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Prealgebra 2e

Chapter 1

Prealgebra 2eChapter 1
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  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

1.1

215215

1.2

342,006342,006

1.3

1.4

910910

1.5

2,1622,162

1.6

284284

1.7

8181

1.8

1717

1.9

5,3945,394

Try It

1.1
  • 2, 9, 241, 376
  • 0, 2, 9, 241, 376
1.2
  • 7, 13, 201
  • 0, 7, 13, 201
1.3

176

1.4

237

1.5
  • ten millions
  • tens
  • hundred thousands
  • millions
  • ones
1.6
  • billions
  • ten thousands
  • tens
  • hundred thousands
  • hundred millions
1.7

nine trillion, two hundred fifty-eight billion, one hundred thirty-seven million, nine hundred four thousand, sixty-one

1.8

seventeen trillion, eight hundred sixty-four billion, three hundred twenty-five million, six hundred nineteen thousand, four

1.9

three hundred sixteen million, one hundred twenty-eight thousand, eight hundred thirty nine

1.10

thirty one million, five hundred thirty-six thousand

1.11

53,809,051

1.12

2,022,714,466

1.13

34,000,000 miles

1.14

204,000,000 pounds

1.15

160

1.16

880

1.17

17,900

1.18

5,000

1.19

64,000

1.20

156,000

1.21
  • eight plus four; the sum of eight and four
  • eighteen plus eleven; the sum of eighteen and eleven
1.22
  1. twenty-one plus sixteen; the sum of twenty-one and sixteen
  2. one hundred plus two hundred; the sum of one hundred and two hundred
1.29
  1. 0+19=190+19=19
  2. 39+0=3939+0=39
1.30
  1. 0+24=240+24=24
  2. 57+0=5757+0=57
1.31

9+7=16; 7+9=169+7=16; 7+9=16

1.32

8+6=14; 6+8=148+6=14; 6+8=14

1.33

32+54=8632+54=86

1.34

25+74=9925+74=99

1.35

35+98=13335+98=133

1.36

72+89=16172+89=161

1.37

456+376=832456+376=832

1.38

269+578=847269+578=847

1.39

4,597+685=5,2824,597+685=5,282

1.40

5,837+695=6,5325,837+695=6,532

1.41

46,195+397+6,281=52,87346,195+397+6,281=52,873

1.42

53,762+196+7,458=61,41653,762+196+7,458=61,416

1.43

Translate: 17+2617+26; Simplify: 4343

1.44

Translate: 28+1428+14; Simplify: 4242

1.45

Translate: 29+7629+76; Simplify 105105

1.46

Translate 37 + 69; Simplify 106

1.47

He rode 140 miles.

1.48

The total number is 720 students.

1.49

The perimeter is 30 inches.

1.50

The perimeter is 36 inches.

1.51
  1. twelve minus four; the difference of twelve and four
  2. twenty-nine minus eleven; the difference of twenty-nine and eleven
1.52
  1. eleven minus two; the difference of eleven and two
  2. twenty-nine minus twelve; the difference of twenty-nine and twelve
1.59

7 − 0 = 7; 7 + 0 = 7

1.60

6 − 2 = 4; 2 + 4 = 6

1.61

86 − 54 = 32 because 54 + 32 = 86

1.62

99 − 74 = 25 because 74 + 25 = 99

1.63

93 − 58 = 35 because 58 + 35 = 93

1.64

81 − 39 = 42 because 42 + 39 = 81

1.65

439 − 52 = 387 because 387 + 52 = 439

1.66

318 − 75 = 243 because 243 + 75 = 318

1.67

832 − 376 = 456 because 456 + 376 = 832

1.68

847 − 578 = 269 because 269 + 578 = 847

1.69

4,585 − 697 = 3,888 because 3,888 + 697 = 4,585

1.70

5,637 − 899 = 4,738 because 4,738 + 899 = 5,637

1.71
  1. 14 − 9 = 5
  2. 37 − 21 = 16
1.72
  1. 11 − 6 = 5
  2. 67 − 18 = 49
1.73

The difference is 19 degrees Fahrenheit.

1.74

The difference is 17 degrees Fahrenheit.

1.75

The difference is $149.

1.76

The difference is $136.

1.77
  1. eight times seven ; the product of eight and seven
  2. eighteen times eleven ; the product of eighteen and eleven
1.78
  1. thirteen times seven ; the product of thirteen and seven
  2. five times sixteen; the product of five and sixteen
1.81
  1. 00
  2. 00
1.82
  1. 00
  2. 00
1.83
  1. 1919
  2. 3939
1.84
  1. 2424
  2. 5757
1.85

54 and 54; both are the same.

1.86

48 and 48; both are the same.

1.87

512512

1.88

342342

1.89

1,7351,735

1.90

3,2343,234

1.91

3,354

1.92

3,776

1.93
  1. 540
  2. 5,400
1.94
  1. 750
  2. 7,500
1.95

127,995

1.96

653,462

1.97

365,462

1.98

504,108

1.99

13 · 28; 364

1.100

47 · 14; 658

1.101

2(167); 334

1.102

2(258); 516

1.103

Valia donated 144 water bottles.

1.104

Vanessa bought 80 hot dogs.

1.105

Erin needs 28 dahlias.

1.106

There are 36 women in the choir.

1.107

Jane needs 320 tiles.

1.108

Yousef needs 1,080 tiles.

1.109

The area of the rug is 40 square feet.

1.110

The area of the driveway is 900 square feet

1.111
  • eighty-four divided by seven; the quotient of eighty-four and seven
  • eighteen divided by six; the quotient of eighteen and six.
  • twenty-four divided by eight; the quotient of twenty-four and eight
1.112
  • seventy-two divided by nine; the quotient of seventy-two and nine
  • twenty-one divided by three; the quotient of twenty-one and three
  • fifty-four divided by six; the quotient of fifty-four and six
1.115

9 3

1.116

4 5

1.117
  1. 1
  2. 27
1.118
  1. 16
  2. 4
1.119

0 undefined

1.120

0 undefined

1.121

659

1.122

679

1.123

861

1.124

651

1.125

704

1.126

809

1.127

476 with a remainder of 4

1.128

539 with a remainder of 7

1.129

114 R11

1.130

121 R9

1.131

307 R49

1.132

308 R77

1.133

91 ÷ 13; 7

1.134

52 ÷ 13; 4

1.135

Marcus can fill 15 cups.

1.136

Andrea can make 9 bows.

Section 1.1 Exercises

1.
  1. 5, 125
  2. 5, 125
3.
  1. 50, 221
  2. 50, 221
5.

561

7.

407

9.
  1. thousands
  2. hundreds
  3. tens
  4. ten thousands
  5. hundred thousands
11.
  1. hundred thousands
  2. millions
  3. thousands
  4. tens
  5. ten thousands
13.

One thousand, seventy-eight

15.

Three hundred sixty-four thousand, five hundred ten

17.

Five million, eight hundred forty-six thousand, one hundred three

19.

Thirty seven million, eight hundred eighty-nine thousand, five

21.

Fourteen thousand, four hundred ten

23.

Six hundred thirteen thousand, two hundred

25.

Two million, six hundred seventeen thousand, one hundred seventy-six

27.

Twenty three million, eight hundred sixty-seven thousand

29.

One billion, three hundred seventy-seven million, five hundred eighty-three thousand, one hundred fifty-six

31.

412

33.

35,975

35.

11,044,167

37.

3,226,512,017

39.

7,173,000,000

41.

39,000,000,000,000

43.
  1. 390
  2. 2,930
45.
  1. 13,700
  2. 391,800
47.
  1. 1,490
  2. 1,500
49.
  1. 64,00064,000
  2. 63,90063,900
51.

Twenty four thousand, four hundred ninety-three dollars

53.
  1. $24,490
  2. $24,500
  3. $24,000
  4. $20,000
55.
  1. 1,000,000,0001,000,000,000
  2. 1,400,000,0001,400,000,000
  3. 1,356,000,0001,356,000,000
57.

Answers may vary. The whole numbers are the counting numbers with the inclusion of zero.

Section 1.2 Exercises

59.

five plus two; the sum of 5 and 2.

61.

thirteen plus eighteen; the sum of 13 and 18.

63.

two hundred fourteen plus six hundred forty-two; the sum of 214 and 642

65.


No Alt Text

2+4=62+4=6

67.


No Alt Text

8+4=128+4=12

69.


No Alt Text

14+75=8914+75=89

71.


No Alt Text

16+25=4116+25=41

73.


No Alt Text
75.


No Alt Text
77.


No Alt Text
79.
  1. 13
  2. 13
81.
  1. 1111
  2. 1111
83.

7878

85.

9999

87.

8585

89.

142142

91.

493493

93.

861861

95.

1,0311,031

97.

6,8506,850

99.

22,33322,333

101.

1,104,8601,104,860

103.

29,19129,191

105.

101,531101,531

107.

13+18=3113+18=31

109.

90+65=15590+65=155

111.

33+49=8233+49=82

113.

250+599=849250+599=849

115.

628+77=705628+77=705

117.

915+1,482=2,397915+1,482=2,397

119.

The total cost was $1,875.

121.

Ethan rode 138 miles.

123.

The total square footage in the rooms is 1,167 square feet.

125.

Natalie’s total salary is $237,186.

127.

The perimeter of the figure is 44 inches.

129.

The perimeter of the figure is 56 meters.

131.

The perimeter of the figure is 71 yards.

133.

The perimeter of the figure is 62 feet.

135.

The total number of calories was 640.

137.

Yes, he scored 406 points.

138.

Yes, the total weight is 1091 pounds.

139.

Answers will vary.

Section 1.3 Exercises

141.

fifteen minus nine; the difference of fifteen and nine

143.

forty-two minus thirty-five; the difference of forty-two and thirty-five

145.

hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty

147.


No Alt Text
149.


No Alt Text
151.


No Alt Text
153.


No Alt Text
155.


No Alt Text
157.


No Alt Text
159.

5

161.

8

163.

22

165.

33

167.

123

169.

1,321

171.

28

173.

222

175.

346

177.

3,519

179.

1,186

181.

34,668

183.

10 − 3; 7

185.

15 − 4; 11

187.

9 − 6; 3

189.

75 − 28; 47

191.

45 − 20; 25

193.

92 − 67; 25

195.

16 − 12; 4

197.

61 − 38; 23

199.

29

201.

72

203.

1,060

205.

22

207.

75 + 35; 110

209.

41 − 13; 28

211.

100 − 76; 24

213.

The difference between the high and low temperature was 17 degrees

215.

The difference between the third grade and second grade was 13 children.

217.

The difference between the regular price and sale price is $251.

219.

John needs to save $155 more.

221.

157 miles

223.

Answers may vary.

Section 1.4 Exercises

225.

four times seven; the product of four and seven

227.

five times twelve; the product of five and twelve

229.

ten times twenty-five; the product of ten and twenty-five

231.

forty-two times thirty-three; the product of forty-two and thirty-three

233.


No Alt Text
235.


No Alt Text
237.


No Alt Text
239.


No Alt Text
241.


No Alt Text
243.


No Alt Text
245.

0

247.

0

249.

43

251.

28

253.

240,055

255.
  1. 42
  2. 42
257.

395

259.

1,650

261.

23,947

263.

1,976

265.

7,008

267.

2,295

269.

230

271.

3,600

273.

88,000

275.

50,000,000

277.

34,333

279.

422,506

281.

804,285

283.

26,624

285.

245,340

287.

1,476,417

289.

18 · 33; 594

291.

51(67); 3,417

293.

2(249); 498

295.

10(375); 3,750

297.

1,406

299.

148

301.

11,000

303.

11,424

305.

0

307.

15,383

309.

50 − 18; 32

311.

2(35); 70

313.

20 + 980; 1,000

315.

12(875); 10,500

317.

89 − 74; 15

319.

3,075 + 95; 3,170

321.

814 − 366; 448

323.

Tim brought 54 cans of soda to the party.

325.

There were 308 students.

327.

Rey donated 180 t-shirts.

329.

Stephanie should use 20 cups of fruit juice.

331.

There are 100 senators in the U.S. senate.

333.

The area of the wall is 117 square feet.

335.

The area of the room is 1,428 square feet.

337.

The area of the court is 4,700 square feet.

339.

Javier’s portfolio gained $3,600.

341.

Answers will vary.

Section 1.5 Exercises

343.

fifty-four divided by nine; the quotient of fifty-four and nine

345.

thirty-two divided by eight; the quotient of thirty-two and eight

347.

forty-eight divided by six; the quotient of forty-eight and six

349.

sixty-three divided by seven; the quotient of sixty-three and seven

351.


No Alt Text
353.


No Alt Text
355.


No Alt Text
357.


No Alt Text
359.

9

361.

9

363.

7

365.

9

367.

9

369.

5

371.

1

373.

1

375.

23

377.

19

379.

0

381.

undefined

383.

undefined

385.

0

387.

24

389.

12

391.

93

393.

132

395.

871

397.

7,831

399.

2,403

401.

901

403.

704

405.

10,209

407.

352 R6

409.

6,913 R1

411.

86,234 R4

413.

43,338 R2

415.

382 R5

417.

849

419.

96

421.

1,986 R17

423.

3,060

425.

72

427.

1,060

429.

35

431.

45 ÷ 15; 3

433.

288 ÷ 24; 12

435.

Ric can fill 32 bags.

437.

There are 25 groups.

439.

Marta can wrap 16 cakes from 1 roll.

441.

The difference is 28 miles per gallon.

443.

They will need 5 vans for the field trip

445.

Bill hiked 50 miles

447.

LaVonne treated 48 patients last week.

449.

Jenna uses 26 pairs of contact lenses, but there is 1 day left over, so she needs 27 pairs for 365 days.

451.

Answers may vary. Using multiplication facts can help you check your answers once you’ve finished division.

Review Exercises

453.
  1. 2, 99
  2. 0, 2, 99
455.
  1. 4, 90
  2. 0, 4, 90
457.


No Alt Text
459.
  1. tens
  2. hundred thousands
  3. ones
  4. ten thousands
  5. thousands
461.

Five thousand two hundred eighty

463.

Five million twelve thousand five hundred eighty-two

466.

15,253

467.

340,912,061

469.

410

471.

3,560

473.

39,000

475.

81,500

477.

four plus three; the sum of four and three

479.

five hundred seventy-one plus six hundred twenty-nine; the sum of five hundred seventy-one and six hundred twenty-nine

481.


No Alt Text
483.


No Alt Text
485.
  1. 19
  2. 19
487.
  1. 13
  2. 13
489.

79

491.

154

493.

19,827

495.

30 + 12; 42

497.

39 + 25; 64

499.

$76

501.

46 feet

503.

fourteen minus five; the difference of fourteen and five

505.

three hundred fifty-one minus two hundred forty-nine; the difference between three hundred fifty-one and two hundred forty-nine

507.


No Alt Text
509.

3

511.

14

513.

23

515.

322

517.

380

519.

9,985

521.

19 − 13; 6

523.

74 − 8; 66

525.

58 degrees Fahrenheit

527.

eight times five the product of eight and five

529.

ten times ninety-five; the product of ten and ninety-five

531.


No Alt Text
533.


No Alt Text
535.

0

537.

99

539.
  1. 28
  2. 28
541.

27,783

543.

640

545.

79,866

547.

1,873,608

549.

15(28); 420

551.

2(575); 1,150

553.

48 marigolds

555.

1,800 seats

557.

fifty-four divided by nine; the quotient of fifty-four and nine

559.

seventy-two divided by eight; the quotient of seventy-two and eight

561.


No Alt Text
563.

7

565.

13

567.

97

569.

undefined

571.

638

573.

300 R5

575.

64 ÷ 16; 4

577.

9 baskets

Practice Test

579.
  1. 4, 87
  2. 0, 4, 87
581.
  1. 613
  2. 55,208
583.

68

585.

17

587.

32

589.

0

591.

0

593.

66

595.

3,325

597.

490

599.

442

601.

11

603.

16 + 58; 74

605.

32 − 18; 14

607.

2(524); 1,048

609.

300 − 50; 250

611.

Stan had $344 left.

613.

Clayton walked 30 blocks.

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