Skip to Content
OpenStax Logo
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. 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

Try It

6.1

8910089100

6.2

7210072100

6.3

62100,62%62100,62%

6.4

41100,41%41100,41%

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%,or1119%11.1%,or1119%

6.26

16.6%,or1623%16.6%,or1623%

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

n105=60100n105=60100

6.96

n85=40100n85=40100

6.97

36n=2510036n=25100

6.98

27n=3610027n=36100

6.99

n100=3952n100=3952

6.100

n100=2392n100=2392

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.

61006100

3.

321000321000

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

125125

11.

1710017100

13.

13251325

15.

5454

17.

3838

19.

2312523125

21.

1920019200

23.

475475

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.

1720;0.851720;0.85

92.

80%; 0.8

94.

14,12,34,1.14,12,34,1.

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.

415=36135415=36135

246.

125=9640125=9640

248.

57=11516157=115161

250.

81=48681=486

252.

9.3618=2.6059.3618=2.605

254.

18.0411=4.92318.0411=4.923

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.

34cup34cup

288.

$252.50

290.

1.25

292.

48 quarters

294.

19, $58.71

296.

12.8 hours

298.

4 bags

300.

n250=35100n250=35100

302.

n47=110100n47=110100

304.

45n=3010045n=30100

306.

90n=15010090n=150100

308.

1785=p1001785=p100

310.

340260=p100340260=p100

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.

3210032100

334.

13100,13%13100,13%

336.

12251225

338.

64110006411000

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.

38=123238=1232

400.

118=23414118=23414

402.

yes

404.

no

406.

20

408.

4

410.

12

412.

340

414.

13 gallons

416.

n395=62100n395=62100

418.

151000=p100151000=p100

420.

765

422.

$78

Practice Test

424.

0.24,6250.24,625

426.

3.5,3123.5,312

428.

33.333%

430.

25%

432.

40

434.

11.9%

436.

4%

438.

$50

440.

6.2%

442.

−52

Citation/Attribution

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 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

© Sep 16, 2020 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 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.