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Prealgebra

Chapter 6

PrealgebraChapter 6
  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

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. 113250113250
  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. 22502250
  2. 0.440.44
6.15
  1. 310310
  2. 0.30.3
6.16
  1. 12.510012.5100
  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

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

26

6.102

34

6.103

80

6.104

147

6.105

38

6.106

64

6.107

37.5%

6.108

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.

41.7%

75.

266 . 6 % 266 . 6 %

77.

42.9%

79.

55.6%

81.

25%

83.

35%

87.
  1. 110110
  2. approximately $9.50approximately $9.50
90.

17 20 ; 0.85 17 20 ; 0.85

92.

80%; 0.8

94.

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

96.

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

Section 6.2 Exercises

98.

54

100.

26.88

102.

162.5

104.

18,000

106.

112

108.

108

110.

$35

112.

$940

114.

30%

116.

36%

118.

150%

120.

175%

122.

$11.88

124.

$259.80

126.

24.2 grams

128.

2,407 grams

130.

45%

132.

25%

134.

13.2%

136.

125%

138.

72.7%

140.

2.5%

142.

11%

144.

5.5%

146.

21.2%

148.

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%.

150.

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

Section 6.3 Exercises

152.
  1. $4.20
  2. $88.20
154.
  1. $9.68
  2. $138.68
156.
  1. $17.13
  2. $267.13
158.
  1. $61.45
  2. $1,260.45
160.

6.5%

162.

6.85%

164.

$20.25

166.

$975

168.

$859.25

170.

3%

172.

16%

174.

15.5%

176.

$139

177.

$81

178.

$125

180.
  1. $26.97
  2. $17.98
182.
  1. $128.37
  2. $260.63
184.
  1. $332.48
  2. $617.50
186.
  1. $576
  2. 30%
188.
  1. $53.25
  2. 15%
190.
  1. $370
  2. 43.5%
192.
  1. $7.20
  2. $23.20
194.
  1. $0.20
  2. 44.2%
196.
  1. $258.75
  2. $373.75
198.
  1. $131.25
  2. $126.25
  3. 25% off first, then $20 off
200.
  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

202.

$180

204.

$14,000

206.

6.3%

208.

$90

210.

$579.96

212.

$14,167

214.

$3,280

216.

$860

218.

$24,679.91

220.

4%

222.

5.5%

224.

$116

226.

$4,836

228.

3%

230.

3.75%

232.

$35,000

234.

$3,345

236.

$332.10

238.

$195.00

240.

Answers will vary.

242.

Answers will vary.

Section 6.5 Exercises

244.

4 15 = 36 135 4 15 = 36 135

246.

12 5 = 96 40 12 5 = 96 40

248.

5 7 = 115 161 5 7 = 115 161

250.

8 1 = 48 6 8 1 = 48 6

252.

9.36 18 = 2.60 5 9.36 18 = 2.60 5

254.

18.04 11 = 4.92 3 18.04 11 = 4.92 3

256.

yes

258.

no

260.

no

262.

yes

264.

49

266.

7

268.

9

270.

−11

272.

7

274.

2

276.

0.6

278.

4

280.

9 ml

282.

114, no

284.

159 cal

286.

3 4 cup 3 4 cup

288.

$252.50

290.

1.25

292.

48 quarters

294.

19, $58.71

296.

12.8 hours

298.

4 bags

300.

n 250 = 35 100 n 250 = 35 100

302.

n 47 = 110 100 n 47 = 110 100

304.

45 n = 30 100 45 n = 30 100

306.

90 n = 150 100 90 n = 150 100

308.

17 85 = p 100 17 85 = p 100

310.

340 260 = p 100 340 260 = p 100

312.

117

313.

165

314.

16.56

316.

45.5

318.

1464

320.

$45

322.

$164

324.

25%

326.

12.5%

328.

20, 32

330.

Answers will vary.

Review Exercises

332.

32 100 32 100

334.

13 100 , 13% 13 100 , 13%

336.

12 25 12 25

338.

641 1000 641 1000

340.

0.06

342.

1.28

344.
  1. 2720027200
  2. 0.1350.135
346.
  1. 1212
  2. 0.50.5
348.

4%

350.

282%

352.

0.3%

354.

75%

356.

362.5%

358.

40%

360.

161

362.

240

364.

25

366.

68%

368.

$16.70

370.

28.4%

372.

4%

374.
  1. ⓐ $45
  2. ⓑ $795
376.

7.25%

378.

$11,400

380.

15%

382.

$45

384.
  1. $25.47
  2. $59.43
386.
  1. ⓐ $13
  2. ⓑ 26%
388.
  1. ⓐ $0.48
  2. ⓑ $1.28
390.

$450

392.

$4400

394.

$900

396.

2.5%

398.

3 8 = 12 32 3 8 = 12 32

400.

1 18 = 23 414 1 18 = 23 414

402.

yes

404.

no

406.

20

408.

4

410.

12

412.

340

414.

13 gallons

416.

n 395 = 62 100 n 395 = 62 100

418.

15 1000 = p 100 15 1000 = p 100

420.

765

422.

$78

Practice Test

424.

0.24 , 6 25 0.24 , 6 25

426.

3.5 , 3 1 2 3.5 , 3 1 2

428.

33.333%

430.

25%

432.

40

434.

11.9%

436.

4%

438.

$50

440.

6.2%

442.

−52

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