

>>

5.9

<<

5.10

512512

5.11

2020

5.12

294294

5.13

55

5.14

5050

5.15

2.52.5

5.16

2323

5.17

0.240.24

5.18

611611

5.19

8181

5.20

3.853.85

5.21

960960

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
  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. 53105310
  2. 6710067100
  3. 117500117500
5.8
  1. 87108710
  2. 1310013100
  3. 31253125
5.9


This image shows a number line from 0.0 to 1.0 and segmented into tenths.  A point is plotted at 0.6 on the number line.
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

2.452.45

5.60

2.3182.318

5.61

5.275

5.62

6.35

5.63

>

5.64

<

5.65

<

5.66

>

5.67

45,0.82,7845,0.82,78

5.68

34,1316,0.83534,1316,0.835

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. 220147m220147m
  2. 5503087sq. m5503087sq. m
5.78
  1. 4021in.4021in.
  2. 200693sq.in.200693sq.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=−15.3q−3.4=4.5;q=−15.3

5.94

r−2.6=2.5;r=−6.5r−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

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

5.107

2

5.108

5

5.109

21

5.110

5

5.111
  1. 110110
  2. 0.10.1
5.112
  1. 120120
  2. 0.050.05
5.113
  1. 5858
  2. 0.6250.625
5.114
  1. 2828
  2. 0.250.25
5.115
  1. 3838
  2. 3232
5.116
  1. 3838
  2. 3232
5.117
  1. 2525
  2. 103103
5.118
  1. 2929
  2. 5151
5.119

2323

5.120

922922

5.121

378378

5.122

1021910219

5.123

8383

5.124

2929

5.125

123 miles2 hours123 miles2 hours

5.126

121 miles3 hours121 miles3 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 $0.11 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. not a real number
  2. −11
5.143
  1. 7
  2. 5
5.144
  1. 17
  2. 23
5.145

6<38<76<38<7

5.146

9<84<109<84<10

5.147

≈ 3.32

5.148

≈ 3.61

5.149

y

5.150

m

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.

199100199100

29.

1571015710

31.

23910002391000

33.

1310013100

35.

111000111000

37.

71000007100000

39.

625625

41.

71207120

43.

4350043500

45.

10141014

47.

181250181250

49.

14181418

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.

0.50.5

213.

1.361.36

215.

0.1350.135

217.

7

219.

3.025

221.

10.58

223.

<

225.

>

227.

<

229.

<

231.

>

233.

>

235.

0.55,916,350.55,916,35

237.

58,1320,0.70258,1320,0.702

239.

720,13,0.3720,13,0.3

241.

79,34,−0.779,34,−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. 225mile225mile
  2. 7750sq.mile7750sq.mile
277.
  1. 3314yard3314yard
  2. 99224sq.yard99224sq.yard
279.
  1. 5521m5521m
  2. 275504sq.m275504sq.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=34q=34

333.

m=435m=435

335.

y=2524y=2524

337.

f=1120f=1120

339.

a = −0.8

341.

r = −1.45

343.

h = 24

345.

n1.9=3.4;5.3n1.9=3.4;5.3

347.

−6.2x = −4.96; 0.8

349.

y1.7=−5;8.5y1.7=−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.

120,0.05120,0.05

393.

124,0.04160.042124,0.04160.042

395.

25,0.425,0.4

397.

57,0.714285———0.71457,0.714285———0.714

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

Answers will vary.

Section 5.6 Exercises

403.

5959

405.

7878

407.

7373

409.

7373

411.

1515

413.

10171017

415.

5454

417.

2727

419.

114114

421.

1313

423.

623623

425.

82158215

427.

359359

429.

9494

431.

35 calories3 ounces35 calories3 ounces

433.

41 lbs15 sq. in.41 lbs15 sq. in.

435.

488 miles7 hours488 miles7 hours

437.

$1198 hours$1198 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 milesphours793 milesphours

475.

$30.5 lbs.$30.5 lbs.

477.

105 caloriesxounces105 caloriesxounces

479.

y5xy5x

481.

15.2 students per teacher

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

Answers will vary.

487.

Kathryn should swim for approximately 16.35 minutes. Explanations 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<98<70<9

507.

14<200<1514<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.

33403340

549.

3162531625

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.

0.540.54

585.

>

587.

>

589.

>

591.

1115,0.75,791115,0.75,79

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. 94.985 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 = 10.83

623.

$269.10

625.

$40.94

627.

24.5

629.

16 clients

631.

2

633.

15;0.215;0.2

635.

7474

637.

2323

639.

4949

641.

7979

643.

12pounds1square inch12pounds1square inch

645.

$352hours$352hours

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.

aadults45childrenaadults45children

659.

193+n193+n

661.

12

663.

−9

665.

not a real number

667.

17

669.

12<155<1312<155<13

671.

7.55

673.

8b

675.

15mn

677.

7y

679.

11cd

681.

5.5 feet

683.

72 mph

Practice Test

685.

173100173100

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. 52.1
  2. 51.5
  3. 55
709.

The unit prices are $0.172 per ounce for 64 ounces, and $0.177 per ounce for 48 ounces; 64 ounces is the better buy.

711.

12n

713.

15 feet

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