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Prealgebra 2e

Chapter 2

Prealgebra 2eChapter 2
  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

2.1

112112

2.2

180,096180,096

2.3

807807

2.4

expression

2.5

1,0241,024

2.6

7373

2.7

1919

2.8

4242

2.9

x8x8

2.10

44 and 215215

2.11

1515

2.12

2,3,5,6,102,3,5,6,10

2.13

prime

2.13

2424

Try It

2.1
  1. 18 plus 11; the sum of eighteen and eleven
  2. 27 times 9; the product of twenty-seven and nine
  3. 84 divided by 7; the quotient of eighty-four and seven
  4. p minus q; the difference of p and q
2.2
  1. 47 minus 19; the difference of forty-seven and nineteen
  2. 72 divided by 9; the quotient of seventy-two and nine
  3. m plus n; the sum of m and n
  4. 13 times 7; the product of thirteen and seven
2.3
  1. fourteen is less than or equal to twenty-seven
  2. nineteen minus two is not equal to eight
  3. twelve is greater than four divided by two
  4. x minus seven is less than one
2.4
  1. nineteen is greater than or equal to fifteen
  2. seven is equal to twelve minus five
  3. fifteen divided by three is less than eight
  4. y minus three is greater than six
2.5
  1. >
  2. <
2.6
  1. <
  2. >
2.7
  1. equation
  2. expression
2.8
  1. expression
  2. equation
2.9

415

2.10

79

2.11
  1. 4 · 4 · 4 · 4 · 4 · 4 · 4 · 4
  2. a · a · a · a · a · a · a
2.12
  1. 8 · 8 · 8 · 8 · 8 · 8 · 8 · 8
  2. b · b · b · b · b · b
2.13
  1. 125
  2. 1
2.14
  1. 49
  2. 0
2.15
  1. 2
  2. 14
2.16
  1. 35
  2. 99
2.17

18

2.18

9

2.19

16

2.20

23

2.21

86

2.22

1

2.23

81

2.24

75

2.25
  1. 10
  2. 19
2.26
  1. 4
  2. 12
2.27
  1. 13
  2. 5
2.28
  1. 8
  2. 16
2.29

64

2.30

216

2.31

64

2.32

81

2.33

33

2.34

10

2.35

40

2.36

9

2.37

The terms are 4x, 3b, and 2. The coefficients are 4, 3, and 2.

2.38

The terms are 9a, 13a2, and a3, The coefficients are 9, 13, and 1.

2.39

9 and 15; 2x3 and 8x3; y2 and 11y2

2.40

4x3 and 6x3; 8x2 and 3x2; 19 and 24

2.41

16x + 17

2.42

17y + 7

2.43

4x2 + 14x

2.44

12y2 + 15y

2.45
  1. 47 − 41
  2. 5x ÷ 2
2.46
  1. 17 + 19
  2. 7x
2.47
  1. x + 11
  2. 11a − 14
2.48
  1. j + 19
  2. 2x − 21
2.49
  1. 4(p + q)
  2. 4p + q
2.50
  1. 2x − 8
  2. 2(x − 8)
2.51

w − 5

2.52

l + 2

2.53

6q − 7

2.54

4n + 8

2.55

no

2.56

yes

2.57

yes

2.58

yes

2.59

x + 1 = 7; x = 6

2.60

x + 3 = 4; x = 1

2.61

x = 13

2.62

x = 5

2.63

y = 28

2.64

y = 46

2.65

x = 22

2.66

y = 4

2.67

a = 37

2.68

n = 41

2.69

7 + 6 = 13

2.70

8 + 6 = 14

2.71

6 ⋅ 9 = 54

2.72

21 ⋅ 3 = 63

2.73

2(x − 5) = 30

2.74

2(y − 4) = 16

2.75

x + 7 = 37; x = 30

2.76

y + 11 = 28; y = 17

2.77

z − 17 = 37; z = 54

2.78

x − 19 = 45; x = 64

2.79
  1. yes
  2. no
2.80
  1. no
  2. yes
2.81
  1. yes
  2. no
2.82
  1. no
  2. yes
2.83
  1. no
  2. yes
2.84
  1. yes
  2. no
2.85
  1. yes
  2. no
2.86
  1. no
  2. yes
2.87

Divisible by 2, 3, 5, and 10

2.88

Divisible by 2 and 3, not 5 or 10.

2.89

Divisible by 2, 3, not 5 or 10.

2.90

Divisible by 3 and 5.

2.91

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

2.92

1, 2, 4, 5, 8, 10, 16, 20, 40, 80

2.93

composite

2.94

prime

2.95

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 24 ⋅ 5

2.96

2 ⋅ 2 ⋅ 3 ⋅ 5, or 22 ⋅ 3 ⋅ 5

2.97

2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 32 ⋅ 7

2.98

2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 72

2.99

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5, or 24 ⋅ 5

2.100

2 ⋅ 2 ⋅ 3 ⋅ 5, or 22 ⋅ 3 ⋅ 5

2.101

2 ⋅ 3 ⋅ 3 ⋅ 7, or 2 ⋅ 32 ⋅ 7

2.102

2 ⋅ 3 ⋅ 7 ⋅ 7, or 2 ⋅ 3 ⋅ 72

2.103

36

2.104

72

2.105

60

2.106

105

2.107

440

2.108

360

Section 2.1 Exercises

1.

16 minus 9, the difference of sixteen and nine

3.

5 times 6, the product of five and six

5.

28 divided by 4, the quotient of twenty-eight and four

7.

x plus 8, the sum of x and eight

9.

2 times 7, the product of two and seven

11.

fourteen is less than twenty-one

13.

thirty-six is greater than or equal to nineteen

15.

3 times n equals 24, the product of three and n equals twenty-four

17.

y minus 1 is greater than 6, the difference of y and one is greater than six

19.

2 is less than or equal to 18 divided by 6; 2 is less than or equal to the quotient of eighteen and six

21.

a is not equal to 7 times 4, a is not equal to the product of seven and four

23.

equation

25.

expression

27.

expression

29.

equation

31.

37

33.

x5

35.

5x5x5

37.

2x2x2x2x2x2x2x2

39.
  1. 43
  2. 55
41.

5

43.

34

45.

58

47.

6

49.

13

51.

4

53.

35

55.

10

57.

41

59.

81

61.

149

63.

50

Section 2.2 Exercises

69.

22

71.

26

73.

144

75.

32

77.

27

79.

21

81.

41

83.

9

84.

225

85.

73

87.

54

89.

15x2, 6x, 2

91.

10y3, y, 2

93.

8

95.

5

97.

x3 and 8x3; 14 and 5

99.

16ab and 4ab; 16b2 and 9b2

101.

13x

103.

26a

105.

7c

107.

12x + 8

109.

10u + 3

111.

12p + 10

113.

22a + 1

115.

17x2 + 20x + 16

117.

8 + 12

119.

14 − 9

121.

9 ⋅ 7

123.

36 ÷ 9

125.

x − 4

127.

6y

129.

8x + 3x

131.

y ÷ 3

133.

8 (y − 9)

135.

5 (x + y)

137.

b + 15

139.

b − 4

141.

2n − 7

143.

He will pay $750. His insurance company will pay $1350.

Section 2.3 Exercises

147.
  1. yes
  2. no
149.
  1. no
  2. yes
151.
  1. yes
  2. no
153.
  1. no
  2. yes
155.
  1. no
  2. yes
157.
  1. no
  2. yes
159.

x + 2 = 5; x = 3

161.

x + 3 = 6; x = 3

163.

a = 16

165.

p = 5

167.

r = 24

169.

x = 7

171.

p = 69

173.

d = 67

175.

y = 22

177.

u = 30

179.

f = 178

181.

n = 32

183.

p = 48

185.

y = 467

187.

8 + 9 = 17

189.

23 − 19 = 4

191.

3 ⋅ 9 = 27

193.

54 ÷ 6 = 9

195.

2(n − 10) = 52

197.

3y + 10 = 100

199.

p + 5 = 21; p = 16

201.

r + 18 = 73; r = 55

203.

d − 30 = 52; d = 82

205.

u − 12 = 89; u = 101

207.

c − 325 = 799; c = 1124

209.

$1300

211.

$460

Section 2.4 Exercises

215.

2, 4, 6, 8, 10 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48

217.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

219.

6, 12, 18, 24, 30, 36, 42, 48

221.

8, 16, 24, 32, 40, 48

223.

10, 20, 30, 40

225.

Divisible by 2, 3, 4, 6

227.

Divisible by 3, 5

229.

Divisible by 2, 3, 4, 6

231.

Divisible by 2, 3, 4, 5, 6, 10

233.

Divisible by 2, 4

235.

Divisible by 3, 5

237.

Divisible by 2, 5, 10

239.

Divisible by 2, 5, 10

241.

Divisible by 3, 5

243.

1, 2, 3, 4, 6, 9, 12, 18, 36

245.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

247.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72,144

249.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588

251.

prime

253.

composite

255.

prime

257.

composite

259.

composite

261.

composite

263.


This table has nine rows and three columns. The first row is a header row that labels each column. The first column is labeled “Weeks after opening the account”, the second is labeled “Total number of dollars Gina put in the account”, and the last is labeled “Simplified Total”. Under the “Weeks after opening the account” column are the values: 0, 1, 2, 3, 4, 5, 6, 20, and the letter x. Under the “Total number of dollars Gina put in the account” column are the expressions: 75; 75 plus 20; 75 plus 20 times 2; 75 plus 20 times 3; 75 plus 20 times empty set of brackets; 75 plus empty set of brackets; the last three rows are blank. Under the “Simplified Total” column are the values: 75, 95, 115, the last six rows are blank.

Section 2.5 Exercises

267.

2 ⋅ 43

269.

2 ⋅ 2 ⋅ 3 ⋅ 11

271.

3 ⋅ 3 ⋅ 7 ⋅ 11

273.

5 ⋅ 23

275.

3 ⋅ 3 ⋅ 5 ⋅ 5 ⋅ 11

277.

2 ⋅ 2 ⋅ 2 ⋅ 7

279.

2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 7

281.

17 ⋅ 23

283.

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3

285.

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 5

287.

2 ⋅ 3 ⋅ 5 ⋅ 5

289.

3 ⋅ 5 ⋅ 5 ⋅ 7

291.

2 ⋅ 2 ⋅ 3 ⋅ 3

293.

2 ⋅ 5 ⋅ 5 ⋅ 7

295.

24

297.

30

299.

120

301.

300

303.

24

305.

120

307.

420

309.

42

311.

120

313.

40

Review Exercises

317.

3 times 8, the product of three and eight.

319.

24 divided by 6, the quotient of twenty-four and six.

321.

50 is greater than or equal to 47

323.

The sum of n and 4 is equal to 13

325.

equation

327.

expression

329.

23

331.

x6

333.

8 ⋅ 8 ⋅ 8 ⋅ 8

335.

yyyyy

337.

81

339.

128

341.

20

343.

18

345.

74

347.

31

349.

58

351.

26

353.

12n2,3n, 1

355.

6

357.

3 and 4; 3x and x

359.

24a

361.

14x

363.

12n + 11

365.

10y2 + 2y + 3

367.

x − 6

369.

3n ⋅ 9

371.

5(y + 1)

373.

c + 3

375.
  1. yes
  2. no
377.
  1. yes
  2. no
379.
  1. no
  2. yes
381.

x + 3 = 5; x = 2

383.

c = 6

385.

x = 11

387.

y = 23

389.

p = 34

391.

7 + 33 = 44

393.

4 ⋅ 8 = 32

395.

2(n − 3) = 76

397.

x + 8 = 35; x = 27

399.

q − 18 = 57; q = 75

401.

h = 42

403.

z = 33

405.

q = 8

407.

v = 56

409.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

411.

8, 16, 24, 32, 40, 48

413.

2, 3, 6

415.

2, 3, 5, 6, 10

417.

1, 2, 3, 5, 6, 10, 15, 30

419.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

421.

prime

423.

composite

425.

2 ⋅ 2 ⋅ 3 ⋅ 7

427.

2 ⋅ 5 ⋅ 5 ⋅ 7

429.

45

431.

175

433.

Answers will vary

Practice Test

435.

15 minus x, the difference of fifteen and x.

437.

equation

439.
  1. n6
  2. 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 243
441.

36

443.

5

445.

45

447.

125

449.

36

451.

x + 5

453.

3(ab)

455.

n = 31

457.

y − 15 = 32; y = 47

459.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

461.

23 ⋅ 33 ⋅ 5

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