Chapter 1 · PDF fileTwo million, twelve in standard form is 2,000,012. 37. Two hundred sixty thousand, nine hundred ninety-seven in standard form is 260,997. 38. ... 49. 3470 = 3000

1

Chapter 1

Section 1.2

Practice Problems

1. The place value of the 8 in 38,760,005 is millions.

2. The place value of the 8 in 67,890 is hundreds.

3. The place value of the 8 in 481,922 is ten-thousands.

4. 54 is written as fifty-four.

5. 678 is written as six hundred seventy-eight.

6. 93,205 is written as ninety-three thousand, two hundred five.

7. 679,430,105 is written as six hundred seventy-nine million, four hundred thirty thousand, one hundred five.

8. Thirty-seven in standard form is 37.

9. Two hundred twelve in standard form is 212.

10. Eight thousand, two hundred seventy-four in standard form is 8,274 or 8274.

11. Five million, fifty-seven thousand, twenty-six in standard form is 5,057,026.

12. 4,026,301 = 4,000,000 + 20,000 + 6000 + 300 + 1

13. a. Find Norway in the left-hand column. Read from left to right until the “gold” column is reached. Norway won 96 gold medals.

b. Find the countries for which the entry in the first column (gold) is greater than 100. Germany and Russia have won more than 100 gold medals.

Vocabulary and Readiness Check

1. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... are called whole numbers.

2. The number 1,286 is written in standard form.

3. The number “twenty-one” is written in words.

4. The number 900 + 60 + 5 is written in expanded form.

5. In a whole number, each group of 3 digits is called a period.

6. The place value of the digit 4 in the whole number 264 is ones.

Exercise Set 1.2

1. The place value of the 5 in 657 is tens.

2. The place value of the 5 in 905 is ones.

3. The place value of the 5 in 5423 is thousands.

4. The place value of the 5 in 6527 is hundreds.

5. The place value of the 5 in 43,526,000 is hundred-thousands.

6. The place value of the 5 in 79,050,000 is ten-thousands.

7. The place value of the 5 in 5,408,092 is millions.

8. The place value of the 5 in 51,682,700 is ten-millions.

9. 354 is written as three hundred fifty-four.

10. 316 is written as three hundred sixteen.

11. 8279 is written as eight thousand, two hundred seventy-nine.

12. 5445 is written as five thousand, four hundred forty-five.

13. 26,990 is written as twenty-six thousand, nine hundred ninety.

14. 42,009 is written as forty-two thousand, nine.

15. 2,388,000 is written as two million, three hundred eighty-eight thousand.

16. 3,204,000 is written as three million, two hundred four thousand.

17. 24,350,185 is written as twenty-four million, three hundred fifty thousand, one hundred eighty-five.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall

Chapter 1: The Whole Numbers ISM: Prealgebra

2

18. 47,033,107 is written as forty-seven million, thirty-three thousand, one hundred seven.

19. 65,773 is written as sixty-five thousand, seven hundred seventy-three.

20. 40,000 is written as forty thousand.

21. 1679 is written as one thousand, six hundred seventy-nine.

22. 6912 is written as six thousand, nine hundred twelve.

23. 2,800,000 is written as two million, eight hundred thousand.

24. 15,200,000 is written as fifteen million, two hundred thousand.

25. 11,239 is written as eleven thousand, two hundred thirty-nine.

26. 14,433 is written as fourteen thousand, four hundred thirty-three.

27. 202,700 is written as two hundred two thousand, seven hundred.

28. 799,000 is written as seven hundred ninety-nine thousand.

29. Six thousand, five hundred eighty-seven in standard form is 6587.

30. Four thousand, four hundred sixty-eight ion standard form is 4468.

31. Fifty-nine thousand, eight hundred in standard form is 59,800.

32. Seventy-three thousand, two in standard form is 73,002.

33. Thirteen million, six hundred one thousand, eleven in standard form is 13,601,011.

34. Sixteen million, four hundred five thousand, sixteen in standard form is 16,405,016.

35. Seven million, seventeen in standard form is 7,000,017.

36. Two million, twelve in standard form is 2,000,012.

37. Two hundred sixty thousand, nine hundred ninety-seven in standard form is 260,997.

38. Six hundred forty thousand, eight hundred eighty-one in standard form is 640,881.

39. Three hundred fifty-three in standard form is 353.

40. Two hundred thirty-four thousand in standard form is 234,000.

41. Four hundred eighty-four thousand, two hundred thirty-five in standard form is 484,235.

42. One thousand, eight hundred fifteen in standard form is 1815.

43. Fifty-four million, five hundred thousand in standard form is 54,500,000.

44. Fifty million, thirteen thousand, eight hundred fifty-nine in standard form is 50,013,859.

45. Seven hundred fourteen in standard form is 714.

46. Seven hundred fifty-five in standard form is 755.

47. 209 = 200 + 9

48. 789 = 700 + 80 + 9

49. 3470 = 3000 + 400 + 70

50. 6040 = 6000 + 40

51. 80,774 = 80,000 + 700 + 70 + 4

52. 20,215 = 20,000 + 200 + 10 + 5

53. 66,049 = 60,000 + 6000 + 40 + 9

54. 99,032 = 90,000 + 9000 + 30 + 2

55. 39,680,000 = 30,000,000 + 9,000,000 + 600,000 + 80,000

56. 47,703,029 = 40,000,000 + 7,000,000 + 700,000 + 3000 + 20 + 9

57. The elevation of Mt. Clay is 5532 which is five thousand, five hundred thirty-two in words.

58. The elevation of Mt. Washington is 6288 which is six thousand, two hundred eighty-eight in words.


ISM: Prealgebra Chapter 1: The Whole Numbers

3

59. The height of Boott Spur is 5492 which is 5000 + 400 + 90 + 2 in expanded form.

60. The height of Mt. Jefferson is 5712 which is 5000 + 700 + 10 + 2 in expanded form.

61. Mt. Washington is the tallest mountain in New England.

62. Mt. Adams is the second tallest mountain in New England.

63. Chihuahua has fewer dogs registered than Golden retriever.

64. Beagle has more dogs registered than Yorkshire terrier.

65. Labrador retrievers have the most registrations; 146,714 is written as one hundred forty-six thousand, seven hundred fourteen.

66. Chihuahuas have the fewest registrations; 24,853 is written as twenty-four thousand, eight hundred fifty-three.

67. The maximum weight of an average-size Dachshund is 25 pounds.

68. The maximum height of an average-size Yorkshire terrier is 9 inches.

69. The largest number is 9861.

70. The largest number is 77,753.

71. No; 105.00 should be written as one hundred five.

72. Yes

73. answers may vary


75. 135.5 trillion in standard form is 135,500,000,000,000.

Section 1.3

Practice Problems

1. 4135252

4387+

2.

1 1 1 147,364

135,898183, 262

+

3. Notice 12 + 8 = 20 and 4 + 6 = 10. 12 + 4 + 8 + 6 + 5 = 20 + 10 + 5 = 35

4.

1 2 26432789

5428

7303+

5. a. 14 − 6 = 8 because 8 + 6 = 14.

b. 20 − 8 = 12 because 12 + 8 = 20

c. 93 − 93 = 0 because 0 + 93 = 93.

d. 42 − 0 = 42 because 42 + 0 = 42.

6. a. 9123142

8981−

Check: 8981142

9123+

b. 978851127

− Check: 127

851978

+

7. a. 8 17

69 74 9

64 8−

Check: 64849

697+

b. 2 12326245

81−

Check: 81245326

+

c. 1234822412

− Check: 412

8221234+

8. a.

9310104 0 01 6 42 3 6

− Check: 236

164400

+



4

b.

991010

10 0 07 6 22 3 8

− Check: 238

7621000+

9. 2 cm + 8 cm + 15 cm + 5 cm = 30 cm The perimeter is 30 centimeters.

10. 647 + 647 + 647 = 1941 The perimeter is 1941 feet.

11. 15,759458

15,301−

The radius of Neptune is 15,301 miles.

12. a. The model with the fewest seats corresponds to the shortest bar, which is the F-100.

b. Add the number of seats for each model. 37087

141598

+

The total number of seats in the B747-400, F-100, and B737-400 is 598.

Calculator Explorations

1. 89 + 45 = 134

2. 76 + 97 = 173

3. 285 + 55 = 340

4. 8773 + 652 = 9425

5. 985 + 1210 + 562 + 77 = 2834

6. 465 + 9888 + 620 + 1550 = 12,523

7. 865 − 95 = 770

8. 76 − 27 = 49

9. 147 − 38 = 109

10. 366 − 87 = 279

11. 9625 − 647 = 8978

12. 10,711 − 8925 = 1786


1. The sum of 0 and any number is the same number.

2. In 35 + 20 = 55, the number 55 is called the sum and 35 and 20 are each called an addend.

3. The difference of any number and that same number is 0.

4. The difference of any number and 0 is the same number.

5. In 37 − 19 = 18, the number 37 is the minuend, the 19 is the subtrahend, and the 18 is the difference.

6. The distance around a polygon is called its perimeter.

7. Since 7 + 10 = 10 + 7, we say that changing the order in addition does not change the sum. This property is called the commutative property of addition.

8. Since (3 + 1) + 20 = 3 + (1 + 20), we say that changing the grouping in addition does not change the sum. This property is called the associative property of addition.

Exercise Set 1.3

1. 142236

+

2 273158

+

3. 62230292

+

4. 37542579

+

5. 12132449

+



5

6. 23453098

+

7. 5267132

5399+

8. 23662436479

+

9.

1 1 122,781

186, 297209,078

+

10.

117,427

821,059838, 486

+

11. 89251

25+

12. 35857

28+

13.

2 28117237912

212+

14.

2 26428562532

205+

15.

1 1 224

9006489

240711,926+

16.

1 1 216

1056748

77709590

+

17.

1 1 16 8204 2715 626

16,717+

18.

1 11 1678943215555

16,665+

19.

1 1 2 249

6285 762

29, 46235,901

+

20.

1 1 126

5824 763

62,51167,882

+



6

21.

1 2 2 2 1121,74257, 27926,586

426,782632,389

+

22.

1 11 2 1 2504, 218321,92038,507

594,6871,459,332+

23. 623725

− Check:

1253762

+

24. 552926

− Check:

1262955

+

25. 749149600

− Check: 600

149749

+

26. 957257700

− Check: 700

257957

+

27. 922634288

− Check:

11288634922

+

28. 674299375

− Check:

1 1375299674

+

29. 600432168

− Check:

1 1168432600

+

30. 300149151

− Check:

11151149300

+

31. 6283560

5723−

Check: 15723560

6283+

32. 5349720

4629−

Check: 14629

7205349+

33. 53329

504−

Check: 1

50429

533+

34. 72416

708−

Check: 1

70816

724+

35. 19831904

79−

Check: 179

19041983

+

36. 19831914

69−

Check: 169

19141983

+

37. 50,00017, 28932,711

− Check:

1 1 1 132,71117,28950,000

+

38. 40,00023,58216,418

− Check:

1 1 1116, 41823,58240,000

+

39. 702019795041

− Check:

111504119797020

+

40. 605018784172

− Check:

11 1417218786050

+



7

41. 51,11119,89831, 213

− Check:

1 1 1 131,21319,89851,111

+

42. 62, 22239,89822,324

− Check:

1 1 1 122,32439,89862,222

+

43. 98648

1034+

44. 98648

938−

45. 7667

9−

46.

2809317

92

201+

47. 9000482

8518−

48. 10,00017868214

−

49.

1 1 110,962

4 8517 063

22,876+

50.

1 1 112, 4683 2111 988

17,667+

51. 7 + 8 + 10 = 25 The perimeter is 25 feet.

52. 3 + 4 + 5 = 12 The perimeter is 12 centimeters.

53. Opposite sides of a rectangle have the same length. 4 + 8 + 4 + 8 = 12 + 12 = 24 The perimeter is 24 inches.

54. Opposite sides of a rectangle have the same length. 8 + 4 + 8 + 4 = 12 + 12 = 24 The perimeter is 24 miles.

55. 8 + 3 + 5 + 7 + 5 + 1 = 29 The perimeter is 29 inches.

56. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37 The perimeter is 37 inches.

57. The unknown vertical side has length 12 − 5 = 7 meters. The unknown horizontal side has length 10 − 5 = 5 meters. 10 + 12 + 5 + 7 + 5 + 5 = 44 The perimeter is 44 meters.

58. The unknown vertical side has length 3 + 5 = 8 feet. The unknown horizontal side has length 8 + 4 = 12 feet. 8 + 3 + 4 + 5 + 12 + 8 = 40 The perimeter is 40 feet.

59. “Find the sum” indicates addition. 111297

17962093

+

The sum of 297 and 1796 is 2093.

60. “Find the sum” indicates addition. 1802

64877289

+




8

61. “Find the total” indicates addition. 1 3

7639

817

126266

+

The total of 76, 39, 8, 17, and 126 is 266.

62. “Find the total” indicates addition. 1 2

89452

19341496

+

The total of 89, 45, 2, 19, and 341 is 496.

63. “Find the difference” indicates subtraction. 412120

−

The difference of 41 and 21 is 20.

64. “Find the difference” indicates subtraction. 16

511

−


65. “Increased by” indicates addition. 145292

544+

452 increased by 92 is 544.

66. “Increased by” indicates addition. 712

38750

+

712 increased by 38 is 750.

67. “Less” indicates subtraction. 1083672

−

108 less 36 is 72.

68. “Less” indicates subtraction. 251213

−

25 less 12 is 13.

69. “Subtracted from” indicates subtraction. 100

1288

−

12 subtracted from 100 is 88.

70. “Subtracted from” indicates subtraction. 90864

−


71. Subtract 36,039 thousand from 38,067 thousand. 38,06736,039

2 028−

California’s projected population increase is 2028 thousand.

72. Subtract 12,699 thousand from 12,917 thousand. 12,91712,699

218−

Illinois’ projected population increase is 218 thousand.

73. Subtract the cost of the DVD player from the amount in her savings account.

914295619

−

She will have $619 left.

74. Subtract the discount from the regular price. 547

99448

−

The sale price is $448.

75. 189,00075,000

264,000+

The total U.S. land area drained by the Upper Mississippi and Lower Mississippi sub-basins is 264,000 square miles.



9

76. 164,00040,000

204,000+

The total U.S. land area drained by the Ohio and Tennessee sub-basins is 204,000 square miles.

77. 530,000247,000283,000

−

The Missouri sub-basin drains 283,000 square miles more than the Arkansas Red-White sub-basin.

78. 189,00075,000

114,000−

The Upper Mississippi sub-basin drains 114,000 square miles more than the Lower Mississippi sub-basin.

79. 70 + 78 + 90 + 102 = 340 The homeowner needs 340 feet of fencing.

80. Opposite sides of a rectangle have the same length. 60 + 45 + 60 + 45 = 210 The perimeter is 210 feet.

81. 503239264

−

She must read 264 more pages.

82. 59,32055,492

3 828−

They traveled 3828 miles on their trip.

83. 386,119426,990813,109

+

The total number sold in the U.S. in 2005 was 813,109.

84.

11 1 114,141,199

35,758,80139,900,000

+

The sheep population was 39,900,000.

85. Live rock music has a decibel level of 100 dB.

86. The shortest bar corresponds to the quietest reading. Leaves rustling is the quietest.

87. 883058

−

The sound of snoring is 58 dB louder than normal conversation.

88. 1007030

−

The difference in sound intensity between live rock music and loud television is 30 dB.

89.

111569633469042

+

There were 9042 stores worldwide.

90. 1199920

−

The difference in volume between the mid-size and a sub-compact car is 20 cubic feet.

91. Each side of a square has the same length. 31 + 31 + 31 + 31 = 124 The perimeter of the playing board is 124 feet.

92. Opposite sides of a rectangle have the same length. 18 + 12 + 18 + 12 = 60 The perimeter of the puzzle is 60 inches.

93. California has the most Target stores.

94. Arizona has the fewest Target stores.

95.

1 120512195

421+

The total number of Target stores in California, Texas, and Florida is 421 stores.

96. 41 + 205 + 95 + 44 + 75 + 49 + 53 + 64 + 49 + 121 = 796 The total number in the ten states listed in 796 stores.



10

97. Florida and Georgia: 19544

139+

Michigan and Ohio: 115349

102+

Florida and Georgia have more Target stores.

98. The total number of stores listed in the table is 796 stores.

796601

1397+

There are 1397 Target stores in the United States.

99.

1202938655894

+

The total highway mileage in Delaware is 5894 miles.

100.

1519312226415

+

The total highway mileage in Rhode Island is 6415 miles.

101. The minuend is 48 and the subtrahend is 1.





106. answers may vary.

107.

1566932871

2369+

The given sum is correct.

108.

2 1773659481

1913+

The given sum is correct.

109.

2 214

17386

257530

+

The given sum is incorrect, the correct sum is 530.

110.

1 219

21449

651933

+

The given sum is incorrect, the correct sum is 933.

111.

1167556

731+

The given difference is incorrect. 74156

685−

112.

1 1389

89478

+

The given difference is correct.

113. 141888

1029+

The given difference is correct.



11

114.

117168547

7715+

The given difference is incorrect. 7615547

7068−

115. 526923852884

−

116. 10,2448 5341 710

−



119.

1 2 1 3 2289,462369, 477218, 287121,685998,911

+

Since 998,911 is less than one million, they did not reach their goal.

1,000,000998,911

1 089−

They need to read 1089 more pages.

Section 1.4

Practice Problems

1. a. To round 57 to the nearest ten, observe that the digit in the ones place is 7. Since the digit is at least 5, we add 1 to the digit in the tens place. The number 57 rounded to the nearest ten is 60.

b. To round 641 to the nearest ten, observe that the digit in the ones place is 1. Since the digit is less than 5, we do not add 1 to the digit in the tens place. The number 641 rounded to the nearest ten is 640.

c. To round 325 to the nearest ten observe that the digit in the ones place is 5. Since the digit is at least 5, we add 1 to the digit in the

tens place. The number 325 rounded to the nearest ten is 330.

2. a. To round 72,304 to the nearest thousand, observe that the digit in the hundreds place is 3. Since the digit is less than 5, we do not add 1 to the digit in the thousands place. The number 72,304 rounded to the nearest thousand is 72,000.

b. To round 9222 to the nearest thousand, observe that the digit in the hundreds place is 2. Since the digit is less than 5, we do not add 1 to the digit in the thousands place. The number 9222 rounded to the nearest thousand is 9000.

c. To round 671,800 to the nearest thousand, observe that the digit in the hundreds place is 8. Since this digit is at least 5, we add 1 to the digit in the thousands place. The number 671,800 rounded to the nearest thousand is 672,000.

3. a. To round 3474 to the nearest hundred, observe that the digit in the tens place is 7. Since this digit is at least 5, we add 1 to the digit in the hundreds place. The number 3474 rounded to the nearest hundred is 3500.

b. To round 76,243 to the nearest hundred, observe that the digit in the tens place is 4. Since this digit is less than 5, we do not add 1 to the digit in the hundreds place. The number 76,243 rounded to the nearest hundred is 76,200.

c. To round 978,865 to the nearest hundred, observe that the digit in the tens place is 6. Since this digit is at least 5, we add 1 to the digit in the hundreds place. The number 978,865 rounded to the nearest hundred is 978,900.

4. 49 rounds to 5025 rounds to 3032 rounds to 3051 rounds to 5098 rounds to + 100

260

5. 3785 rounds to 40002479 rounds to 2000

2000− −



12

6. 11 rounds to 1016 rounds to 2019 rounds to 2031 rounds to + 30

80+

The total distance is approximately 80 miles.

7. 120,710 rounds to 120,00022,878 rounds to 20,00045,974 rounds to + 50,000

190,000+

The total number of cases is approximately 190,000.


1. To graph a number on a number line, darken the point representing the location of the number.

2. Another word for approximating a whole number is rounding.

3. The number 65 rounded to the nearest ten is 70 but the number 61 rounded to the nearest ten is 60.

4. An exact number of products is 1265, but an estimate is 1000.

Exercise Set 1.4

1. To round 423 to the nearest ten, observe that the digit in the ones place is 3. Since this digit is less than 5, we do not add 1 to the digit in the tens place. The number 423 rounded to the nearest ten is 420.


3. To round 635 to the nearest ten, observe that the digit in the ones place is 5. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 635 rounded to the nearest ten is 640.


5. To round 2791 to the nearest hundred, observe that the digit in the tens place is 9. Since this digit is at least 5, we add 1 to the digit in the hundreds place. The number 2791 rounded to the nearest hundred is 2800.

6. To round 8494 to the nearest hundred, observe that the digit in the tens place is 9. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 8494 rounded to the nearest hundred is 8500.



9. To round 21,094 to the nearest thousand, observe that the digit in the hundreds place is 0. Since this digit is less than 5, we do not add 1 to the digit in the thousands place. The number 21,094 rounded to the nearest thousand is 21,000.


11. To round 33,762 to the nearest thousand, observe that the digit in the hundreds place is 7. Since this digit is at least 5, we add 1 to the digit in the thousands place. The number 33,762 rounded to the nearest thousand is 34,000.

12. To round 42,682 to the nearest ten-thousand, observe that the digit in the thousands place is 2. Since this digit is less than 5, we do not add 1 to the digit in the ten-thousands place. The number 42,682 rounded to the nearest ten-thousand is 40,000.

13. To round 328,495 to the nearest hundred, observe that the digit in the tens place is 9. Since this digit is at least 5, we add 1 to the digit in the hundreds place. The number 328,495 rounded to the nearest hundred is 328,500.



13

14. To round 179,406 to the nearest hundred, observe that the digit in the tens place is 0. Since this digit is less than 5, we do not add 1 to the digit in the hundreds place. The number 179,406 rounded to the nearest hundred is 179,400.



17. To round 39,994 to the nearest ten, observe that the digit in the ones place is 4. Since this digit is less than 5, we do not add 1 to the digit in the tens place. The number 39,994 rounded to the nearest ten is 39,990.

18. To round 99,995 to the nearest ten, observe that the digit in the ones place is 5. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 99,995 rounded to the nearest ten is 100,000.

19. To round 29,834,235 to the nearest ten-million, observe that the digit in the millions place is 9. Since this digit is at least 5, we add 1 to the digit in the ten-millions place. The number 29,834,235 rounded to the nearest ten-million is 30,000,000.

20. To round 39,523,698 to the nearest million, observe that the digit in the hundred-thousands place is 5. Since this digit is at least 5, we add 1 to the digit in the millions place. The number 39,523,698 rounded to the nearest million is 40,000,000.

21. Estimate 5281 to a given place value by rounding it to that place value. 5281 rounded to the tens place is 5280, to the hundreds place is 5300, and to the thousands place is 5000.




25. Estimate 14,876 to a given place value by rounding it to that place value. 14,876 rounded to the tens place is 14,880, to the hundreds place is 14,900, and to the thousands place is 15,000.

26. Estimate 85,049 to a given place value by rounding it to that place value. 85,049 rounded to the tens place is 85,050, to the hundreds place is 85,000, and to the thousands place is 85,000.

27. To round 19,264 to the nearest thousand, observe that the digit in the hundreds place is 2. Since this digit is less than 5, we do not add 1 to the digit in the thousands place. Therefore, 19,264 rounded to the nearest thousand is 19,000.

28. To round 85,907,423 to the nearest hundred-thousand, observe that the digit in the ten-thousands place is 0. Since this digit is less than 5, we do not add 1 to the digit in the hundred-thousands place. Therefore 85,907,423 passengers rounded to the nearest hundred-thousand is 85,900,000 passengers.

29. To round 38,387 to the nearest thousand, observe that the digit in the hundreds place is 3. Since this digit is less than 5, we do not add 1 to the digit in the thousands place. Therefore, 38,387 points rounded to the nearest thousand is 38,000 points.

30. To round 60,149 to the nearest hundred, observe that the digit in the tens place is 4. Since this digit is less than 5, we do not add 1 to the digit in the hundreds place. Therefore, 60,149 days rounded to the nearest hundred is 60,100 days.

31. To round 67,520,000,000 to the nearest billion, observe that the digit in the hundred-millions place is 5. Since this digit is at least 5, we add 1 to the digit in the billions place. Therefore, $67,520,000,000 rounded to the nearest billion is $68,000,000,000.



14

32. To round 281,421,906 to the nearest million, observe that the digit in the hundred-thousands place is 4. Since this digit is less than 5, we do not add 1 to the digit in the millions place. Therefore, 281,421,906 rounded to the nearest million is 281,000,000.

33. To round 3,023,894 to the nearest hundred-thousand, observe that the digit in the ten-thousands place is 2. Since this digit is less than 5, we do not add 1 to the digit in the hundred-thousands place. Therefore, $3,023,894 rounded to the nearest hundred-thousand is $3,000,000.

34. To round 56,720,000,000 to the nearest billion, observe that the digit in the hundred-millions place is 7. Since this digit is at least 5, we add 1 to the digit in the billions place. Therefore, $56,720,000,000 rounded to the nearest billion is $57,000,000,000.

35. U.S.: To round 207,897,000 to the nearest million, observe that the digit in the hundred-thousands place is 8. Since this digit is at least 5, we add 1 to the digit in the millions place. The number 207,897,000 rounded to the nearest million is 208,000,000. India: To round 69,193,300 to the nearest million, observe that the digit in the hundred-thousands place is 1. Since this digit is less than 5, we do not add 1 to the digit in the millions place. The number 69,193,300 rounded to the nearest million is 69,000,000.

36. To round 114,878,000 to the nearest ten-million, observe that the digit in the millions place is 4. Since this digit is less than 5, we do not add 1 to the digit in the ten-millions place. Therefore, 114,878,000 bushels rounded to the nearest ten-million is 110,000,000 bushels.

37. 39452217+

rounds torounds torounds torounds to

40502020

130+

38. 52 rounds to 5033 rounds to 3015 rounds to 2029 rounds to + 30

130+


80− −


320− −

41. 191318861925+

rounds torounds torounds to

1900190019005700

+

42. 4050 rounds to 41003133 rounds to 31001220 rounds to 1200

8400+ +


300− −


100− −

45. 399525494944+


400025004900

11, 400+


271 rounds to + 3002800

+

47. 463 + 219 is approximately 460 + 220 = 680. The answer of 680 is incorrect because 463 + 219 = 682.

48. 522 + 785 is approximately 520 + 790 = 1310. The answer of 1307 is correct.

49. 229 + 443 + 606 is approximately 230 + 440 + 600 = 1270. The answer of 1278 is correct.

50. 542 + 789 + 198 is approximately 540 + 790 + 200 = 1530. The answer of 2139 is incorrect.



15

51. 7806 + 5150 is approximately 7800 + 5200 = 13,000. The answer of 12,956 is correct.

52. 5233 + 4988 is approximately 5200 + 5000 = 10,200. The answer of 9011 is incorrect.

53. 8991499999+


900150010003400

+

The total cost is approximately $3400.


100 rounds to 10079 rounds to 8075 rounds to 8082 rounds to + 80

530+

The total score is approximately 530.


900− −

Boston in approximately 900 miles farther from Kansas City than Chicago is.

56. 588 rounds to 600689 rounds to 700277 rounds to 300143 rounds to 10059 rounds to 100

802 rounds to + 8002600

+


57. 20,32014,410−

rounds torounds to

20,00014,000

6 000−

The difference in elevation is approximately 6000 feet.


400− −

The difference in price is approximately $400.

59. 782,623 rounds to 780,000382,894 rounds to 380,000

400,000− −

Jacksonville was approximately 400,000 larger than Miami.


133 rounds to + 130230

+


61. 909,608906,993−

rounds torounds to

910,000907,000

3 000−

The decrease in enrollment is approximately 3000 children.

62. 51,746 rounds to 52,00049,713 rounds to 50,000

2 000− −

The increase is approximately 2000 credit hours.

63. $339 million is $339,000,000 in standard form. $339,000,000 rounded to the nearest ten-million is $340,000,000. $339,000,000 rounded to the nearest hundred-million is $300,000,000.




67. 5723, for example, rounded to the nearest hundred is 5700.

68. 5698, for example, rounded to the nearest ten is 5700.



16

69. a. The smallest possible number that rounds to 8600 is 8550.

b. The largest possible number that rounds to 8600 is 8649.

70. The largest possible number that rounds to 1,500,000 when rounded to the nearest hundred-thousand is 1,549,999.


72. 5950 rounds to 6 0007693 rounds to 7 7008203 rounds to 8 200

21,900+ +

The perimeter is approximately 21,900 miles.

73. 54 rounds to 50 17 rounds to 20 50 + 20 + 50 + 20 = 140 The perimeter is approximately 140 meters.

Section 1.5

Practice Problems

1. a. 6 × 0 = 0

b. (1)8 = 8

c. (50)(0) = 0

d. 75 ⋅ 1 = 75

2. a. 6(4 + 5) = 6 ⋅ 4 + 6 ⋅ 5

b. 30(2 + 3) = 30 ⋅ 2 + 30 ⋅ 3

c. 7(2 + 8) = 7 ⋅ 2 + 7 ⋅ 8

3. a. 296

54120174

×

b. 6485

40200

30003240

×

4. 30681

30624 48024,786

×

5. 726142

1 45229 04072 600

103,092

×

6. Area length width(360 miles)(280 miles)100,800 square miles

= ⋅==

The area of Wyoming is 100,800 square miles.

7. 164580

640720

×

The printer can print 720 pages in 45 minutes.

8. 8 11 885 9 45× =× =

18845

133+

The total cost is $133.


80,000× ×

There are approximately 80,000 words on 391 pages.


1. 72 × 48 = 3456

2. 81 × 92 = 7452

3. 163 ⋅ 94 = 15,322

4. 285 ⋅ 144 = 41,040

5. 983(277) = 272,291

6. 1562(843) = 1,316,766



17


1. The product of 0 and any number is 0.

2. The product of 1 and any number is the number.

3. In 8 ⋅ 12 = 96, the 96 is called the product and 8 and 12 are each called a factor.

4. Since 9 ⋅ 10 = 10 ⋅ 9, we say that changing the order in multiplication does not change the product. This property is called the commutative property of multiplication.

5. Since (3 ⋅ 4) ⋅ 6 = 3 ⋅ (4 ⋅ 6), we say that changing the grouping in multiplication does not change the product. This property is called the associative property of multiplication.

6. Area measures the amount of surface of a region.

7. Area of a rectangle = length ⋅ width.

8. We know 9(10 + 8) = 9 ⋅ 10 + 9 ⋅ 8 by the distributive property.

Exercise Set 1.5

1. 1 ⋅ 24 = 24

2. 55 ⋅ 1 = 55

3. 0 ⋅ 19 = 0

4. 27 ⋅ 0 = 0

5. 8 ⋅ 0 ⋅ 9 = 0

6. 7 ⋅ 6 ⋅ 0 = 0

7. 87 ⋅ 1 = 87

8. 1 ⋅ 41 = 41

9. 6(3 + 8) = 6 ⋅ 3 + 6 ⋅ 8

10. 5(8 + 2) = 5 ⋅ 8 + 5 ⋅ 2

11. 4(3 + 9) = 4 ⋅ 3 + 4 ⋅ 9

12. 6(1 + 4) = 6 ⋅ 1 + 6 ⋅ 4

13. 20(14 + 6) = 20 ⋅ 14 + 20 ⋅ 6

14. 12(12 + 3) = 12 ⋅ 12 + 12 ⋅ 3

15. 648

512×

16. 793

237×

17. 6136

3678×

18. 6385

3190×

19. 2776

1662×

20. 8822

1764×

21. 10746

6444×

22. 90213

27,063×

23. 8913

267890

1157

×

24. 9172

18263706552

×

25. 42158

3 36821 05024,418

×



18

26. 52623

1 57810 52012,098

×

27. 30681

30624 48024,786

×

28. 70821

70814 16014,868

×

29. 78020

15,600×

30. 72080

57,600×

31. (495)(13)(0) = 0

32. (593)(47)(0) = 0

33. (640)(1)(10) = (640)(10) = 6400

34. (240)(1)(20) = (240)(20) = 4800

35. 123439

1110637 02048,126

×

36. 135779

12 21394 990

107,203

×

37. 609234

2 43618 270

121 800142,506

×

38. 807127

5 64916 14080 700

102, 489

×

39. 8649274

34 596605 430

1 729 8002,369,826

×

40. 1234567

8 63874 040

617 000699,678

×

41. 589110

5 89058 90064,790

×

42. 426110

4 26042 60046,860

×

43. 19412035

9 70558 230

3 882 0003,949,935

×



19

44. 18761407

13 132750 400

1 876 0002,639,532

×

45. Area (length)(width)(9 meters)(7 meters)63 square meters

===

46. Area (length)(width)(13 inches)(3 inches)39 square inches

===

47. Area (length)(width)(40 feet)(17 feet)680 square feet

===

48. Area (length)(width)(25 centimeters)(20 centimeters)500 square centimeters

===

49. 576354×

rounds torounds to

600400

240,000×


700,000× ×


300,000× ×


100,000× ×

53. 38 × 42 is approximately 40 × 40, which is 1600. The best estimate is c.

54. 2872 × 12 is approximately 2872 × 10, which is 28,720. The best estimate is b.

55. 612 × 29 is approximately 600 × 30, which is 18,000. The best estimate is c.

56. 706 × 409 is approximately 700 × 400, which is 280,000. The best estimate is d.

57. 80 11 (8 10) 118 (10 11)8 110880

× = × ×= × ×= ×=

58. 70 12 (7 10) 127 (10 12)7 120840

× = × ×= × ×= ×=

59. 6 × 700 = 4200

60. 9 × 900 = 8100

61. 22402

4480×

62. 33103

9930×

63. 1253

375×

There are 375 calories in 3 tablespoons of olive oil.

64. 148

112×

There are 112 grams of fat in 8 ounces of hulled sunflower seeds.

65. 9435

47028203290

×


66. 3414

136340476

×

There are 476 seats in the room.



20

67. a. 4 × 5 = 20 There are 20 boxes in one layer.

b. 205

100×

There are 100 boxes on the pallet.

c. 10020

2000×

The weight of the cheese on the pallet is 2000 pounds.

68. a. 5 × 4 = 20 There are 20 apartments on one floor.

b. 203

60×

There are 60 apartments in the building.


===

The area is 8800 square feet.


===

The area is 2700 square feet.

71. Area (length)(width)(350 feet)(160 feet)56,000 square feet

===

The area is 56,000 square feet.

72. Area (length)(width)(776 meters)(639 meters)495,864 square meters

===

The area is 495,864 square meters.

73. 9462

18856405828

×

There are 5828 pixels on the screen.

74. 70017

4 9007 000

11,900

×

The 17 discs hold 11,900 MB.

75. 6035

3001 8002 100

×

There are 2100 characters in 35 lines.

76. 3653

1095×

A cow eats 1095 pounds of grain each year.

77. 1608

1280×

There are 1280 calories in 8 ounces.

78. 131678

130208

×

There are 208 grams of fat in 16 ounces.

79. T-

Shirt Size

Number of Shirts Ordered

Cost per

Shirt

Cost per Size

Ordered

S 4 $10 $40

M 6 $10 $60

L 20 $10 $200

XL 3 $12 $36

XXL 3 $12 $36

Total Cost $372



21

80.

Person

Number of

persons

Cost per person

Cost per Category

Student 24 $5 $120

Nonstudent 4 $7 $28

Children under 12

5 $2 $10

Total Cost $158

81. There are 31 days in March. 31 700,000 31 7 100,000

217 100,00021,700,000

× = × ×= ×=

They would use 21,700,000 quarts in March.

82. 3 × 2,641,000 = 7,923,000 There were 7,923,000 widows in 2005.

83. 1287

135+

84. 1268

118−

85. 13416

80413402144

×

86. 47 + 26 + 10 + 231 + 50 = 364

87. 194

23+


88. 194

76×

The product of 19 and 4 is 76.

89. 194

15−


90. 194

23+

The total of 19 and 4 is 23.

91. 6 + 6 + 6 + 6 + 6 = 5 ⋅ 6 or 6 ⋅ 5

92. 11 + 11 + 11 + 11 + 11 + 11 = 6 ⋅ 11 or 11 ⋅ 6

93. a. 3 ⋅ 5 = 5 + 5 + 5 = 3 + 3 + 3 + 3 + 3

b. answers may vary

94. a. 4 ⋅ 5 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4

b. answers may vary

95. 20314

81220302842

×

96. 3150

1550×

97. 42 × 3 = 126 42 × 9 = 378 The problem is 42

93×

98. 57 × 3 = 171 57 × 6 = 342 The problem is 57

63×


100. 3 × 110 = 330 2 × 641 = 1282 330 + 1282 + 539 = 2151 Nowitzki scored 2151 points during the 2005−2006 regular season.



22

101. On a side with 7 windows per row, there are 7 × 23 = 161 windows. On a side with 4 windows per row, there are 4 × 23 = 92 windows. 161 + 161 + 92 + 92 = 506 There are 506 windows on the building.

Section 1.6

Practice Problems

1. a. 8

9 72 because 8 ⋅ 9 = 72.

b. 40 ÷ 5 = 8 because 8 ⋅ 5 = 40.

c. 24 46= because 4 ⋅ 6 = 24.

2. a. 7 17= because 1 ⋅ 7 = 7.

b. 5 ÷ 1 = 5 because 5 ⋅ 1 = 5.

c. 11

1 11 because 11 ⋅ 1 = 11.

d. 4 ÷ 1 = 4 because 4 ⋅ 1 = 4.

e. 10 101= because 10 ⋅ 1 = 10.

f. 21 ÷ 21 = 1 because 1 ⋅ 21 = 21.

3. a. 0 05= because 0 ⋅ 5 = 0.

b. 0

8 0 because 0 ⋅ 8 = 0.

c. 7 ÷ 0 is undefined because if 7 ÷ 0 is a number, then the number times 0 would be 7.

d. 0 ÷ 14 = 0 because 0 ⋅ 14 = 0.

4. a. 818

6 49084810648480

−

−

−

Check: 8186

4908×

b. 553

4 2212202120

12120

−

−

−

Check: 5534

2212×

c. 251

3 75361515

0330

−

−

−

Check: 2513

753×

5. a. 304

7 21282102

028280

−

−

−

Check: 304 × 7 = 2128



23

b. 5 100

9 45,900450 9

9000

−

−

Check: 5100 × 9 = 45,900

6. a. 234 R 3

4 939 81312

1916

3

−

−

−

Check: 234 ⋅ 4 + 3 = 939

b. 657 R 2

5 3287 302825

37352

−

−

−

Check: 657 ⋅ 5 + 2 = 3287

7. a. 9067 R 2

9 81,605 810 6

0605465632

−

−

−

−

Check: 9067 ⋅ 9 + 2 = 81,605

b. 5827 R 2

4 23,310 20

3 33 2

11830282

−

−

−

−

Check: 5827 ⋅ 4 + 2 = 23,310

8. 524 R 12

17 8920854234

806812

−

−

−

9. 49 R 60

678 33,28227 12

6 1626 102

60

−

−

10. 57

3 1711521210

−

−

Each student got 57 CDs.

11. 44

12 53248

52484

−

−

There will be 44 full boxes and 4 printers left over.



24

12. Find the sum and divide by 7.

47

3516

93

52126+

18

7 126756560

−

−

The average time is 18 minutes.


1. 848 ÷ 16 = 53

2. 564 ÷ 12 = 47

3. 5890 ÷ 95 = 62

4. 1053 ÷ 27 = 39

5. 32,886 261

126=

6. 143,088 542

264=

7. 0 ÷ 315 = 0

8. 315 ÷ 0 is an error.


1. In 90 ÷ 2 = 45, the answer 45 is called the quotient, 90 is called the dividend, and 2 is called the divisor.

2. The quotient of any number and 1 is the same number.

3. The quotient of any number (except 0) and the same number is 1.

4. The quotient of 0 and any number (except 0) is 0.

5. The quotient of any number and 0 is undefined.

6. The average of a list of numbers is the sum of the numbers divided by the number of numbers.

Exercise Set 1.6

1. 54 ÷ 9 = 6

2. 72 ÷ 9 = 8

3. 36 ÷ 3 = 12

4. 24 ÷ 3 = 8

5. 0 ÷ 8 = 0

6. 0 ÷ 4 = 0

7. 31 ÷ 1 = 31

8. 38 ÷ 1 = 38

9. 18 118

=

10. 49 149

=

11. 24 83=

12. 45 59=

13. 26 ÷ 0 = undefined.

14. 12 undefined0=

15. 26 ÷ 26 = 1

16. 6 ÷ 6 = 1

17. 0 ÷ 14 = 0

18. 7 ÷ 0 = undefined

19. 18 ÷ 2 = 9

20. 18 ÷ 3 = 6



25

21. 29

3 8762727

0

−

−

Check: 3 ⋅ 29 = 87

22. 17

5 85535350

−

−

Check: 17 ⋅ 5 = 85

23. 74

3 2222112120

−

−

Check: 74 ⋅ 3 = 222

24. 80

8 64064

00−

Check: 80 ⋅ 8 = 640

25. 338

3 1014911924240

−

−

−

Check: 3 ⋅ 338 = 1014

26. 526

4 210420

10824240

−

−

−

Check: 526 ⋅ 4 = 2104

27. 300

is undefined.

28. 0 0

30=

Check: 0 ⋅ 30 = 0

29. 9

7 63630

−

Check: 7 ⋅ 9 = 63

30. 7

8 56560

−

Check: 7 ⋅ 8 = 56

31. 25

6 15012

3030

0

−

−

Check: 25 ⋅ 6 = 150

32. 11

11 1211111110

−

−

Check: 11 ⋅ 11 = 121

33. 68 R 3

7 479 425956

3

−

−

Check: 7 ⋅ 68 + 3 = 479

34. 60 R 6

7 426 42

06−

Check: 60 ⋅ 7 + 6 = 426



26

35. 236 R 5

6 1421 12

22184136

5

−

−

−

Check: 236 ⋅ 6 + 5 = 1421

36. 413 R 1

3 1240 1204

310

91

−

−

−

Check: 413 ⋅ 3 + 1 = 1240

37. 38 R 1

8 30524

6564

1

−

−

Check: 8 ⋅ 38 + 1 = 305

38. 55 R 2

3 167 15

17152

−

−

Check: 55 ⋅ 3 + 2 = 167

39. 326 R 4

7 2286211814

46424

−

−

−

Check: 326 ⋅ 7 + 4 = 2286

40. 833 R 1

4 3333 321312

1312

1

−

−

−

Check: 833 ⋅ 4 + 1 = 3333

41. 13

55 71555165165

0

−

−

Check: 55 ⋅ 13 = 715

42. 32

23 73669

46460

−

−

Check: 32 ⋅ 23 = 736

43. 49

23 112792207207

0

−

−

Check: 49 ⋅ 23 = 1127

44. 48

42 2016168

336336

0

−

−

Check: 48 ⋅ 42 = 2016

45. 97 R 8

97 9417873

687679

8

−

−

Check: 97 ⋅ 97 + 8 = 9417



27

46. 44 R 2

44 1938 176

178176

2

−

−

Check: 44 ⋅ 44 + 2 = 1938

47. 209 R 11

15 3146 30140

146135

11

−

−

−

Check: 209 ⋅ 15 + 11 = 3146

48. 612 R 10

12 7354 721512

342410

−

−

−

Check: 612 ⋅ 12 + 10 = 7354

49. 506

13 65786507

078780

−

−

−

Check: 13 ⋅ 506 = 6578

50. 405

14 567056

0707070

0

−

−

−

Check: 405 ⋅ 14 = 5670

51. 202 R 7

46 92999209099927

−

−

−

Check: 202 ⋅ 46 + 7 = 9299

52. 39 R 9

64 2505192585576

9

−

−

Check: 39 ⋅ 64 + 9 = 2505

53. 54

236 127441180

944944

0

−

−

Check: 236 ⋅ 54 = 12,744

54. 47

123 5781492861861

0

−

−

Check: 47 ⋅ 123 = 5781

55. 99 R 100

103 10,297 9 271 027

927100

−

−

Check: 99 ⋅ 103 + 100 = 10,297

56. 96 R 52

240 23,092 21 60

1 4921 440

52

−

−

Check: 96 ⋅ 240 + 52 = 23,092



28

57. 202 R 15

102 20619204

210

219204

15

−

−

−

Check: 102 ⋅ 202 + 15 = 20,619

58. 201 R 50

203 40,853 40 6

250

25320350

−

−

−

Check: 201 ⋅ 203 + 50 = 40,853

59. 579 R 72

423 244,989 211 533 4829 61

3 8793 807

72

−

−

−

Check: 579 ⋅ 423 + 72 = 244,989

60. 303 R 63

543 164,592162 9

1 690

1 6921 629

63

−

−

−

Check: 303 ⋅ 543 + 63 = 164,592

61. 17

7 119749490

−

−

62. 13

8 104824240

−

−

63. 511 R 3

7 3580 350871073

−

−

−

64. 603 R 2

5 3017 3001017152

−

−

−

65. 2132 R 32

40 85312 805340131120

1128032

−

−

−

−

66. 1714 R 47

50 85,747 5035 735 0

745024720047

−

−

−

−



29

67. 6 080

142 863,36085211 3

011 3611 36

0000

−

−

−

−

68. 3 040

214 650,560642

8 50

8 568 56

0000

−

−

−

−

69. 23 R 2

5 117 1017152

−

−

The quotient is 23 R 2.

70. 13 R 3

7 94 724213

−

−


71. 5 R 25

35 20017525

−

200 divided by 35 is 5 R 25.

72. 3 R 20

32 116 9620

−

116 divided by 32 is 3 R 20.

73. 20 R 2

3 62 60202

−

−


74. 15 R 3

5 78 52825

3

−

−


75. 33

65 2145195

195195

0

−

−

There are 33 students in the group.

76. 58

85 4930425

680680

0

−

−

There are 58 students in the group.

77. 165

318 524703182067190815901590

0

−

−

−

The person weighs 165 pounds on Earth.



30

78. 252000

21 529200042109105

42420

−

−

−

Each person received $252,000.

79. 310

18 558054

18180

−

−

The distance is 310 yards.

80. 412

14 5768561614

28280

−

−

−

The truck hauls 412 bushels on each trip.

81. 88 R 1

3 265 242524

1

−

−

There are 88 bridges every 3 miles over the 265 miles, plus the first bridge, for a total of 89 bridges.

82. Lane divider = 25 + 25 = 50 105

50 528050280

28025030

−

−

−

There are 105 whole lane dividers.

83. 10

492 5280492

360−

There should be 10 poles, plus the first pole for a total of 11 light poles.

84. 23 R 1

8 185 16

2524

1

−

−

Yes, she has enough for a 22-student class. There is one 8-foot length and 1 additional foot of rope left over. That is, she has 9 feet of extra rope.

85. 5

5280 2640026400

0−

Broad Peak is 5 miles tall.

86. 28

6 1681248480

−

−

Alexander scored 28 touchdowns.

87. 1760

3 528032221

18180

−

−

−

There are 1760 yards in 1 mile.

88. 16

320 528032020801920

160

−

−

There are 16 whole feet in 1 rod.



31

89. 2102435221712

120+

20

6 1201200

−

120Average 206

= =

90. 3372615295122

180+

306 180

1800

−

180Average 306

= =

91. 1205972210161

1548+

387

4 154812

343228280

−

−

−

1548Average 3874

= =

92. 2 1121200185176163845

+

169

5 8455343045450

−

−

−

845Average 1695

= =

93.

28679816980

395+

79

5 3953545450

−

−

395Average 795

= =

94. 2929690859279

534+

89

6 53448

54540

−

−

534Average 896

= =

95. 2697776

222+

74

3 2222112120

−

−

The average temperature is 74°.

96. 534030

123+

41

3 123120330

−

−

The average temperature is 41°.

97.

11 182

46329

87049278

+

98.

1123

40792

70117533

+



32

99. 54628

4 36810 92015, 288

×

100. 71254

2 84835 60038,448

×

101. 72243

679−

102. 71254

658−

103. 450

is undefined.

104. 0 023

= because 0 ⋅ 23 = 0

105. 9 R 12

24 228 21612

−

106. 9 R 25

31 304 279

25−

107. The quotient of 40 and 8 is 40 ÷ 8, which is choice c.

108. The quotient of 200 and 20 is 200 ÷ 20, which is choice b.

109. 200 divided by 20 is 200 ÷ 20, which is choice b.

110. 40 divided by 8 is 40 ÷ 8, which is choice c.

111. 797,000,000667,000,000

1,464,000,000+

732,000,000

2 1, 464,000,0001 4

0660440

−

−

−

The average amount spent is $732,000,000.

112. 797,000,000667,000,000544,000,000528,000,000

2,536,000,000+

634,000,000

4 2,536,000,0002 4

1312

16160

−

−

−

The average amount spent is $634,000,000.

113. The average will increase; answers may vary.

114. The average will decrease; answers may vary.

115. No; answers may vary Possible answer: The average cannot be less than each of the four numbers.

116. 12

5 6051010

0

−

−

The length is 12 feet. Notice that Area = length × width = 12 × 5 = 60.




33

118.

265

215

165

115651

−

−

−

−

−

Therefore, 26 ÷ 5 = 5 R 1

The Bigger Picture

1.

18239

121+

2. 823943

−

3. 8239

73824603198

×

4. 89 R 11

29 259223227226111

−

−

5. 0 ⋅ 15 = 0

6. 0 ÷ 11 = 0

7. 26 ⋅ 1 = 26

8. 36 ÷ 0 is undefined.

9. 82 ÷ 1 = 82

10. 2000156

1844−

Integrated Review

1.

1426389

194+

2. 7006451

6555−

3. 8752

17443504524

×

4. 562

8 4496404948

16160

−

−

−

5. 1 ⋅ 67 = 67

6. 360

is undefined.

7. 16 ÷ 16 = 1

8. 5 ÷ 1 = 5

9. 0 ⋅ 21 = 0

10. 7 ⋅ 0 ⋅ 8 = 0

11. 0 ÷ 7 = 0

12. 12 ÷ 4 = 3

13. 9 ⋅ 7 = 63

14. 45 ÷ 5 = 9

15. 20769

138−



34

16.

1207

69276

+

17. 371825491169

−

18. 11186179659826

+

19. 182 R 4

7 1278 75756

1814

4

−

−

−

20. 125963

3 77775 54079,317

×

21. 1099 R 2

7 7695 706

0696365632

−

−

−

−

22. 111 R 1

9 100091091091

−

−

−

23. 663 R 24

32 21, 240 19 2

2 041 92

1209624

−

−

−

24. 1 076 R 60

65 70,000 655 0

05 004 55

450390

60

−

−

−

−

25. 400029631037

−

26. 10,000101

9 899−

27. 303101303

30 30030,603

×

28. (475)(100) = 47,500

29.

1629

71+

The total of 62 and 9 is 71.

30. 629

558×




35

31. 6 R 8

9 62 54

8−

The quotient of 62 and 9 is 6 R 8.

32. 629

53−


33. 20017

183−


34. 432201231

−


35. 9735 rounded to the nearest ten is 9740. 9735 rounded to the nearest hundred is 9700. 9735 rounded to the nearest thousand is 10,000.

36. 1429 rounded to the nearest ten is 1430. 1429 rounded to the nearest hundred is 1400. 1429 rounded to the nearest thousand is 1000.

37. 20,801 rounded to the nearest ten is 20,800. 20,801 rounded to the nearest hundred is 20,800. 20,801 rounded to the nearest thousand is 21,000.

38. 432,198 rounded to the nearest ten is 432,200. 432,198 rounded to the nearest hundred is 432,200. 432,198 rounded to the nearest thousand is 432,000.

39. 6 + 6 + 6 + 6 = 24 6 × 6 = 36 The perimeter is 24 feet and the area is 36 square feet.

40. 14 + 7 + 14 + 7 = 42 147

98×

The perimeter is 42 inches and the area is 98 square inches.

41. 1396

28+

The perimeter is 28 miles.

42. The unknown vertical side has length 4 + 3 = 7 meters. The unknown horizontal side has length 3 + 3 = 6 meters.

343763

26+

The perimeter is 26 meters.

43.

31915253724

120+

24

5 120102020

0

−

−

120Average 245

= =

44. 1 210813198

159496

+

124

4 496409

816160

−

−

−

496Average 1244

= =

45. 28,54726,372

2 175−

The Lake Pontchartrain Bridge is longer by 2175 feet.



36

46. 34718

277634706246

×

The amount spent on toys is $6246.

Section 1.7

Practice Problems

1. 48 8 8 8 8⋅ ⋅ ⋅ =

2. 33 3 3 3⋅ ⋅ =

3. 510 10 10 10 10 10⋅ ⋅ ⋅ ⋅ =

4. 2 65 5 4 4 4 4 4 4 5 4⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅

5. 24 4 4 16= ⋅ =

6. 38 8 8 8 512= ⋅ ⋅ =

7. 111 11=

8. 22 3 2 3 3 18⋅ = ⋅ ⋅ =

9. 9 3 8 4 27 8 4 27 2 25⋅ − ÷ = − ÷ = − =

10. 248 3 2 48 3 4 16 4 64÷ ⋅ = ÷ ⋅ = ⋅ =

11. 4 2 4 2(10 7) 2 3 3 2 381 2 981 1899

− + ⋅ = + ⋅= + ⋅= +=

12. 3 3

336 [20 (4 2)] 4 6 36 [20 8] 4 6

36 12 4 636 12 64 63 64 661

÷ − ⋅ + − = ÷ − + −

= ÷ + −= ÷ + −= + −=

13. 325 8 2 3 25 8 2 27

2(3 2) 2(1)25 16 27

2142

7

+ ⋅ − + ⋅ −=

−+ −

=

=

=

14. 36 6 3 5 6 3 5 18 5 23÷ ⋅ + = ⋅ + = + =

15. 2

2Area (side)

(12 centimeters)144 square centimeters

=

==

The area of the square is 144 square centimeters.


1. 63 729=

2. 65 15,625=

3. 54 1024=

4. 67 117,649=

5. 112 2048=

6. 86 1,679,616=

7. 4 37 5 2526+ =

8. 4 412 8 16,640− =

9. 63 ⋅ 75 − 43 ⋅ 10 = 4295

10. 8 ⋅ 22 + 7 ⋅ 16 = 288

11. 4(15 ÷ 3 + 2) − 10 ⋅ 2 = 8

12. 155 − 2(17 + 3) + 185 = 300


1. In 52 32,= the 2 is called the base and the 5 is called the exponent.

2. To simplify 8 + 2 ⋅ 6, which operation should be performed first? multiplication

3. To simplify (8 + 2) ⋅ 6, which operation should be performed first? addition

4. To simplify 9(3 − 2) ÷ 3 + 6, which operation should be performed first? subtraction

5. To simplify 8 ÷ 2 ⋅ 6, which operation should be performed first? division



37

Exercise Set 1.7

1. 34 4 4 4⋅ ⋅ =

2. 45 5 5 5 5⋅ ⋅ ⋅ =

3. 67 7 7 7 7 7 7⋅ ⋅ ⋅ ⋅ ⋅ =

4. 76 6 6 6 6 6 6 6⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =

5. 312 12 12 12⋅ ⋅ =

6. 310 10 10 10⋅ ⋅ =

7. 2 36 6 5 5 5 6 5⋅ ⋅ ⋅ ⋅ = ⋅

8. 2 34 4 3 3 3 4 3⋅ ⋅ ⋅ ⋅ = ⋅

9. 29 8 8 9 8⋅ ⋅ = ⋅

10. 37 4 4 4 7 4⋅ ⋅ ⋅ = ⋅

11. 43 2 2 2 2 3 2⋅ ⋅ ⋅ ⋅ = ⋅

12. 44 6 6 6 6 4 6⋅ ⋅ ⋅ ⋅ = ⋅

13. 4 53 2 2 2 2 5 5 5 5 5 3 2 5⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅

14. 2 46 6 2 9 9 9 9 6 2 9⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅

15. 28 8 8 64= ⋅ =

16. 26 6 6 36= ⋅ =

17. 35 5 5 5 125= ⋅ ⋅ =

18. 36 6 6 6 216= ⋅ ⋅ =

19. 52 2 2 2 2 2 32= ⋅ ⋅ ⋅ ⋅ =

20. 53 3 3 3 3 3 243= ⋅ ⋅ ⋅ ⋅ =

21. 101 1 1 1 1 1 1 1 1 1 1 1= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =

22. 121 1 1 1 1 1 1 1 1 1 1 1 1 1= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =

23. 17 7=

24. 18 8=

25. 72 2 2 2 2 2 2 2 128= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =

26. 45 5 5 5 5 625= ⋅ ⋅ ⋅ =

27. 82 2 2 2 2 2 2 2 2 256= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =

28. 33 3 3 3 27= ⋅ ⋅ =

29. 44 4 4 4 4 256= ⋅ ⋅ ⋅ =

30. 34 4 4 4 64= ⋅ ⋅ =

31. 39 9 9 9 729= ⋅ ⋅ =

32. 38 8 8 8 512= ⋅ ⋅ =

33. 212 12 12 144= ⋅ =

34. 211 11 11 121= ⋅ =

35. 210 10 10 100= ⋅ =

36. 310 10 10 10 1000= ⋅ ⋅ =

37. 120 20=

38. 114 14=

39. 63 3 3 3 3 3 3 729= ⋅ ⋅ ⋅ ⋅ ⋅ =

40. 54 4 4 4 4 4 1024= ⋅ ⋅ ⋅ ⋅ =

41. 63 2 3 2 2 2 2 2 2 192⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =

42. 25 3 5 3 3 45⋅ = ⋅ ⋅ =

43. 42 3 2 3 3 3 3 162⋅ = ⋅ ⋅ ⋅ ⋅ =

44. 22 7 2 7 7 98⋅ = ⋅ ⋅ =

45. 15 + 3 ⋅ 2 = 15 + 6 = 21

46. 24 + 6 ⋅ 3 = 24 + 18 = 42

47. 28 ÷ 7 ⋅ 1 + 3 = 4 ⋅ 1 + 3 = 4 + 3 = 7

48. 100 ÷ 10 ⋅ 5 + 4 = 10 ⋅ 5 + 4 = 50 + 4 = 54



38

49. 32 ÷ 4 − 3 = 8 − 3 = 5

50. 42 ÷ 7 − 6 = 6 − 6 = 0

51. 2413 13 3 168

+ = + =

52. 832 32 4 362

+ = + =

53. 6 ⋅ 5 + 8 ⋅ 2 = 30 + 16 = 46

54. 3 ⋅ 4 + 9 ⋅ 1 = 12 + 9 = 21

55. 75 12 4 5 3 8 8

1 11+ ÷ +

= = =

56. 26 9 3 6 3 9 1

9 93+ ÷ +

= = =

57. 2 3 3

3(7 5 ) 4 2 (7 25) 4 2

32 4 232 4 88 864

+ ÷ ⋅ = + ÷ ⋅

= ÷ ⋅= ÷ ⋅= ⋅=

58. 2 26 (10 8) 6 2 36 2 72⋅ − = ⋅ = ⋅ =

59. 2 3 2 2 3 25 (10 8) 2 5 5 2 2 525 2 8 2550 8 2583

⋅ − + + = ⋅ + += ⋅ + += + +=

60. 3 2 3 3 2 35 (10 15) 9 3 5 25 9 3125 25 81 275 81 27113

÷ + + + = ÷ + += ÷ + += + +=

61. 4 218 6 24 24 2

16 4 122 2+

= = =−−

62. 2 240 8 48 48 3

25 9 165 3+

= = =−−

63. (3 + 5) ⋅ (9 − 3) = 8 ⋅ 6 = 48

64. (9 − 7) ⋅ (12 + 18) = 2 ⋅ 30 = 60

65. 27(9 6) 3 7(3) 3 21 3 24 4

9 3 6 63 3− + + +

= = = =−−

66. 25(12 7) 4 5(5) 4 25 4 21 3

25 18 25 18 75 18− − − −

= = = =− −−

67. 8 ÷ 0 + 37 = undefined

68. 18 − 7 ÷ 0 = undefined

69. 4 42 4 (25 5) 2 4 516 4 564 559

⋅ − ÷ = ⋅ −= ⋅ −= −=

70. 3 32 3 (100 10) 2 3 108 3 1024 1014

⋅ − ÷ = ⋅ −= ⋅ −= −=

71. 4 4

43 [35 (12 6)] 3 [35 6]

3 2981 2952

− − − = − −

= −= −=

72. 5 5

5[40 (8 2)] 2 [40 6] 2

34 234 322

− − − = − −

= −= −=

73. (7 5) [9 (3 3)] (7 5) [9 (1)]35 944

⋅ + ÷ ÷ = ⋅ + ÷= +=

74. (18 6) [(3 5) 2] (18 6) (8 2)3 (8 2)3 1619

÷ + + ⋅ = ÷ + ⋅= + ⋅= +=

75. 2 28 [2 (6 1) 2] 50 2 8 (2 5 2) 50 28 (4 5 2) 50 28 (4 10) 50 28 14 50 2112 50 2112 10012

⋅ + − ⋅ − ⋅ = ⋅ + ⋅ − ⋅= ⋅ + ⋅ − ⋅= ⋅ + − ⋅= ⋅ − ⋅= − ⋅= −=



39

76. 2 2

2 235 [3 (9 7) 2 ] 10 3

35 [3 2 2 ] 10 335 [9 2 4] 10 335 7 10 35 10 35 3035

÷ + − − + ⋅

= ÷ + − + ⋅= ÷ + − + ⋅= ÷ + ⋅= + ⋅= +=

77. 2 2 29 2 1 81 4 1

8 2 3 1 3 4 3 1 385 1

12 1 384

12 3844

21

+ − + −=

÷ ⋅ ⋅ ÷ ⋅ ⋅ ÷−

=⋅ ÷

=÷

=

=

78. 2 3 45 2 1 25 8 1 18 18 9

10 5 4 1 4 2 4 1 4 8 4 2− + − +

= = = =÷ ⋅ ⋅ ÷ ⋅ ⋅ ÷ ÷

79. 2

2 22 4 2 16

5(20 16) 3 5 5(4) 3 518

5(4) 9 518

20 9 518

11 5186

3

+ +=

− − − − −

=− −

=− −

=−

=

=

80. 2

2 23 9 3 81

3(10 6) 2 1 3(4) 2 184

3(4) 4 184

12 4 184

8 1847

12

+ +=

− − − − −

=− −

=− −

=−

=

=

81. 29 3 5 2 10 9 3 25 2 103 25 2 103 50 1043

÷ + ⋅ − = ÷ + ⋅ −= + ⋅ −= + −=

82. 310 2 3 2 20 10 2 27 2 205 27 2 205 54 2039

÷ + ⋅ − = ÷ + ⋅ −= + ⋅ −= + −=

83. 5 2 5 2

2

2

2

[13 (20 7) 2 ] (2 3) [13 13 2 ] 5[13 13 32] 5[1 32] 533 533 258

÷ − + − + = ÷ + −

= ÷ + −

= + −

= −= −=

84. 2 2 2 2

2

2

2

[15 (11 6) 2 ] (5 1) [15 5 2 ] 4[15 5 4] 4[3 4] 47 47 1623

÷ − + + − = ÷ + +

= ÷ + +

= + +

= += +=

85. 2 2

2 2

2 2

2 2

2

2

7 {18 [40 (5 1) 2] 5 }7 {18 [40 5 2] 5 }7 {18 [8 2] 5 }7 {18 10 5 }7 {18 10 25}7 3349 3316

− − ÷ ⋅ + +

= − − ÷ + +

= − − + +

= − − +

= − − +

= −= −=

86. 29{5 3[8 (10 8)] 50} 29 {5 3[8 2] 50}29 {5 3(16) 50}29 {5 48 50}29 326

+ ⋅ − − = − + ⋅ −= − + −= − + −= −=

87. 2

2Area of a square (side)

(7 meters)49 square meters

=

==

88. 2



=

==

89. 2


(23 miles)529 square miles

=

==



40

90. 2


(41 feet)1681 square feet

=

==

91. The statement is true.

92. The statement is true.

93. 52 2 2 2 2 2= ⋅ ⋅ ⋅ ⋅ The statement is false.

94. 94 4 4 4 4 4 4 4 4 4= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ The statement is false.

95. (2 + 3) ⋅ 6 − 2 = 5 ⋅ 6 − 2 = 30 − 2 = 28

96. (2 + 3) ⋅ (6 − 2) = (5) ⋅ (4) = 20

97. 24 (3 2) 2 5 24 6 2 5 4 10 14÷ ⋅ + ⋅ = ÷ + ⋅ = + =

98. 24 (3 2 2) 5 24 (6 2) 524 8 53 515

÷ ⋅ + ⋅ = ÷ + ⋅= ÷ ⋅= ⋅=

99. The unknown vertical length is 30 − 12 = 18 feet. The unknown horizontal length is 60 − 40 = 20 feet. Perimeter = 60 + 30 + 40 + 18 + 20 + 12 = 180 The total perimeter of seven homes is 7(180) = 1260 feet.

100. 3 3

325 (45 7 5) 5 25 (45 35) 5

25 (10) 515,625 10 5156, 250 5781,250

⋅ − ⋅ ⋅ = ⋅ − ⋅

= ⋅ ⋅= ⋅ ⋅= ⋅=

101. 4 5 5 4 2 5 2

5 2(7 2 ) (3 2 ) (7 16) (243 16)

23 2276, 436,343 51,5296,384,814

+ − − = + − −

= −= −=


103. answers may vary; possible answer: (20 10) 5 25 3 10 5 25 3

50 25 32 35

− ⋅ ÷ + = ⋅ ÷ += ÷ += +=

The Bigger Picture

1. 36 6 6 6 216= ⋅ ⋅ =

2. 3 12 6 2 2 2 6 48⋅ = ⋅ ⋅ ⋅ =

3. 28 5 8 5 5 200⋅ = ⋅ ⋅ =

4. 1 + 2(3 + 4) = 1 + 2(7) = 1 + 14 = 15

5. 2 + 5(10 − 3) = 2 + 5(7) = 2 + 35 = 37

6. 200 ÷ 2 ⋅ 2 = 100 ⋅ 2 = 200

7. 978179799

−

8. 7230

2160×

9. 10 R 34

58 614 58340

34

−

−

10. 2 2

2 23[(7 3) (25 22) ] 6

3[4 3 ] 63(16 9) 63(7) 621 627

− − − +

= − += − += += +=

Section 1.8

Practice Problems

1. x − 2 = 7 − 2 = 5

2. y(x − 3) = 4(8 − 3) = 4(5) = 20

3. 6 18 6 24 4

6 6yx+ +

= = =

4. 3 325 25 2 1 25 8 1 18z x− + = − + = − + =

5. 5( 32) 5(41 32) 5(9) 45 5

9 9 9 9F − −

= = = =



41

6. 3( 6) 63(8 6) 6

3(2) 66 6 True

y − =−

=

�

�

Yes, 8 is a solution.

7. 5n + 4 = 34 Let n be 10. 5(10) 4 34

50 4 3454 34 False

++

=

�

�

No, 10 is not a solution. Let n be 6. 5(6) 4 34

30 4 3434 34 True

++

=

�

�

Yes, 6 is a solution. Let n be 8. 5(8) 4 34

40 4 3444 34 False

++

=

�

�

No, 8 is not a solution.

8. a. Twice a number is 2x.

b. 8 increased by a number is 8 + x or x + 8.

c. 10 minus a number is 10 − x.

d. 10 subtracted from a number is x − 10.

e. The quotient of 6 and a number is 6 ÷ x or 6 .x


1. A combination of operations on letters (variables) and numbers is an expression.

2. A letter that represents a number is a variable.

3. 3x − 2y is called an expression and the letters x and y are variables.

4. Replacing a variable in an expression by a number and then finding the value of the expression is called evaluating an expression.

5. A statement of the form “expression = expression” is called an equation.

6. A value for the variable that makes the equation a true statement is called a solution.



42

Exercise Set 1.8

1. a b a + b a − b a ⋅ b a ÷ b

21 7 21 + 7 = 28 21 − 7 = 14 21 ⋅ 7 = 147 21 ÷ 7 = 3

2. a b a + b a − b a ⋅ b a ÷ b

24 6 24 + 6 = 30 24 − 6 = 18 24 ⋅ 6 = 144 24 ÷ 6 = 4

3. a b a + b a − b a ⋅ b a ÷ b

152 0 152 + 0 = 152 152 − 0 = 152 152 ⋅ 0 = 0 152 ÷ 0 is undefined.

4. a b a + b a − b a ⋅ b a ÷ b

298 0 298 + 0 = 298 298 − 0 = 298 298 ⋅ 0 = 0 298 ÷ 0 is undefined.

5. a b a + b a − b a ⋅ b a ÷ b

56 1 56 + 1 = 57 56 − 1 = 55 56 ⋅ 1 = 56 56 ÷ 1 = 56

6. a b a + b a − b a ⋅ b a ÷ b

82 1 82 + 1 = 83 82 − 1 = 81 82 ⋅ 1 = 82 82 ÷ 1 = 82

7. 3 + 2z = 3 + 2(3) = 3 + 6 = 9

8. 7 + 3z = 7 + 3(3) = 7 + 9 = 16

9. 3xz − 5x = 3(2)(3) − 5(2) = 18 − 10 = 8

10. 4yz + 2x = 4(5)(3) + 2(2) = 60 + 4 = 64

11. z − x + y = 3 − 2 + 5 = 1 + 5 = 6

12. x + 5y − z = 2 + 5(5) − 3 = 2 + 25 − 3 = 24

13. 4x − z = 4(2) − 3 = 8 − 3 = 5

14. 2y + 5z = 2(5) + 5(3) = 10 + 15 = 25

15. 3 34 5 4(2) 125 4(2) 125 8 117y x− = − = − = − =

16. 3 35 3 125 3 122y z− = − = − =

17. 2 22 6 2(2)(5) 62 2 25 6100 694

xy − = −= ⋅ ⋅ −= −=



43

18. 2 23 1 3(5)(3) 13 5 9 1135 1136

yz + = += ⋅ ⋅ += +=

19. 8 − (y − x) = 8 − (5 − 2) = 8 − 3 = 5

20. 3 (2 4) 3 (2 5 4)3 (10 4)3 69

y+ − = + ⋅ −= + −= +=

21. 5 5

5( ) 2 (5 3)

2 232 234

x y z+ − = + −

= += +=

22. 4 4 4( ) 2 (5 3) 2 2 16 2 14x y z− − = − − = − = − =

23. 6 6 2 5 60 20

3 3xyz

⋅ ⋅= = =

24. 8 8 5 3 120 815 15 15yz ⋅ ⋅

= = =

25. 2 2 2(5) 2 10 2 8 4

2 2 2yx− − −

= = = =

26. 6 3 6 3(2) 6 6 12 4

3 3 3x

z+ + +

= = = =

27. 2 2 2 5 2 10 12 4

3 3 3x yz+ + ⋅ +

= = = =

28. 2 6 2 3 6 6 6 12 4

3 3 3 3z + ⋅ + +

= = = =

29. 5 10 5(2) 10 10 2 2 2 0

5 5 5xy y− = − = − = − =

30. 70 15 70 15 70 15 7 5 22 2 5 3 10 3y z

− = − = − = − =⋅

31. 2 22 4 3 2 5 4 5 32 25 4 5 350 20 333

y y− + = ⋅ − ⋅ += ⋅ − ⋅ += − +=

32. 2 23 2 5 3 2 2 2 53 4 2 2 512 4 511

x x+ − = ⋅ + ⋅ −= ⋅ + ⋅ −= + −=

33. 3 3

3

3

(4 5 ) (4 5 5 3)(20 15)(5)125

y z− = ⋅ − ⋅

= −

==

34. 2 2

2

2

(4 3 ) (4 5 3 3)(20 9)29841

y z+ = ⋅ + ⋅

= +

==

35. 2 2 2 2( 1) (2 5 1) (10 1) 11 121xy + = ⋅ + = + = =

36. 4 4 4 4( 5) (2 3 5) (6 5) 1 1xz − = ⋅ − = − = =

37. 2 (4 ) 2 5(4 3 2)2 5(12 2)2 5(10)10(10)100

y z x− = ⋅ ⋅ −= ⋅ −= ⋅==

38. 3 ( ) 3 2(5 3) 3 2(8) 6(8) 48x y z+ = ⋅ + = ⋅ = =

39. (5 ) 2 5(5 3 2)2 5(6)10(6)60

xy z x+ − = ⋅ + −= ⋅==

40. (2 ) 2 3(2 5 2 3)2 3(10 2 3)2 3(9)6(9)54

xz y x z+ − = ⋅ ⋅ + −= ⋅ + −= ⋅==

41. 7 2 7(2) 2(5) 14 10 24 4

3 3(2) 6 6x yx+ + +

= = = =

42. 6 2 6 3 2 5

4 418 10

4284

7

z y+ ⋅ + ⋅=

+=

=

=



44

43. t 1 2 3 4

216t 216 1 16 1 16⋅ = ⋅ = 216 2 16 4 64⋅ = ⋅ = 216 3 16 9 144⋅ = ⋅ = 216 4 16 16 256⋅ = ⋅ =

44. F 50 59 68 77

5( 32)9F −

5(50 32) 5(18) 10

9 9−

= = 5(59 32) 5(27) 15

9 9−

= = 5(68 32) 5(36) 20

9 9−

= = 5(77 32) 5(45) 25

9 9−

= =

45. Let n be 10. 8 2

10 8 22 2 True

n − =−

=�


46. Let n be 9. 2 7

9 2 77 7 True

n − =−

=�


47. Let n be 3. 24 8024 80 324 240 False

n=⋅

=�


48. Let n be 50. 250 5250 5(50)250 250 True

n=

=�


49. Let n be 7. 3 5 10

3(7) 5 1021 5 10

16 10 False

n − =−−

=

�

�


50. Let n be 8. 11 3 91

11(8) 3 9188 3 91

91 91 True

n + =++

=

�

�




45

51. Let n be 20. 2( 17) 6

2(20 17) 62(3) 6

6 6 True

n − =−

=

�

�


52. Let n be 0. 5( 9) 405(0 9) 40

5(9) 4045 40 False

n + =+

=

�

�


53. Let x be 0. 5 3 4 13

5(0) 3 4(0) 130 3 0 13

3 13 False

x x+ = ++ ++ +

=

�

�


54. Let x be 2. 3 6 5 10

3(2) 6 5(2) 106 6 10 10

0 0 True

x x− = −− −− −

=

�

�


55. Let f be 8. 7 64

7(8) 64 856 56 True

f f= −−

=�


56. Let x be 5. 8 30 2

8(5) 30 2(5)40 30 10

10 10 True

x x− =−−

=

�

�


57. n − 2 = 10 Let n be 10. 10 2 10

8 10 False−

=�

Let n be 12. 12 2 10

10 10 True−

=�

Let n be 14. 14 2 10

12 10 False−

=�

12 is a solution.

58. n + 3 = 16 Let n be 9. 9 3 16

12 16 False+

=�

Let n be 11. 11 3 16

14 16 False+

=�

Let n be 13. 13 3 16

16 16 True+

=�

13 is a solution.

59. 5n = 30 Let n be 6. 5 6 30

30 30 True⋅

=�

Let n be 25. 5 25 30

125 30 False⋅

=�

Let n be 30. 5 30 30

150 30 False⋅

=�

6 is a solution.

60. 3n = 45 Let n be 15. 3 15 45

45 45 True⋅

=�

Let n be 30. 3 30 45

90 45 False⋅

=�

Let n be 45. 3 45 45

135 45 False⋅

=�

15 is a solution.

61. 6n + 2 = 26 Let n be 0. 6(0) 2 26

0 2 262 26 False

++

=

�

�

Let n be 2. 6(2) 2 26

12 2 2614 26 False

++

=

�

�

Let n be 4. 6(4) 2 26

24 2 2626 26 True

++

=

�

�

4 is a solution.



46

62. 4n − 14 = 6 Let n be 0. 4 0 14 6

0 14 614 6 False

⋅ −−− =

�

�

Let n be 5. 4 5 14 620 14 6

6 6 True

⋅ −−

=

�

�

Let n be 10. 4 10 14 6

40 14 626 6 False

⋅ −−

=

�

�

5 is a solution.

63. 3( 4) 10n − = Let n be 5. 3(5 4) 10

3(1) 103 10 False

−

=

�

�

Let n be 7. 3(7 4) 10

3(3) 109 10 False

−

=

�

�

Let n be 10. 3(10 4) 10

3(6) 1018 10 False

−

=

�

�

None are solutions.

64. 6(n + 2) = 23 Let n be 1. 6(1 2) 23

6(3) 2318 23 False

+

=

�

�

Let n be 3. 6(3 2) 23

6(5) 2330 23 False

+

=

�

�

Let n be 5. 6(5 2) 23

6(7) 2342 23 False

+

=

�

�

None are solutions.

65. 7x − 9 = 5x + 13 Let x be 3. 7(3) 9 5(3) 13

21 9 15 1312 28 False

− +− +

=

�

�

Let x be 7.

7(7) 9 5(7) 1349 9 35 13

40 48 False

− +− +

=

�

�

Let x be 11. 7(11) 9 5(11) 13

77 9 55 1368 68 True

− +− +

=

�

�

11 is a solution.

66. 9x − 15 = 5x + 1 Let x be 2. 9 2 15 5 2 1

18 15 10 13 11 False

⋅ − ⋅ +− +

=

�

�

Let x be 4. 9 4 15 5 4 136 15 20 1

21 21 True

⋅ − ⋅ +− +

=

�

�

Let x be 11. 9 11 15 5 11 1

99 15 55 184 56 False

⋅ − ⋅ +− +

=

�

�

4 is a solution.

67. Eight more than a number is x + 8.

68. The sum of three and a number is 3 + x.

69. The total of a number and 8 is x + 8.

70. The difference of a number and five hundred is x − 500.

71. Twenty decreased by a number is 20 − x.

72. A number less thirty is x − 30.

73. The product of 512 and a number is 512x.

74. A number times twenty is 20x.

75. The quotient of six and a number is 6 .x

76. A number divided by 11 is .11x

77. The sum of seventeen and a number added to the product of five and the number is 5x + (17 + x).

78. The difference of twice a number, and four is 2x − 4.

79. The product of five and a number is 5x.



47

80. The quotient of twenty and a number, decreased

by three is 20 3.x−

81. A number subtracted from 11 is 11 − x.

82. Twelve subtracted from a number is x − 12.

83. A number less 5 is x − 5.

84. The product of a number and 7 is 7x.

85. 6 divided by a number is 6 ÷ x or 6 .x

86. The sum of a number and 7 is x + 7.

87. Fifty decreased by eight times a number is 50 − 8x.

88. Twenty decreased by twice a number is 20 − 2x.

89. 4 2 4 223 72279,841 5184274,657

x y− = −= −=

90. 2 2

22( ) 2(23 72)

2(95)2(9025)18,050

x y+ = +

===

91. 2 25 112 23 5(72) 112529 360 112777

x y+ − = + −= + −=

92. 3 316 20 16 72 20 23 231152 460 12,16712,859

y x x− + = ⋅ − ⋅ += − +=

93. 5x is the largest; answers may vary.

94. 3x

is the smallest; answers may vary.

95. As t gets larger, 216t gets larger.

96. As F gets larger, 5( 32)

9F −

gets larger.

Chapter 1 Vocabulary Check

1. The whole numbers are 0, 1, 2, 3, ...

2. The perimeter of a polygon is its distance around or the sum of the lengths of its sides.

3. The position of each digit in a number determines its place value.

4. An exponent is a shorthand notation for repeated multiplication of the same factor.

5. To find the area of a rectangle, multiply length times width.

6. The digits used to write numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

7. A letter used to represent a number is called a variable.

8. An equation can be written in the form “expression = expression.”

9. A combination of operations on variables and numbers is called an expression.

10. A solution of an equation is a value of the variable that makes the equation a true statement.

11. A collection of numbers (or objects) enclosed by braces is called a set.

12. The 21 above is called the sum.

13. The 5 above is called the divisor.

14. The 35 above is called the dividend.

15. The 7 above is called the quotient.

16. The 3 above is called a factor.

17. The 6 above is called the product.

18. The 20 above is called the minuend.

19. The 9 above is called the subtrahend.

20. The 11 above is called the difference.

21. The 4 above is called an addend.



48

Chapter 1 Review

1. The place value of 4 in 7640 is tens.

2. The place value of 4 in 46,200,120 is ten-millions.

3. 7640 is written as seven thousand, six hundred forty.

4. 46,200,120 is written as forty-six million, two hundred thousand, one hundred twenty.

5. 3158 = 3000 + 100 + 50 + 8

6. 403,225,000 = 400,000,000 + 3,000,000 + 200,000 + 20,000 + 5000

7. Eighty-one thousand, nine hundred in standard form is 81,900.

8. Six billion, three hundred four million in standard form is 6,304,000,000.

9. Locate Houston, Texas in the city column and read across to the number in the 2000 column. The population was 1,953,631.

10. Locate Los Angeles, California in the city column and read across to the number in the 2005 column. the population was 3,844,829.

11. Locate the smallest number in the 2005 column. San Jose, CA had the smallest population in 2005.

12. Locate the largest number in the 2005 column. New York, NY had the largest population in 2005.

13.

1184967

+

14.

1283967

+

15. 462397

65−

16. 583279304

−

17. 42821

449+

18.

1819

21840

+

19. 400086

3914−

20. 800092

7908−

21.

1 2 191

3623497

4211+

22.

1182

1647238

1967+

23.

1174

342918

1334+

The sum of 74, 342, and 918 is 1334.

24.

249

529308886

+

The sum of 49, 529, and 308 is 886.

25. 25,8627 965

17,897−

7965 subtracted from 25,862 is 17,897.



49

26. 39,0074 349

34,658−

4349 subtracted from 39,007 is 34,658.

27.

1205

73187523

+

The total distance is 7523 miles.

28.

1 1 162,58965,34069,770

197,699+

Her total earnings were $197,699.

29. 40 + 52 + 52 + 72 = 216 The perimeter is 216 feet.

30. 11 + 20 + 35 = 66 The perimeter is 66 kilometers.

31. 1,256,5091,144,646

111,863−

The population increased by 111,863.

32. 1,517,5501, 463,281

54,269−

The population decreased by 54,269.

33. Find the shortest bar. The balance was the least in May.

34. Find the tallest bar. The balance was the greatest in August.

35. 280170110

−

The balance decreased by $110 from February to April.

36. 490250240

−

The balance increased by $240 from June to August.




40. To round 493 to the nearest hundred, observe that the digit in the tens place is 9. Since this digit is at least 5, we add 1 to the digit in the hundreds place. The number 493 rounded to the nearest hundred is 500.

41. To round 3829 to the nearest hundred, observe that the digit in the tens place is 2. Since this digit is less than 5, we do not add 1 to the digit in the hundreds place. The number 3829 rounded to the nearest hundred is 3800.


43. To round 39,583,819 to the nearest million, observe that the digit in the hundred-thousands place is 5. Since this digit is at least 5, we add 1 to the digit in the millions place. The number 39,583,819 rounded to the nearest million is 40,000,000.

44. To round 768,542 to the nearest hundred-thousand, observe that the digit in the ten-thousands place is 6. Since this digit is at least 5, we add 1 to the digit in the hundred-thousands place. The number 768,542 rounded to the nearest hundred-thousand is 800,000.

45. 3785 rounds to 648 rounds to

2866 rounds to+

23800

60029007300

+



50


4100− −

47. 630 rounds to 600192 rounds to 200271 rounds to 30056 rounds to 100

703 rounds to 700454 rounds to 500329 rounds to 300

2700+ +

They traveled approximately 2700 miles.

48. 1, 461,575 rounds to 1,500,0001, 213,825 rounds to 1,200,000

300,000− −

The population of Phoenix is approximately 300,000 larger than that of Dallas.

49. 2768

2208×

50. 3494

1396×

51. 5740

2280×

52. 6942

13827602898

×

53. 20(7)(4) = 140(4) = 560

54. 25(9)(4) = 225(4) = 900 or 25(4)(9) = 100(9) = 900

55. 26 ⋅ 34 ⋅ 0 = 0

56. 62 ⋅ 88 ⋅ 0 = 0

57. 58629

5 27411 72016,994

×

58. 24237

169472608954

×

59. 642177

4 49444 94064 200

113,634

×

60. 347129

3 1236 940

34 70044,763

×

61. 1026401

1 026410 400411, 426

×

62. 2107302

4 214632 100636,314

×

63. “Product” indicates multiplication. 250

61500×


64. “Product” indicates multiplication. 820

64920×




51

65. 3215

160320480

× 38

1138

380418

×

480418898

+


66. 482020

96, 400×

The total cost is $96,400.

67. Area (length)(width)(13 miles)(7 miles)91 square miles

===

68. Area (length)(width)(25 centimeters)(20 centimeters)500 square centimeters

===

69. 49 77= Check: 7

749×

70. 36 49= Check: 9

436×

71. 5 R 2

5 27 252

−

Check: 5 × 5 + 2 = 27

72. R 24

4 18 162

−

Check: 4 × 4 + 2 = 18


74. 0 ÷ 668 = 0 Check: 0 ⋅ 668 = 0

75. 33 R 2

5 167 15

17152

−

−

Check: 33 × 5 + 2 = 167

76. 19 R 7

8 159 879727

−

−

Check: 19 × 8 + 7 = 159

77. 24 R 2

26 626 52106104

2

−

−

Check: 24 × 26 + 2 = 626

78. 35 R 15

19 68057110

9515

−

−

Check: 35 × 19 + 15 = 680

79. 506 R 10

47 23,792 23 5

290

29228210

−

−

−

Check: 506 × 47 + 10 = 23,792



52

80. 907 R 40

53 48,11147 7

410

41137140

−

−

−

Check: 907 × 53 + 40 = 48,111

81. 2793 R 140

207 578,291 414164 2144 9

19 3918 63

761621140

−

−

−

−

Check: 2793 × 207 + 140 = 578,291

82. 2012 R 60

306 615,732 612

3 70

3 733 06

67261260

−

−

−

−

Check: 2012 × 306 + 60 = 615,732

83. 18 R 2

5 92 542402

−

−


84. R 221

4 86 806

42

−

−


85. 27

24 64848168168

0

−

−

27 boxes can be filled with cans of corn.

86. 13

1760 22,88017 60

5 2805 280

0

−

−

There are 13 miles in 22,880 yards.

87. Divide the sum by 4.

76493247

204+

51

4 20420

0440

−

−

The average is 51.


23856266

236+

59

4 23620

36360

−

−

The average is 59.

89. 28 8 8 64= ⋅ =

90. 35 5 5 5 125= ⋅ ⋅ =

91. 25 9 5 9 9 405⋅ = ⋅ ⋅ =

92. 24 10 4 10 10 400⋅ = ⋅ ⋅ =



53

93. 18 ÷ 2 + 7 = 9 + 7 = 16

94. 12 − 8 ÷ 4 = 12 − 2 = 10

95. 2

25(6 3) 5(36 3) 5(33) 165 15

9 2 11 113 2− −

= = = =++

96. 37(16 8) 7(8) 56 7

8 82−

= = =

97. 48 ÷ 8 ⋅ 2 = 6 ⋅ 2 = 12

98. 27 ÷ 9 ⋅ 3 = 3 ⋅ 3 = 9

99. 5

52 3[1 (20 17) 3] 5 2

2 3[1 3 3] 5 22 3[1 3 3] 5 22 3[1 9] 5 22 3 10 5 22 30 1042

+ + − ⋅ + ⋅

= + + ⋅ + ⋅= + + ⋅ + ⋅= + + + ⋅= + ⋅ + ⋅= + +=

100. 4

421 [2 (7 5) 10] 8 2

21 [2 2 10] 8 221 [16 2 10] 8 221 4 8 221 4 1633

− − − − + ⋅

= − − − + ⋅= − − − + ⋅= − + ⋅= − +=

101. 2 219 2(3 2 ) 19 2(9 4)19 2(5)19 109

− − = − −= −= −=

102. 2 216 2(4 3 ) 16 2(16 9)16 2(7)16 142

− − = − −= −= −=

103. 4 ⋅ 5 − 2 ⋅ 7 = 10 − 14 = 6

104. 8 ⋅ 7 − 3 ⋅ 9 = 56 − 27 = 29

105. 3 2 3 2

3

3

(6 4) [10 (3 17)] (6 4) [10 20](6 4) [100 20]2 58 540

− ⋅ ÷ + = − ⋅ ÷

= − ⋅ ÷

= ⋅= ⋅=

106. 3 2 3 2

3

3

(7 5) [9 (2 7)] (7 5) [9 9](7 5) [81 9]2 98 972

− ⋅ ÷ + = − ⋅ ÷

= − ⋅ ÷

= ⋅= ⋅=

107. 25 7 3 5 35 15 20 20 5

2(11 9) 2(2) 42(11 3 )⋅ − ⋅ −

= = = =−−

108. 34 8 1 11 32 11 21 21 7

3(9 8) 3(1) 33(9 2 )⋅ − ⋅ −

= = = =−−

109. 2 2Area (side) (7 meters) 49 square meters= = =

110. 2 2Area (side) (3 inches) 9 square inches= = =

111. 2 2 5 10 5

2 2xz

⋅= = =

112. 4x − 3 = 4 ⋅ 5 − 3 = 20 − 3 = 17

113. 7 5 7

0xy+ +

= is undefined.

114. 0 0 0

5 5 5 25yx= = =

⋅

115. 3 32 5 2 2 125 2 2 125 4 121x z− = − ⋅ = − ⋅ = − =

116. 7 7 5 12 23 3 2 6xz+ +

= = =⋅

117. 2 2 2( ) (0 2) 2 4y z+ = + = =

118. 100 100 0 20 0 20

3 5 3y

x+ = + = + =

119. Five subtracted from a number is x − 5.

120. Seven more than a number is x + 7.

121. Ten divided by a number is 10 ÷ x or 10 .x

122. The product of 5 and a number is 5x.



54

123. Let n be 5. 12 20 3

5 12 20 317 17 True

n + = −+ −

=�


124. Let n be 23. 8 10 6

23 8 10 615 16 False

n − = +− +

=�


125. Let n = 14. 30 3( 3)30 3(14 3)30 3(11)30 33 False

n= −−

=

�

�


126. Let n be 20. 5( 7) 65

5(20 7) 655(13) 65

65 65 True

n − =−

=

�

�


127. 7n = 77 Let n be 6. 7 6 77

42 77 False⋅

=�

Let n be 11. 7 11 77

77 77 True⋅

=�

Let n be 20. 7 20 77

140 77 False⋅

=�

11 is a solution.

128. n − 25 = 150 Let n be 125. 125 25 150

100 150 False−

=�

Let n be 145. 145 25 150

120 150 False−

=�

Let n be 175. 175 25 150

150 150 True−

=�

175 is a solution.

129. 5(n + 4) = 90 Let n be 14. 5(14 4) 90

5(18) 9090 90 True

+

=

�

�

Let n be 16. 5(16 4) 90

5(20) 90100 90 False

+

=

�

�

Let n be 26. 5(26 4) 90

5(30) 90150 90 False

+

=

�

�

14 is a solution.

130. 3n − 8 = 28 Let n be 3. 3(3) 8 28

9 8 281 28 False

−−

=

�

�

Let n be 7. 3(7) 8 28

21 8 2813 28 False

−−

=

�

�

Let n be 15. 3(15) 8 28

45 8 2837 28 False

−−

=

�

�

None are solutions.

131. 48568

417−

132. 72947

682−

133. 7323

2196×

134. 6294

2516×

135.

2 237429

6981101+



55

136.

2 159352

7661411+

137. 458 R 8

13 5962 527665112104

8

−

−

−

138. 237 R 1

18 4267 36

6654127126

1

−

−

−

139. 196836

11 80859 04070,848

×

140. 532418

42 59253 24095,832

×

141. 2000356

1644−

142. 9000519

8481−


144. To round 258,371 to the nearest hundred-thousand, observe that the digit in the ten-thousands place is 5. Since this digit is at least 5, we add 1 to the digit in the hundred-thousands place. The number 258,371 rounded to the nearest hundred-thousand is 300,000.

145. 24 ÷ 4 ⋅ 2 = 6 ⋅ 2 = 12

146. 3(15 3) (8 5) (18)(3) 54 6

8 1 92 1+ ⋅ −

= = =++

147. Let n be 9. 5 6 40

5 9 6 4045 6 40

39 40 False

n − =⋅ −−

=

�

�


148. Let n be 3. 2 6 5 15

2(3) 6 5(3) 156 6 15 15

0 0 True

n n− = −− −− −

=

�

�


149. 53

32 1714160

1149618

−

−

There are 53 full boxes with 18 left over.

150. 272

54×

84

32×

543286

+

The total bill before taxes is $86.

Chapter 1 Test

1. 82,426 in words is eighty-two thousand, four hundred twenty-six.

2. Four hundred two thousand, five hundred fifty in standard form is 402,550.



56

3.

15982

141+

4. 600487113

−

5. 49630

14,880×

6. 766 R 42

69 52,89648 3

4 594 14

45641442

−

−

−

7. 3 22 5 2 2 2 5 5 200⋅ = ⋅ ⋅ ⋅ ⋅ =

8. 98 ÷ 1 = 98

9. 0 ÷ 49 = 0


11. 4(2 5) 3 (16 5) 3 11 3 33− ⋅ = − ⋅ = ⋅ =

12. 16 9 3 4 7 16 3 4 716 12 728 721

+ ÷ ⋅ − = + ⋅ −= + −= −=

13. 1 36 2 6 2 2 2 48⋅ = ⋅ ⋅ ⋅ =

14. 2 2 2 22[(6 4) (22 19) ] 10 2[2 3 ] 102[4 9] 102[13] 1026 1036

− + − + = + += + += += +=

15. 5698 ⋅ 1000 = 5,698,000


26279849095

410+

82

5 41040

10100

−

−

The average is 82.


18. 6289 rounds to 6 3005403 rounds to 5 4001957 rounds to + 2 000

13,700+


1600− −

20. 1071592

−

21. 15107122

+

22. 10715

53510701605

×

23. 7 R 2

15 107 105

2−



57

24. 17

29 49329203203

0

−

−

Each can cost $17.

25. 725599126

−

The higher-priced one is $126 more.

26. 458

360×

There are 360 calories in 8 tablespoons of white granulated sugar.

27. 43016

258043006880

× 205

51025×

688010257905

+


28. Perimeter (5 5 5 5) centimeters20 centimeters

= + + +=

2

2Area (side)


=

==

29. Perimeter (20 10 20 10) yards 60 yards= + + + =

Area (length)(width)(20 yards)(10 yards)200 square yards

===

30. Let x be 2. 3 35( 2) 5(2 2) 5(8 2) 5(6) 30x − = − = − = =

31. Let x be 7 and y be 8. 3 5 3(7) 5 21 5 16 1

2 2 8 16 16xy− − −

= = = =⋅

32. a. The quotient of a number and 17 is x ÷ 17 or

.17x

b. Twice a number, decreased by 20 is 2x − 20.

33. Let n be 6. 5 11 19

5(6) 11 1930 11 19

19 19 True

n − =−−

=

�

�

6 is a solution.

34. n + 20 = 4n − 10 Let n be 0. 0 20 4 0 10

20 0 1020 10 False

+ ⋅ −−

= −

�

�

Let n be 10. 10 20 4 10 10

30 40 1030 30 True

+ ⋅ −−

=

�

�

Let n be 20. 20 20 4 20 10

40 80 1040 70 False

+ ⋅ −−

=

�

�

10 is a solution.


Documents

Chapter 1 · PDF fileTwo million, twelve in standard form is 2,000,012. 37. Two hundred sixty thousand, nine hundred ninety-seven in standard form is 260,997. 38. ... 49. 3470 = 3000