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Prealgebra 2e

Chapter 6

Prealgebra 2eChapter 6

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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

6.1

33 5 33 5

6.2

0.6 0.6

6.3

31 50 31 50

6.4

32 32

6.5

10.71 10.71

6.6

5 5

6.7

63 63

6.8

324 324

6.9

75 75

6.10

6.67 6.67

6.11

1 12 1 12

6.12

80 80

6.13

24 miles 2 hours 24 miles 2 hours

Try It

6.1

89 100 89 100

6.2

72 100 72 100

6.3

62 100 , 62% 62 100 , 62%

6.4

41 100 , 41% 41 100 , 41%

6.5
  1. 12251225
  2. 11101110
6.6
  1. 16251625
  2. 3232
6.7
  1. 161250161250
  2. 2323
6.8
  1. 17401740
  2. 780780
6.9
  1. 0.09
  2. 0.87
6.10
  1. ⓐ 0.03
  2. ⓑ 0.91
6.11
  1. ⓐ 1.15
  2. ⓑ 0.235
6.12
  1. ⓐ 1.23
  2. ⓑ 0.168
6.13
  1. 625625
  2. 0.240.24
6.14
  1. 11251125
  2. 0.440.44
6.15
  1. 310310
  2. 0.30.3
6.16
  1. 1818
  2. 0.1250.125
6.17
  1. 1%
  2. 17%
6.18
  1. 4%
  2. 41%
6.19
  1. 175%
  2. 8.25%
6.20
  1. 225%
  2. 9.25%
6.21
  1. 62.5%
  2. 275%
  3. 340%
6.22
  1. 87.5%
  2. 225%
  3. 160%
6.23

42.9%

6.24

57.1%

6.25

11. 1 %, or 11 1 9 % 11. 1 %, or 11 1 9 %

6.26

16 . 6 %, or 16 2 3 % 16 . 6 %, or 16 2 3 %

6.27

36

6.28

33

6.29

117

6.30

126

6.31

68

6.32

64

6.33

$26

6.34

$36

6.35

75%

6.36

80%

6.37

125%

6.38

175%

6.39

$14.67

6.40

$2.16

6.41

24.1 grams

6.42

2,375 mg

6.43

26%

6.44

37%

6.45

8.8%

6.46

50%

6.47

6.3%

6.48

10%

6.49
  1. ⓐ $45.25
  2. ⓑ $769.25
6.50
  1. ⓐ $20.50
  2. ⓑ $270.50
6.51

9%

6.52

7.5%

6.53

$273

6.54

$394.20

6.55

4%

6.56

5.5%

6.57

$450

6.58

$82

6.59
  1. ⓐ $11.60
  2. ⓑ $17.40
6.60
  1. ⓐ $256.75
  2. ⓑ $138.25
6.61
  1. $184.80
  2. 33%
6.62
  1. $60
  2. 15%
6.63
  1. $600
  2. $1,800
6.64
  1. $2,975
  2. $11,475
6.65

$160

6.66

$56

6.67

$2,750

6.68

$3,560

6.69

4.5%

6.70

6.5%

6.71

$142.50

6.72

$7,020

6.73

6%

6.74

4%

6.75

$11,450

6.76

$9,600

6.77

$57.00

6.78

$143.50

6.79
  1. 59=203659=2036
  2. 711=2844711=2844
  3. 2.508=3.75122.508=3.7512
6.80
  1. 67=364267=3642
  2. 836=1254836=1254
  3. 3.756=2.5043.756=2.504
6.81
  1. ⓐ no
  2. ⓑ yes
6.82
  1. ⓐ no
  2. ⓑ no
6.83

77

6.84

104

6.85

65

6.86

24

6.87

−7

6.88

−9

6.89

12 ml

6.90

180 mg

6.91

300

6.92

5 pieces

6.93

590 Euros

6.94

56,460 yen

6.95

n 105 = 60 100 n 105 = 60 100

6.96

n 85 = 40 100 n 85 = 40 100

6.97

36 n = 25 100 36 n = 25 100

6.98

27 n = 36 100 27 n = 36 100

6.99

n 100 = 39 52 n 100 = 39 52

6.100

n 100 = 23 92 n 100 = 23 92

6.101

n 40 = 65 100 ; n = 26 n 40 = 65 100 ; n = 26

6.102

n 40 = 85 100 ; n = 34 n 40 = 85 100 ; n = 34

6.103

n 64 = 125 100 ; n = 80 n 64 = 125 100 ; n = 80

6.104

n 84 = 175 100 ; n = 147 n 84 = 175 100 ; n = 147

6.105

3.23 n = 8.5 100 ; n = 38 3.23 n = 8.5 100 ; n = 38

6.106

4.64 n = 7.25 100 ; n = 64 4.64 n = 7.25 100 ; n = 64

6.107

27 72 = n 100 ; n = 37.5% 27 72 = n 100 ; n = 37.5%

6.108

23 92 = n 100 ; n = 25% 23 92 = n 100 ; n = 25%

Section 6.1 Exercises

1.

6 100 6 100

3.

32 1000 32 1000

5.
  1. 5710057100
  2. 57%57%
7.
  1. 4210042100
  2. 42%42%
9.

1 25 1 25

11.

17 100 17 100

13.

13 25 13 25

15.

5 4 5 4

17.

3 8 3 8

19.

23 125 23 125

21.

19 200 19 200

23.

4 75 4 75

25.

0.05

27.

0.01

29.

0.63

31.

0.4

33.

1.15

35.

1.5

37.

0.214

39.

0.078

41.
  1. 32003200
  2. 0.0150.015
43.
  1. 702310,000702310,000
  2. 0.70230.7023
45.
  1. 14 14
  2. 0.250.25
47.
  1. 35 35
  2. 0.60.6
49.

1%

51.

18%

53.

135%

55.

300%

57.

0.9%

59.

8.75%

61.

150%

63.

225.4%

65.

25%

67.

37.5%

69.

175%

71.

680%

73.

41 2 3 % o r 41. 6 % 41 2 3 % o r 41. 6 %

75.

266 . 6 % 266 . 6 %

77.

42.9%

79.

55. 5 % 55. 5 %

81.

25%

83.

35%

85.
Fraction Decimal Percent
1212 0.50.5 50%50%
920920 0.450.45 45%45%
950950 0.180.18 18%18%
1313 0.30.3 33.3%33.3%
11251125 0.0080.008 0.8%0.8%
22 2.02.0 200%200%
87.
  1. 110110
  2. approximately $9.50approximately $9.50
89.

17 20 ; 0.85 17 20 ; 0.85

91.

80%; 0.8

93.

1 4 , 1 2 , 3 4 , 1 . 1 4 , 1 2 , 3 4 , 1 .

95.

The Szetos sold their home for five times what they paid 30 years ago.

Section 6.2 Exercises

97.

54

99.

26.88

101.

162.5

103.

18,000

105.

112

107.

108

109.

$35

111.

$940

113.

30%

115.

36%

117.

150%

119.

175%

121.

$11.88

123.

$259.80

125.

24.2 grams

127.

2,407 mg

129.

45%

131.

25%

133.

13.2%

135.

125%

137.

72.7%

139.

2.5%

141.

11%

143.

5.5%

145.

21.2%

147.

The original number should be greater than 44.80% is less than 100%, so when 80% is converted to a decimal and multiplied to the base in the percent equation, the resulting amount of 44 is less. 44 is only the larger number in cases where the percent is greater than 100%.

149.

Alex should have packed half as many shorts and twice as many shirts.

Section 6.3 Exercises

151.
  1. $4.20
  2. $88.20
153.
  1. $9.68
  2. $138.68
155.
  1. $17.13
  2. $267.13
157.
  1. $61.45
  2. $1,260.45
159.

6.5%

161.

6.85%

163.

$20.25

165.

$975

167.

$859.25

169.

3%

171.

16%

173.

15.5%

175.

$139

176.

$81

177.

$125

179.
  1. $26.97
  2. $17.98
181.
  1. $128.37
  2. $260.63
183.
  1. $332.48
  2. $617.47
185.
  1. $576
  2. 30%
187.
  1. $53.25
  2. 15%
189.
  1. $370
  2. 43.5%
191.
  1. $7.20
  2. $23.20
193.
  1. $0.20
  2. $0.80
195.
  1. $258.75
  2. $373.75
197.
  1. $131.25
  2. $126.25
  3. 25% off first, then $20 off
199.
  1. Priam is correct. The original price is 100%. Since the discount rate was 40%, the sale price was 60% of the original price.
  2. Yes.

Section 6.4 Exercises

201.

$180

203.

$14,000

205.

6.3%

207.

$90

209.

$579.96

211.

$14,167

213.

$3,280

215.

$860

217.

$24,679.91

219.

4%

221.

5.5%

223.

$116

225.

$4,836

227.

3%

229.

3.75%

231.

$35,000

233.

$3,345

235.

$332.10

237.

$195.00

239.

Answers will vary.

241.

Answers will vary.

Section 6.5 Exercises

243.

4 15 = 36 135 4 15 = 36 135

245.

12 5 = 96 40 12 5 = 96 40

247.

5 7 = 115 161 5 7 = 115 161

249.

8 1 = 48 6 8 1 = 48 6

251.

9.36 18 = 2.60 5 9.36 18 = 2.60 5

253.

18.04 11 = 4.92 3 18.04 11 = 4.92 3

255.

yes

257.

no

259.

no

261.

yes

263.

x = 49

265.

z = 7

267.

a = 9

269.

p = −11

271.

a = 7

273.

c = 2

275.

j = 0.6

277.

m = 4

279.

9 ml

281.

114 beats/minute. Carol has not met her target heart rate.

283.

159 cal

285.

3 4 cup 3 4 cup

287.

$252.50

289.

0.8 Euros

291.

48 quarters

293.

19 gallons, $58.71

295.

12.8 hours

297.

4 bags

299.

n 250 = 35 100 n 250 = 35 100

301.

n 47 = 110 100 n 47 = 110 100

303.

45 n = 30 100 45 n = 30 100

305.

90 n = 150 100 90 n = 150 100

307.

17 85 = p 100 17 85 = p 100

309.

340 260 = p 100 340 260 = p 100

311.

n 180 = 65 100 n 180 = 65 100

313.

n 92 = 18 100 n 92 = 18 100

315.

n 26 = 175 100 n 26 = 175 100

317.

n 488 = 300 100 n 488 = 300 100

319.

7.65 n = 17 100 7.65 n = 17 100

321.

13.53 n = 8.25 100 13.53 n = 8.25 100

323.

14 56 = p 100 14 56 = p 100

325.

12 96 = p 100 12 96 = p 100

327.

He must add 20 oz of water to obtain a final solution of 32 oz.

329.

Answers will vary.

Review Exercises

331.

32 100 32 100

333.

13 100 , 13% 13 100 , 13%

335.

12 25 12 25

337.

641 1000 641 1000

339.

0.06

341.

1.28

343.
  1. 2720027200
  2. 0.1350.135
345.
  1. 1212
  2. 0.50.5
347.

4%

349.

282%

351.

0.3%

353.

75%

355.

362.5%

357.

40%

359.

161

361.

240

363.

25

365.

68%

367.

$16.70

369.

28.4%

371.

4%

373.
  1. ⓐ $45
  2. ⓑ $795
375.

7.25%

377.

$11,400

379.

15%

381.

$45

383.
  1. $25.47
  2. $59.43
385.
  1. ⓐ $13
  2. ⓑ 26%
387.
  1. ⓐ $0.48
  2. ⓑ $1.28
389.

$450

391.

$4400

393.

$900

395.

2.5%

397.

3 8 = 12 32 3 8 = 12 32

399.

1 18 = 23 414 1 18 = 23 414

401.

yes

403.

no

405.

20

407.

4

409.

12 ml

411.

340 calories

413.

13 gallons

415.

n 395 = 62 100 n 395 = 62 100

417.

15 1000 = p 100 15 1000 = p 100

419.

n 900 = 85 100 , 765 n 900 = 85 100 , 765

421.

3.51 n = 4.5 100 , $78 3.51 n = 4.5 100 , $78

Practice Test

423.

0.24 , 6 25 0.24 , 6 25

425.

3.5 , 7 2 3.5 , 7 2

427.

33. 3 ¯ % o r 33 1 3 % 33. 3 ¯ % o r 33 1 3 %

429.

25%

431.

40

433.

11.9%

435.

4%

437.

$70

439.

6.25%

441.

−52

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