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Prealgebra

Chapter 7

PrealgebraChapter 7

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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

Try It

7.1
  1. −24 1 −24 1
  2. 357 100 357 100
7.2
  1. −19 1 −19 1
  2. 841 100 841 100
7.3
  1. rational
  2. rational
  3. irrational
7.4
  1. rational
  2. rational
  3. irrational
7.5
  1. rational
  2. irrational
7.6
  1. irrational
  2. rational
7.9
  1. −4 + 7 = 7 + (−4)
  2. 6 · 12 = 12 · 6
7.10
  1. 14 + (−2) = −2 + 14
  2. 3(−5) = (−5)3
7.11
  1. ( 1 + 0.7 ) + 0.3 = 1 + ( 0.7 + 0.3 ) ( 1 + 0.7 ) + 0.3 = 1 + ( 0.7 + 0.3 )
  2. ( −9 · 8 ) · 3 4 = −9 ( 8 · 3 4 ) ( −9 · 8 ) · 3 4 = −9 ( 8 · 3 4 )
7.12
  1. ( 4 + 0.6 ) + 0.4 = 4 + ( 0.6 + 0.4 ) ( 4 + 0.6 ) + 0.4 = 4 + ( 0.6 + 0.4 )
  2. ( −2 · 12 ) · 5 6 = −2 ( 12 · 5 6 ) ( −2 · 12 ) · 5 6 = −2 ( 12 · 5 6 )
7.13

32x

7.14

−63y

7.15
  1. 0.84
  2. 0.84
7.16
  1. 0.975
  2. 0.975
7.17
  1. 24
  2. 24
7.18
  1. 15
  2. 15
7.19

−48a

7.20

−92x

7.21

5 49 5 49

7.22

11 25 11 25

7.23

22 15 22 15

7.24

11 9 11 9

7.25

15.58c

7.26

17.79d

7.27

10.53

7.28

70.4

7.29

24y

7.30

60z

7.31

32rs

7.32

41m + 6n

7.33

4x + 8

7.34

6x + 42

7.35

27y + 72

7.36

25w + 45

7.37

7x − 42

7.38

8x − 40

7.39

2 5 p + 4 2 5 p + 4

7.40

3 7 u + 9 3 7 u + 9

7.41

5y + 3

7.42

4n + 9

7.43

70 + 15p

7.44

4 + 35d

7.45

rs − 2r

7.46

yz − 8y

7.47

xp + 2p

7.48

yq + 4q

7.49

−18m − 15

7.50

−48n − 66

7.51

−10 + 15a

7.52

−56 + 105y

7.53

z + 11

7.54

x + 4

7.55

−3x + 3

7.56

2x − 20

7.57

5x − 66

7.58

7x − 13

7.59
  1. 120
  2. 120
7.60
  1. 126
  2. 126
7.61
  1. 30
  2. 30
7.62
  1. 3
  2. 3
7.63
  1. −32
  2. −32
7.64
  1. −45
  2. −45
7.65
  1. identity property of addition
  2. identity property of multiplication
7.66
  1. identity property of multiplication
  2. additive identity
7.67
  1. −18 −18
  2. 7 9 7 9
  3. −1.2 −1.2
7.68
  1. −47 −47
  2. 7 13 7 13
  3. −8.4 −8.4
7.69
  1. 1 5 1 5
  2. −7 −7
  3. 10 3 10 3
7.70
  1. 1 18 1 18
  2. 5 4 5 4
  3. 5 3 5 3
7.71
  1. 0
  2. 0
  3. 0
7.72
  1. 0
  2. 0
  3. 0
7.73
  1. 0
  2. 0
  3. 0
7.74
  1. 0
  2. 0
  3. 0
7.75
  1. undefined
  2. undefined
  3. undefined
7.76
  1. undefined
  2. undefined
  3. undefined
7.77

9

7.78

−18

7.79

p

7.80

r

7.81

0

7.82

0

7.83

undefined

7.84

undefined

7.85

20y + 50

7.86

12z + 16

7.87

2.5 feet

7.88

54 feet

7.89

8600 pounds

7.90

102,000,000 pounds

7.91

440,000,000 yards

7.92

151,200 minutes

7.93

16 cups

7.94

48 teaspoons

7.95

9 lbs. 8 oz

7.96

21 ft. 6 in.

7.97

4 lbs. 8 oz.

7.98

11 gal. 2 qts.

7.99

5000 m

7.100

250 cm

7.101

2.8 kilograms

7.102

4.5 kilograms

7.103
  1. 0.00725 kL
  2. 6300 mL
7.104
  1. 35,000 L
  2. 410 cL
7.105

83 cm

7.106

1.04 m

7.107

2 L

7.108

2.4 kg

7.109

2.12 quarts

7.110

3.8 liters

7.111

19,328 ft

7.112

3,470 mi

7.113

15°C

7.114

5°C

7.115

59°F

7.116

50°F

Section 7.1 Exercises

1.
  1. 5 1 5 1
  2. 319 100 319 100
3.
  1. −12 1 −12 1
  2. 9279 1000 9279 1000
5.

Rational: 0.75,0.2230.75,0.223. Irrational: 1.39174…1.39174…

7.

Rational: 0.450.45, 3.593.59. Irrational: 1.919293…1.919293…

9.
  1. rational
  2. irrational
11.
  1. irrational
  2. rational
13.


The table has seven rows and six columns. The first row is a header row that labels each column. The first column is labeled “Number”, the second column “Whole”, the third “Integer”, the fourth “Rational” the fifth “Irrational” and the sixth “Real”. Each row has a number in the “Number” column then an x in each column that corresponds to the type of number it is. The second row has the number negative 8 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The third row has the number 0 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The fourth row has the number 1.95286 followed by and ellipsis in the “Number” column and an x marked in the “Irrational” and “Real” columns. The fifth row has the number 12 fifths in the “Number” column and an x marked in the “Rational” and “Real” columns. The sixth row has the number square root of 36 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The last row has the number 9 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns.
15.


The table has seven rows and six columns. The first row is a header row that labels each column. The first column is labeled “Number”, the second column “Whole”, the third “Integer”, the fourth “Rational” the fifth “Irrational” and the sixth “Real”. Each row has a number in the “Number” column then an x in each column that corresponds to the type of number it is. The second row has the number negative 100 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The third row has the number negative 7 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The fourth row has the number negative 8 thirds in the “Number” column and an x marked in the “Rational” and “Real” columns. The fifth row has the number negative 1 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The sixth row has the number 0.77 in the “Number” column and an x marked in the “Rational” and “Real” columns. The last row has the number 3 and 1 quarter in the “Number” column and an x marked in the “Rational” and “Real” columns.
17.
  1. 4
  2. Teachers cannot be divided
  3. It would result in a lower number.
19.

Answers will vary.

Section 7.2 Exercises

21.

7 + 6 = 6 + 7

23.

7(−13) = (−13)7

25.

(−12)(−18) = (−18)(−12)

27.

−15 + 7 = 7 + (−15)

29.

y + 1 = 1 + y

31.

−3m = m(−3)

33.

(21 + 14) + 9 = 21 + (14 + 9)

35.

(14 · 6) · 9 = 14(6 · 9)

37.

(−2 + 6) + 7 = −2 + (6 + 7)

39.

( 13 · 2 3 ) · 18 = 13 ( 2 3 · 18 ) ( 13 · 2 3 ) · 18 = 13 ( 2 3 · 18 )

41.

4(7x) = (4 · 7)x

43.

(17 + y) + 33 = 17 + (y + 33)

45.
  1. 0.97
  2. 0.97
47.
  1. 2.375
  2. 2.375
49.
  1. 21
  2. 21
51.
  1. −8
  2. −8
53.

23

55.

5 12 5 12

57.

25 7 25 7

59.

65 23 65 23

61.

−176

63.

13 12 13 12

65.

23 15 23 15

67.

9.89d

69.

36

71.

29.193

73.

72w

75.

−46n

77.

12q

79.

42u + 30v

81.

−57p + (−10q)

83.

a + 6 5 b a + 6 5 b

85.

7.41m + 6.57n

87.
  1. $975
  2. $700
  3. $1675
  4. $185
  5. $270
  6. $1220
89.

Answers will vary.

Section 7.3 Exercises

91.

3a + 27

93.

27w + 63

95.

7y − 91

97.

35u − 20

99.

1 3 u + 3 1 3 u + 3

101.

4 5 m + 4 4 5 m + 4

103.

3x − 4

105.

2 + 9s

107.

uv − 10u

109.

ax + 7x

111.

−3a − 33

113.

−81a − 36

115.

−4q + 28

117.

−42x + 48

119.

q − 11

121.

−5p + 4

123.

8u + 4

125.

−4x + 10

127.

−42n + 39

129.

r + 15

131.

c + 6

133.

3y + 1

135.

47u + 60

137.

24x + 4

139.

6n − 72

141.

17n + 76

143.
  1. 56
  2. 56
145.
  1. 9 2 9 2
  2. 9 2 9 2
147.
  1. −89
  2. −89
149.
  1. −525
  2. −525
151.
  1. 160
  2. 160
153.
  1. −1.03
  2. −1.03
155.
  1. 3(4 − 0.03) = 11.91
  2. $1.42

Section 7.4 Exercises

159.

identity property of multiplication

161.

identity property of addition

163.

1 14 1 14

165.

1 19 1 19

167.

13 8 13 8

169.

12 5 12 5

171.

5 2 5 2

173.

−2

175.

0

177.

0

179.

undefined

181.

0

183.

0

185.

undefined

187.

16

189.

31s

191.

p

193.

2n

195.

0

197.

0

199.

0

201.

undefined

203.

undefined

205.

undefined

207.

20q − 35

209.

225h + 360

211.
  1. 8 hours
  2. 8
  3. associative property of multiplication
213.

Answers will vary.

Section 7.5 Exercises

215.

24 inches

217.

3.75 feet

219.

58 inches

221.

90 feet

223.

0.98 miles

225.

300,000 pounds

227.

110 tons

229.

162 hours

231.

8100 seconds

233.

256 tablespoons

235.

128 ounces

237.

111 ounces

239.

31.25 gallons

241.

4 lbs. 1 oz.

243.

5 weeks and 1 day

245.

9 ft 2 in

247.

8 yards

249.

8000 meters

251.

245 centimeters

253.

10.911 kilometers

255.

3000 milligrams

257.

25,000 milligrams

259.

3800 grams

261.

0.3 liters

263.

65 centimeters

265.

1.82 kilograms

267.

16.8 grams

269.

42,000 milligrams

271.

106.7 centimeters

273.

8.2 meters

275.

41,500 kilograms

277.

5.2 feet

279.

33 pounds

281.

30.4 liters

283.

25°C

285.

−10°C

287.

−15.5°C

289.

48.9°C

291.

77°F

293.

5°F

295.

46.4°F

297.

60.8°F

299.

110 reflectors

Review Exercises

303.

5 1 5 1

305.

18 10 18 10

307.

0. 16 , 1.95 0. 16 , 1.95

309.
  1. irrational
  2. rational
311.
  1. 4 4
  2. 5 , 4 , 4 5 , 4 , 4
  3. 5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4 5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4
  4. none
  5. 5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4 5 , 2 1 4 , 4 , 0. 25 , 13 5 , 4
313.

−14·5 = 5(−14)

315.

a + 8 = 8 + a

317.

(22 + 7) + 3 = 22 + (7 + 3)

319.

1 2 ( 22 y ) = ( 1 2 · 22 ) y 1 2 ( 22 y ) = ( 1 2 · 22 ) y

321.
  1. 5.39
  2. 5.39
323.
  1. 13
  2. 13
325.

11 15 11 15

327.

−60

329.

5.98 d

331.

25 q

333.

34 m + (−25 n)

335.

9y − 36

337.

56a + 96

339.

yp + 10p

341.

−4x + 68

343.
  1. 9
  2. 9
345.
  1. 36
  2. 36
347.

identity property of addition

349.

identity property of multiplication

351.

−19.4

353.

7 15 7 15

355.

1 5 1 5

357.

9 4 9 4

359.

0

361.

0

363.

n + 7

365.

34

367.

54x − 84

369.

3.5 feet

371.

15 yards

373.

9000 pounds

375.

64 tablespoons

377.

1.9 gallons

379.

7 hours 10 minutes

381.

3 yards, 12 inches

383.

8.85 kilometers

385.

13,000 milligrams

387.

0.65 liters

389.

855 milliliters

391.

10,000 milligrams

393.

25.6 meters

395.

171.6 pounds

397.

11.4 kilograms

399.

−5°C

401.

17.8°C

403.

23°F

405.

75.2°F

Practice Test

407.

144 = 12 therefore rational. 144 = 12 therefore rational.

409.

x·14 = 14·x

411.

(8·2)·3 = 8·(2·3)

413.
  1. 2 5 2 5
  2. 5 2 5 2
415.

15y

417.

23 15 23 15

419.

30y − 4z

421.

30x − 24

423.

2a + 3

425.

66p − 2

427.

0

429.

0

431.

.276 grams

433.

9.317 miles

435.

95°F

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