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Chapter 1 Section 1.2 4. The number 900 + 60 + 5 is written in expanded form. Practice Problems 5. In a whole number, each group of 3 digits is called a period. 1. The place value of the 8 in 38,760,005 is millions. 6. The place value of the digit 4 in the whole number 264 is ones. 2. The place value of the 8 in 67,890 is hundreds. 3. The place value of the 8 in 481,922 is tenthousands. Exercise Set 1.2 1. The place value of the 5 in 657 is tens. 4. 54 is written as fifty-four. 2. The place value of the 5 in 905 is ones. 5. 678 is written as six hundred seventy-eight. 3. The place value of the 5 in 5423 is thousands. 6. 93,205 is written as ninety-three thousand, two hundred five. 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. 7. 679,430,105 is written as six hundred seventynine million, four hundred thirty thousand, one hundred five. 8. Thirty-seven in standard form is 37. 6. The place value of the 5 in 79,050,000 is tenthousands. 9. Two hundred twelve in standard form is 212. 7. The place value of the 5 in 5,408,092 is millions. 10. Eight thousand, two hundred seventy-four in standard form is 8,274 or 8274. 8. The place value of the 5 in 51,682,700 is tenmillions. 11. Five million, fifty-seven thousand, twenty-six in standard form is 5,057,026. 9. 354 is written as three hundred fifty-four. 10. 316 is written as three hundred sixteen. 12. 4,026,301 = 4,000,000 + 20,000 + 6000 + 300 + 1 13. a. 11. 8279 is written as eight thousand, two hundred seventy-nine. Find Norway in the left-hand column. Read from left to right until the “gold” column is reached. Norway won 96 gold medals. 12. 5445 is written as five thousand, four hundred forty-five. 13. 26,990 is written as twenty-six thousand, nine hundred ninety. 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. 14. 42,009 is written as forty-two thousand, nine. 15. 2,388,000 is written as two million, three hundred eighty-eight thousand. Vocabulary and Readiness Check 1. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... are called whole numbers. 16. 3,204,000 is written as three million, two hundred four thousand. 2. The number 1,286 is written in standard form. 17. 24,350,185 is written as twenty-four million, three hundred fifty thousand, one hundred eighty-five. 3. The number “twenty-one” is written in words. 1 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 18. 47,033,107 is written as forty-seven million, thirty-three thousand, one hundred seven. 37. Two hundred sixty thousand, nine hundred ninety-seven in standard form is 260,997. 19. 65,773 is written as sixty-five thousand, seven hundred seventy-three. 38. Six hundred forty thousand, eight hundred eighty-one in standard form is 640,881. 20. 40,000 is written as forty thousand. 39. Three hundred fifty-three in standard form is 353. 21. 1679 is written as one thousand, six hundred seventy-nine. 40. Two hundred thirty-four thousand in standard form is 234,000. 22. 6912 is written as six thousand, nine hundred twelve. 41. Four hundred eighty-four thousand, two hundred thirty-five in standard form is 484,235. 23. 2,800,000 is written as two million, eight hundred thousand. 42. One thousand, eight hundred fifteen in standard form is 1815. 24. 15,200,000 is written as fifteen million, two hundred thousand. 43. Fifty-four million, five hundred thousand in standard form is 54,500,000. 25. 11,239 is written as eleven thousand, two hundred thirty-nine. 44. Fifty million, thirteen thousand, eight hundred fifty-nine in standard form is 50,013,859. 26. 14,433 is written as fourteen thousand, four hundred thirty-three. 45. Seven hundred fourteen in standard form is 714. 46. Seven hundred fifty-five in standard form is 755. 27. 202,700 is written as two hundred two thousand, seven hundred. 47. 209 = 200 + 9 28. 799,000 is written as seven hundred ninety-nine thousand. 48. 789 = 700 + 80 + 9 49. 3470 = 3000 + 400 + 70 29. Six thousand, five hundred eighty-seven in standard form is 6587. 50. 6040 = 6000 + 40 30. Four thousand, four hundred sixty-eight ion standard form is 4468. 51. 80,774 = 80,000 + 700 + 70 + 4 52. 20,215 = 20,000 + 200 + 10 + 5 31. Fifty-nine thousand, eight hundred in standard form is 59,800. 53. 66,049 = 60,000 + 6000 + 40 + 9 32. Seventy-three thousand, two in standard form is 73,002. 54. 99,032 = 90,000 + 9000 + 30 + 2 33. Thirteen million, six hundred one thousand, eleven in standard form is 13,601,011. 55. 39,680,000 = 30,000,000 + 9,000,000 + 600,000 + 80,000 34. Sixteen million, four hundred five thousand, sixteen in standard form is 16,405,016. 56. 47,703,029 = 40,000,000 + 7,000,000 + 700,000 + 3000 + 20 + 9 35. Seven million, seventeen in standard form is 7,000,017. 57. The elevation of Mt. Clay is 5532 which is five thousand, five hundred thirty-two in words. 36. Two million, twelve in standard form is 2,000,012. 58. The elevation of Mt. Washington is 6288 which is six thousand, two hundred eighty-eight in words. 2 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 59. The height of Boott Spur is 5492 which is 5000 + 400 + 90 + 2 in expanded form. 1 1 11 2. 60. The height of Mt. Jefferson is 5712 which is 5000 + 700 + 10 + 2 in expanded form. 47,364 + 135,898 183, 262 61. Mt. Washington is the tallest mountain in New England. 3. Notice 12 + 8 = 20 and 4 + 6 = 10. 12 + 4 + 8 + 6 + 5 = 20 + 10 + 5 = 35 62. Mt. Adams is the second tallest mountain in New England. 4. 12 2 63. Chihuahua has fewer dogs registered than Golden retriever. 64. Beagle has more dogs registered than Yorkshire terrier. 6432 789 54 + 28 7303 5. a. 65. Labrador retrievers have the most registrations; 146,714 is written as one hundred forty-six thousand, seven hundred fourteen. b. 20 − 8 = 12 because 12 + 8 = 20 c. 66. Chihuahuas have the fewest registrations; 24,853 is written as twenty-four thousand, eight hundred fifty-three. 93 − 93 = 0 because 0 + 93 = 93. d. 42 − 0 = 42 because 42 + 0 = 42. 6. a. 9123 − 142 8981 Check: 8981 + 142 9123 b. 978 − 851 127 Check: 7. a. 69 7 −49 64 8 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. 127 + 851 978 8 17 70. The largest number is 77,753. 71. No; 105.00 should be written as one hundred five. 72. Yes Check: 648 + 49 697 2 12 73. answers may vary b. 326 − 245 81 Check: 81 + 245 326 c. 1234 − 822 412 Check: 412 + 822 1234 Check: 236 + 164 400 74. answers may vary 75. 135.5 trillion in standard form is 135,500,000,000,000. Section 1.3 Practice Problems 1. 14 − 6 = 8 because 8 + 6 = 14. 4135 + 252 4387 8. a. 9 31010 40 0 −1 6 4 2 3 6 3 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra Vocabulary and Readiness Check 9 910 10 b. 10 0 0 −762 238 Check: 1. The sum of 0 and any number is the same number. 238 + 762 1000 2. In 35 + 20 = 55, the number 55 is called the sum and 35 and 20 are each called an addend. 9. 2 cm + 8 cm + 15 cm + 5 cm = 30 cm The perimeter is 30 centimeters. 3. The difference of any number and that same number is 0. 10. 647 + 647 + 647 = 1941 The perimeter is 1941 feet. 11. 4. The difference of any number and 0 is the same number. 15, 759 − 458 15,301 The radius of Neptune is 15,301 miles. 12. a. 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. The model with the fewest seats corresponds to the shortest bar, which is the F-100. 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. b. Add the number of seats for each model. 370 87 + 141 598 The total number of seats in the B747-400, F-100, and B737-400 is 598. 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 Calculator Explorations 1. 89 + 45 = 134 1. 14 + 22 36 2 27 + 31 58 3. 62 + 230 292 4. 37 + 542 579 5. 12 13 + 24 49 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 4 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra 6. 7. 8. Chapter 1: The Whole Numbers 22 23 45 + 30 98 14. 5267 + 132 5399 1 12 15. 236 + 6243 6479 1 1 1 9. 22, 781 + 186, 297 209, 078 11. 12. 17, 427 + 821, 059 838, 486 16 1056 748 + 7770 9590 11 1 17. 8 9 2 5 +1 25 6 820 4 271 + 5 626 16, 717 1 111 18. 3 5 8 5 +7 28 6789 4321 + 5555 16, 665 11 22 19. 22 13. 24 9006 489 + 2407 11,926 11 2 16. 1 10. 64 28 56 25 + 32 205 81 17 23 79 + 12 212 49 628 5 762 + 29, 462 35,901 111 20. 26 582 4 763 + 62,511 67,882 5 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 1 22 2 1 21. 1 31. 121, 742 57, 279 26,586 + 426, 782 632,389 6283 − 560 5723 Check: 5723 + 560 6283 32. 5349 − 720 4629 Check: 4629 + 720 5349 33. 533 − 29 504 Check: 504 + 29 533 34. 724 − 16 708 Check: 708 + 16 724 35. 1983 − 1904 79 Check: 36. 1983 − 1914 69 Check: 1 1 11 2 1 2 22. 504, 218 321,920 38,507 + 594, 687 1, 459,332 1 1 23. 62 −37 25 Check: 25 + 37 62 24. 55 − 29 26 Check: 26 + 29 55 25. 749 − 149 600 Check: 600 + 149 749 957 − 257 700 Check: 922 −634 288 Check: 674 − 299 375 Check: 1 1 26. 1 1 700 + 257 957 37. 50, 000 − 17, 289 32, 711 Check: 32, 711 + 17, 289 50, 000 288 + 634 922 38. 40, 000 − 23,582 16, 418 Check: 16, 418 + 23,582 40, 000 39. 7020 − 1979 5041 Check: 5041 + 1979 7020 40. 6050 − 1878 4172 Check: 4172 + 1878 6050 11 11 11 28. 375 + 299 674 111 11 29. 600 − 432 168 Check: 300 − 149 151 Check: 168 + 432 600 111 11 30. 69 + 1914 1983 1 1 11 11 27. 79 + 1904 1983 151 + 149 300 6 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 51. 7 + 8 + 10 = 25 The perimeter is 25 feet. 11 11 41. 51,111 − 19,898 31, 213 Check: 31, 213 + 19,898 51,111 52. 3 + 4 + 5 = 12 The perimeter is 12 centimeters. 11 11 Check: 53. Opposite sides of a rectangle have the same length. 4 + 8 + 4 + 8 = 12 + 12 = 24 The perimeter is 24 inches. 42. 62, 222 − 39,898 22,324 43. 986 + 48 1034 54. Opposite sides of a rectangle have the same length. 8 + 4 + 8 + 4 = 12 + 12 = 24 The perimeter is 24 miles. 44. 986 − 48 938 55. 8 + 3 + 5 + 7 + 5 + 1 = 29 The perimeter is 29 inches. 45. 22,324 + 39,898 62, 222 56. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37 The perimeter is 37 inches. 76 − 67 9 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. 2 46. 47. 80 93 17 9 +2 201 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. 9000 − 482 8518 59. “Find the sum” indicates addition. 111 297 + 1796 2093 The sum of 297 and 1796 is 2093. 48. 10, 000 − 1786 8214 60. “Find the sum” indicates addition. 11 1 49. 10,962 4 851 + 7 063 22,876 50. 12, 468 3 211 + 1 988 17, 667 1 802 + 6487 7289 The sum of 802 and 6487 is 7289. 1 11 7 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 68. “Less” indicates subtraction. 25 − 12 13 25 less 12 is 13. 61. “Find the total” indicates addition. 13 76 39 8 17 + 126 266 The total of 76, 39, 8, 17, and 126 is 266. 69. “Subtracted from” indicates subtraction. 100 − 12 88 12 subtracted from 100 is 88. 62. “Find the total” indicates addition. 12 89 45 2 19 + 341 496 The total of 89, 45, 2, 19, and 341 is 496. 70. “Subtracted from” indicates subtraction. 90 − 86 4 86 subtracted from 90 is 4. 71. Subtract 36,039 thousand from 38,067 thousand. 38, 067 − 36, 039 2 028 California’s projected population increase is 2028 thousand. 63. “Find the difference” indicates subtraction. 41 − 21 20 The difference of 41 and 21 is 20. 72. Subtract 12,699 thousand from 12,917 thousand. 12,917 − 12, 699 218 Illinois’ projected population increase is 218 thousand. 64. “Find the difference” indicates subtraction. 16 − 5 11 The difference of 16 and 5 is 11. 65. “Increased by” indicates addition. 73. Subtract the cost of the DVD player from the amount in her savings account. 914 − 295 619 She will have $619 left. 1 452 + 92 544 452 increased by 92 is 544. 66. “Increased by” indicates addition. 712 + 38 750 712 increased by 38 is 750. 74. Subtract the discount from the regular price. 547 − 99 448 The sale price is $448. 67. “Less” indicates subtraction. 108 − 36 72 108 less 36 is 72. 75. 189, 000 + 75, 000 264, 000 The total U.S. land area drained by the Upper Mississippi and Lower Mississippi sub-basins is 264,000 square miles. 8 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra 76. 77. 78. Chapter 1: The Whole Numbers 86. The shortest bar corresponds to the quietest reading. Leaves rustling is the quietest. 164, 000 + 40, 000 204, 000 The total U.S. land area drained by the Ohio and Tennessee sub-basins is 204,000 square miles. 530, 000 − 247, 000 283, 000 The Missouri sub-basin drains 283,000 square miles more than the Arkansas Red-White subbasin. 189, 000 − 75, 000 114, 000 The Upper Mississippi sub-basin drains 114,000 square miles more than the Lower Mississippi sub-basin. 87. 88 − 30 58 The sound of snoring is 58 dB louder than normal conversation. 88. 100 − 70 30 The difference in sound intensity between live rock music and loud television is 30 dB. 111 5696 89. + 3346 9042 There were 9042 stores worldwide. 79. 70 + 78 + 90 + 102 = 340 The homeowner needs 340 feet of fencing. 90. 80. Opposite sides of a rectangle have the same length. 60 + 45 + 60 + 45 = 210 The perimeter is 210 feet. 81. 82. 83. 91. Each side of a square has the same length. 31 + 31 + 31 + 31 = 124 The perimeter of the playing board is 124 feet. 503 − 239 264 She must read 264 more pages. 92. Opposite sides of a rectangle have the same length. 18 + 12 + 18 + 12 = 60 The perimeter of the puzzle is 60 inches. 59,320 − 55, 492 3 828 They traveled 3828 miles on their trip. 93. California has the most Target stores. 94. Arizona has the fewest Target stores. 386,119 + 426,990 813,109 The total number sold in the U.S. in 2005 was 813,109. 11 95. 111 11 84. 119 − 99 20 The difference in volume between the mid-size and a sub-compact car is 20 cubic feet. 4,141,199 + 35, 758,801 39,900, 000 The sheep population was 39,900,000. 205 121 + 95 421 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. 85. Live rock music has a decibel level of 100 dB. 9 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 97. Florida and Georgia: 21 108. 1 95 + 44 139 Michigan and Ohio: 773 659 + 481 1913 The given sum is correct. 11 22 53 + 49 102 Florida and Georgia have more Target stores. 109. 98. The total number of stores listed in the table is 796 stores. 796 + 601 1397 There are 1397 Target stores in the United States. 1 2 110. 19 214 49 + 651 933 The given sum is incorrect, the correct sum is 933. 111. 675 + 56 731 The given difference is incorrect. 741 − 56 685 112. 389 + 89 478 The given difference is correct. 113. 141 + 888 1029 The given difference is correct. 1 99. 2029 + 3865 5894 The total highway mileage in Delaware is 5894 miles. 11 1 100. 14 173 86 + 257 530 The given sum is incorrect, the correct sum is 530. 5193 + 1222 6415 The total highway mileage in Rhode Island is 6415 miles. 101. The minuend is 48 and the subtrahend is 1. 11 102. The minuend is 2863 and the subtrahend is 1904. 103. The minuend is 70 and the subtrahend is 7. 104. The minuend is 86 and the subtrahend is 25. 105. answers may vary 106. answers may vary. 1 107. 566 932 + 871 2369 The given sum is correct. 10 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers tens place. The number 325 rounded to the nearest ten is 330. 11 114. 7168 + 547 7715 The given difference is incorrect. 7615 − 547 7068 115. 5269 − 2385 2884 116. 10, 244 − 8 534 1 710 2. a. 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. 117. answers may vary 118. answers may vary 121 3 2 119. 3. a. 289, 462 369, 477 218, 287 + 121, 685 998,911 Since 998,911 is less than one million, they did not reach their goal. 1, 000, 000 − 998,911 1 089 They need to read 1089 more pages. c. Practice Problems 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. 4. 49 25 32 51 98 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 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. 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. Section 1.4 1. 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. 5. 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 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. rounds to rounds to rounds to rounds to rounds to 3785 − 2479 50 30 30 50 + 100 260 rounds to rounds to 11 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall 4000 − 2000 2000 Chapter 1: The Whole Numbers 6. 11 16 19 + 31 rounds to rounds to rounds to rounds to ISM: Prealgebra 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. 10 20 20 + 30 80 The total distance is approximately 80 miles. 7. 120, 710 22,878 + 45,974 rounds to rounds to rounds to 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. 120,000 20,000 + 50,000 190,000 7. To round 495 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 495 rounded to the nearest ten is 500. The total number of cases is approximately 190,000. Vocabulary and Readiness Check 1. To graph a number on a number line, darken the point representing the location of the number. 8. To round 898 to the nearest ten, observe that the digit in the ones place is 8. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 898 rounded to the nearest ten is 900. 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. 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. 4. An exact number of products is 1265, but an estimate is 1000. Exercise Set 1.4 10. To round 82,198 to the nearest thousand, observe that the digit in the hundreds place is 1. Since this digit is less than 5, we do not add 1 to the digit in the thousands place. The number 82,198 rounded to the nearest thousand is 82,000. 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. 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. 2. To round 273 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 273 rounded to the nearest ten is 270. 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. 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. 4. To round 846 to the nearest ten, observe that the digit in the ones place is 6. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 846 rounded to the nearest ten is 850. 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. 12 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 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. 23. Estimate 9444 to a given place value by rounding it to that place value. 9444 rounded to the tens place is 9440, to the hundreds place is 9400, and to the thousands place is 9000. 24. Estimate 7777 to a given place value by rounding it to that place value. 7777 rounded to the tens place is 7780, to the hundreds place is 7800, and to the thousands place is 8000. 15. To round 36,499 to the nearest thousand, observe that the digit in the hundreds place is 4. Since this digit is less than 5, we do not add 1 to the digit in the thousands place. The number 36,499 rounded to the nearest thousand is 36,000. 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. 16. To round 96,501 to the nearest thousand, observe that the digit in the hundreds place is 5. Since this digit is at least 5, we add 1 to the digit in the thousands place. The number 96,501 rounded to the nearest thousand is 97,000. 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. 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. 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. 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. 28. To round 85,907,423 to the nearest hundredthousand, observe that the digit in the tenthousands place is 0. Since this digit is less than 5, we do not add 1 to the digit in the hundredthousands place. Therefore 85,907,423 passengers rounded to the nearest hundredthousand is 85,900,000 passengers. 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. 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. 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. 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. 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. 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. 22. Estimate 7619 to a given place value by rounding it to that place value. 7619 rounded to the tens place is 7620, to the hundreds place is 7600, and to the thousands place is 8000. 13 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 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 hundredthousand, observe that the digit in the tenthousands place is 2. Since this digit is less than 5, we do not add 1 to the digit in the hundredthousands 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 hundredthousands 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 hundredthousands 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 tenmillion is 110,000,000 bushels. 37. 38. 39 45 22 + 17 rounds to rounds to rounds to rounds to 40 50 20 + 20 130 52 33 15 + 29 rounds to rounds to rounds to rounds to 50 30 20 + 30 130 39. 449 − 373 rounds to rounds to 450 − 370 80 40. 555 − 235 rounds to rounds to 560 − 240 320 41. 1913 1886 + 1925 rounds to rounds to rounds to 1900 1900 + 1900 5700 42. 4050 3133 + 1220 rounds to rounds to rounds to 4100 3100 + 1200 8400 43. 1774 − 1492 rounds to rounds to 1800 − 1500 300 44. 1989 − 1870 rounds to rounds to 2000 − 1900 100 45. 3995 2549 + 4944 rounds to rounds to rounds to 46. 799 1655 + 271 rounds to rounds to rounds to 4000 2500 + 4900 11, 400 800 1700 + 300 2800 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. 14 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 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. 54. 55. 56. 57. 58. 899 1499 + 999 900 1500 + 1000 3400 The total cost is approximately $3400. 89 97 100 79 75 + 82 rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to 60 40 + 130 230 61. 910, 000 − 907, 000 3 000 The decrease in enrollment is approximately 3000 children. 62. 51, 746 − 49, 713 909, 608 − 906,993 rounds to rounds to rounds to rounds to 52,000 − 50, 000 2 000 The increase is approximately 2000 credit hours. 64. $214 million is $214,000,000 in standard form. $214,000,000 rounded to the nearest ten-million is $210,000,000. $214,000,000 rounded to the nearest hundredmillion is $200,000,000. 65. $179 million is $179,000,000 in standard form. $179,000,000 rounded to the nearest ten-million is $180,000,000. $179,000,000 rounded to the nearest hundredmillion is $200,000,000. 20, 000 − 14, 000 6 000 The difference in elevation is approximately 6000 feet. 1895 − 1524 64 41 + 133 rounds to rounds to 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 hundredmillion is $300,000,000. − 600 700 300 100 100 + 800 2600 The total distance is approximately 2600 miles. 20,320 − 14, 410 60. 782, 623 − 382,894 The total distance is approximately 230 miles. 1400 500 900 Boston in approximately 900 miles farther from Kansas City than Chicago is. 588 689 277 143 59 + 802 780, 000 − 380, 000 400, 000 Jacksonville was approximately 400,000 larger than Miami. rounds to rounds to rounds to 90 100 100 80 80 + 80 530 The total score is approximately 530. 1429 − 530 59. rounds to rounds to 66. $155 million is $155,000,000 in standard form. $155,000,000 rounded to the nearest ten-million is $160,000,000. $155,000,000 rounded to the nearest hundredmillion is $200,000,000. rounds to rounds to 1900 − 1500 400 The difference in price is approximately $400. 67. 5723, for example, rounded to the nearest hundred is 5700. 68. 5698, for example, rounded to the nearest ten is 5700. 15 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers 69. a. ISM: Prealgebra The smallest possible number that rounds to 8600 is 8550. 4. 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 hundredthousand is 1,549,999. 5. 5950 7693 + 8203 rounds to rounds to rounds to 6 000 7 700 + 8 200 21,900 6. Area = length ⋅ width = (360 miles)(280 miles) = 100,800 square miles The area of Wyoming is 100,800 square miles. 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. 7. Section 1.5 Practice Problems 1. a. 6×0=0 (50)(0) = 0 9. 6(4 + 5) = 6 ⋅ 4 + 6 ⋅ 5 163 × 391 rounds to rounds to b. 30(2 + 3) = 30 ⋅ 2 + 30 ⋅ 3 c. 3. a. b. 1 88 + 45 133 The total cost is $133. d. 75 ⋅ 1 = 75 2. a. 16 × 45 80 640 720 The printer can print 720 pages in 45 minutes. 8. 8 × 11 = 88 5 × 9 = 45 b. (1)8 = 8 c. 726 142 1 452 29 040 72 600 103, 092 × 71. answers may vary 72. 306 81 306 24 480 24, 786 × 200 × 400 80,000 There are approximately 80,000 words on 391 pages. 7(2 + 8) = 7 ⋅ 2 + 7 ⋅ 8 29 × 6 54 120 174 Calculator Explorations 1. 72 × 48 = 3456 2. 81 × 92 = 7452 3. 163 ⋅ 94 = 15,322 648 × 5 40 200 3000 3240 4. 285 ⋅ 144 = 41,040 5. 983(277) = 272,291 6. 1562(843) = 1,316,766 16 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers Vocabulary and Readiness Check 15. 64 × 8 512 16. 79 × 3 237 17. 613 × 6 3678 18. 638 × 5 3190 19. 277 × 6 1662 20. 882 × 2 1764 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 21. 1074 × 6 6444 1. 1 ⋅ 24 = 24 2. 55 ⋅ 1 = 55 3. 0 ⋅ 19 = 0 22. 9021 × 3 27, 063 23. 89 × 13 267 890 1157 24. 91 × 72 182 6370 6552 25. 421 × 58 3 368 21 050 24, 418 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 17 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers 26. ISM: Prealgebra 37. 526 23 1 578 10 520 12, 098 × 27. 306 81 306 24 480 24, 786 × 28. 38. 708 21 708 14 160 14,868 780 × 20 15, 600 30. 720 × 80 57, 600 39. 1234 567 8 638 74 040 617 000 699, 678 × 31. (495)(13)(0) = 0 32. (593)(47)(0) = 0 41. 589 × 110 5 890 58 900 64, 790 42. 426 × 110 4 260 42 600 46,860 43. 1941 × 2035 9 705 58 230 3 882 000 3,949,935 33. (640)(1)(10) = (640)(10) = 6400 34. (240)(1)(20) = (240)(20) = 4800 36. 8649 274 34 596 605 430 1 729 800 2,369,826 × 40. 35. 807 127 5 649 16 140 80 700 102, 489 × × 29. 609 234 2 436 18 270 121 800 142,506 × 1234 × 39 11 106 37 020 48,126 1357 × 79 12 213 94 990 107, 203 18 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra 44. Chapter 1: The Whole Numbers 56. 706 × 409 is approximately 700 × 400, which is 280,000. The best estimate is d. 1876 1407 13 132 750 400 1 876 000 2, 639,532 × 57. 80 × 11 = (8 × 10) × 11 = 8 × (10 × 11) = 8 × 110 = 880 45. Area = (length)(width) = (9 meters)(7 meters) = 63 square meters 58. 70 × 12 = (7 × 10) × 12 = 7 × (10 × 12) = 7 × 120 = 840 46. Area = (length)(width) = (13 inches)(3 inches) = 39 square inches 59. 6 × 700 = 4200 60. 9 × 900 = 8100 47. Area = (length)(width) = (40 feet)(17 feet) = 680 square feet 48. Area = (length)(width) = (25 centimeters)(20 centimeters) = 500 square centimeters 49. 50. 576 × 354 rounds to rounds to 600 × 400 240, 000 982 × 650 rounds to rounds to 1000 × 700 700, 000 51. 604 × 451 rounds to rounds to 600 × 500 300, 000 52. 111 × 999 rounds to rounds to 100 × 1000 100, 000 61. 2240 × 2 4480 62. 3310 × 3 9930 63. 125 × 3 375 There are 375 calories in 3 tablespoons of olive oil. 64. 14 × 8 112 There are 112 grams of fat in 8 ounces of hulled sunflower seeds. 65. 94 × 35 470 2820 3290 The total cost is $3290. 66. 34 × 14 136 340 476 There are 476 seats in the room. 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. 19 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers 67. a. 4 × 5 = 20 There are 20 boxes in one layer. 74. 700 × 17 4 900 7 000 11,900 The 17 discs hold 11,900 MB. 75. 5 × 4 = 20 There are 20 apartments on one floor. 60 × 35 300 1 800 2 100 There are 2100 characters in 35 lines. 76. 20 × 3 60 There are 60 apartments in the building. 365 × 3 1095 A cow eats 1095 pounds of grain each year. 77. 160 × 8 1280 There are 1280 calories in 8 ounces. 78. 13 × 16 78 130 208 There are 208 grams of fat in 16 ounces. b. 20 × 5 100 There are 100 boxes on the pallet. c. 100 × 20 2000 The weight of the cheese on the pallet is 2000 pounds. 68. a. b. ISM: Prealgebra 69. Area = (length)(width) = (110 feet)(80 feet) = 8800 square feet The area is 8800 square feet. 70. Area = (length)(width) = (60 feet)(45 feet) = 2700 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. 79. TShirt Size Number of Shirts Ordered Cost per Shirt Cost per Size Ordered 72. Area = (length)(width) = (776 meters)(639 meters) = 495,864 square meters The area is 495,864 square meters. S 4 $10 $40 M 6 $10 $60 L 20 $10 $200 73. XL 3 $12 $36 XXL 3 $12 $36 94 × 62 188 5640 5828 There are 5828 pixels on the screen. Total Cost 20 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall $372 ISM: Prealgebra Chapter 1: The Whole Numbers 90. Person Number of persons Cost per person Student 24 $5 $120 19 + 4 23 The total of 19 and 4 is 23. Nonstudent 4 $7 $28 91. 6 + 6 + 6 + 6 + 6 = 5 ⋅ 6 or 6 ⋅ 5 Children under 12 5 $2 $10 80. Total Cost Cost per Category 92. 11 + 11 + 11 + 11 + 11 + 11 = 6 ⋅ 11 or 11 ⋅ 6 93. a. $158 3⋅5=5+5+5=3+3+3+3+3 b. answers may vary 94. a. 81. There are 31 days in March. 31× 700, 000 = 31× 7 × 100, 000 = 217 × 100, 000 = 21, 700, 000 They would use 21,700,000 quarts in March. b. answers may vary 95. 203 × 14 812 2030 2842 96. 31 × 50 1550 82. 3 × 2,641,000 = 7,923,000 There were 7,923,000 widows in 2005. 83. + 128 7 135 − 126 8 118 84. 85. 4 ⋅ 5 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4 97. 42 × 3 = 126 42 × 9 = 378 The problem is 134 × 16 804 1340 2144 98. 57 × 3 = 171 57 × 6 = 342 The problem is 42 × 93 57 × 63 86. 47 + 26 + 10 + 231 + 50 = 364 87. 99. answers may vary 19 + 4 23 The sum of 19 and 4 is 23. 88. 19 × 4 76 The product of 19 and 4 is 76. 89. 19 −4 15 The difference of 19 and 4 is 15. 100. 3 × 110 = 330 2 × 641 = 1282 330 + 1282 + 539 = 2151 Nowitzki scored 2151 points during the 2005−2006 regular season. 21 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 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. 4. a. Section 1.6 Practice Problems 1. a. 8 9 72 because 8 ⋅ 9 = 72. b. 40 ÷ 5 = 8 because 8 ⋅ 5 = 40. c. 2. a. b. 24 = 4 because 4 ⋅ 6 = 24. 6 7 = 1 because 1 ⋅ 7 = 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 = 10 because 10 ⋅ 1 = 10. 1 f. 21 ÷ 21 = 1 because 1 ⋅ 21 = 21. 3. a. b. c. c. 0 = 0 because 0 ⋅ 5 = 0. 5 0 8 0 because 0 ⋅ 8 = 0. 5. a. 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. 818 6 4908 −48 10 −6 48 −48 0 Check: 818 × 6 4908 553 4 2212 −20 21 −20 12 −12 0 Check: 553 × 4 2212 251 753 −6 15 −15 03 −3 0 Check: 251 × 3 753 3 7 304 2128 −21 02 −0 28 −28 0 Check: 304 × 7 = 2128 22 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra b. Chapter 1: The Whole Numbers 5 100 9 45,900 −45 09 −9 000 b. Check: 5100 × 9 = 45,900 6. a. 4 234 R 3 939 −8 13 −12 19 −16 3 524 R 12 8. 17 8920 −85 42 −34 80 −68 12 657 R 2 5 3287 −30 28 −25 37 −35 2 49 R 60 9. 678 33, 282 −27 12 6 162 −6 102 60 Check: 657 ⋅ 5 + 2 = 3287 7. a. 5827 R 2 23,310 −20 33 −3 2 11 −8 30 −28 2 Check: 5827 ⋅ 4 + 2 = 23,310 Check: 234 ⋅ 4 + 3 = 939 b. 4 9067 R 2 9 81, 605 −81 06 −0 60 −54 65 −63 2 57 10. 3 171 −15 21 −21 0 Each student got 57 CDs. 44 532 −48 52 −48 4 There will be 44 full boxes and 4 printers left over. 11. 12 Check: 9067 ⋅ 9 + 2 = 81,605 23 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 12. Find the sum and divide by 7. 18 4 7 126 7 −7 56 35 −56 16 9 0 3 + 52 126 The average time is 18 minutes. 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 Calculator Explorations 7. 31 ÷ 1 = 31 1. 848 ÷ 16 = 53 8. 38 ÷ 1 = 38 2. 564 ÷ 12 = 47 3. 5890 ÷ 95 = 62 4. 1053 ÷ 27 = 39 5. 6. 32,886 = 261 126 143, 088 = 542 264 9. 18 =1 18 10. 49 =1 49 11. 24 =8 3 12. 45 =5 9 7. 0 ÷ 315 = 0 13. 26 ÷ 0 = undefined. 8. 315 ÷ 0 is an error. Vocabulary and Readiness Check 14. 1. In 90 ÷ 2 = 45, the answer 45 is called the quotient, 90 is called the dividend, and 2 is called the divisor. 12 = undefined 0 15. 26 ÷ 26 = 1 16. 6 ÷ 6 = 1 2. The quotient of any number and 1 is the same number. 17. 0 ÷ 14 = 0 3. The quotient of any number (except 0) and the same number is 1. 18. 7 ÷ 0 = undefined 19. 18 ÷ 2 = 9 4. The quotient of 0 and any number (except 0) is 0. 20. 18 ÷ 3 = 6 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. 24 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 29 21. 3 87 −6 27 −27 0 27. 28. Check: 3 ⋅ 29 = 87 30 is undefined. 0 0 =0 30 Check: 0 ⋅ 30 = 0 9 29. 7 63 −63 0 17 22. 5 85 −5 35 −35 0 Check: 7 ⋅ 9 = 63 7 30. 8 56 −56 0 Check: 17 ⋅ 5 = 85 74 23. 3 222 −21 12 −12 0 Check: 7 ⋅ 8 = 56 31. 6 Check: 74 ⋅ 3 = 222 24. 8 80 640 −64 00 25 150 −12 30 −30 0 Check: 25 ⋅ 6 = 150 11 32. 11 121 −11 11 −11 0 Check: 80 ⋅ 8 = 640 338 25. 3 1014 −9 11 −9 24 −24 0 Check: 11 ⋅ 11 = 121 68 R 3 33. 7 479 −42 59 −56 3 Check: 3 ⋅ 338 = 1014 526 26. 4 2104 −20 10 −8 24 −24 0 Check: 7 ⋅ 68 + 3 = 479 34. 7 60 R 6 426 −42 06 Check: 60 ⋅ 7 + 6 = 426 Check: 526 ⋅ 4 = 2104 25 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 236 R 5 35. 6 1421 −12 22 −18 41 −36 5 833 R 1 40. 4 3333 −32 13 −12 13 −12 1 Check: 236 ⋅ 6 + 5 = 1421 Check: 833 ⋅ 4 + 1 = 3333 413 R 1 36. 3 1240 −12 04 −3 10 −9 1 13 41. 55 715 −55 165 −165 0 Check: 55 ⋅ 13 = 715 32 42. 23 736 −69 46 −46 0 Check: 413 ⋅ 3 + 1 = 1240 37. 8 38 R 1 305 −24 65 −64 1 Check: 32 ⋅ 23 = 736 49 43. 23 1127 −92 207 −207 0 Check: 8 ⋅ 38 + 1 = 305 55 R 2 38. 3 167 −15 17 −15 2 Check: 49 ⋅ 23 = 1127 Check: 55 ⋅ 3 + 2 = 167 39. 7 44. 42 326 R 4 2286 −21 18 −14 46 −42 4 48 2016 −168 336 −336 0 Check: 48 ⋅ 42 = 2016 97 R 8 45. 97 9417 −873 687 −679 8 Check: 326 ⋅ 7 + 4 = 2286 Check: 97 ⋅ 97 + 8 = 9417 26 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra 46. 44 Chapter 1: The Whole Numbers 202 R 7 51. 46 9299 −92 09 −0 99 −92 7 44 R 2 1938 −176 178 −176 2 Check: 44 ⋅ 44 + 2 = 1938 209 R 11 47. 15 3146 −30 14 −0 146 −135 11 Check: 202 ⋅ 46 + 7 = 9299 39 R 9 52. 64 2505 −192 585 −576 9 Check: 209 ⋅ 15 + 11 = 3146 Check: 39 ⋅ 64 + 9 = 2505 612 R 10 48. 12 7354 −72 15 −12 34 −24 10 53. 236 54 12744 −1180 944 −944 0 Check: 236 ⋅ 54 = 12,744 47 54. 123 5781 −492 861 −861 0 Check: 612 ⋅ 12 + 10 = 7354 506 49. 13 6578 −65 07 −0 78 −78 0 Check: 47 ⋅ 123 = 5781 99 R 100 55. 103 10, 297 −9 27 1 027 −927 100 Check: 13 ⋅ 506 = 6578 405 50. 14 5670 −56 07 −0 70 −70 0 Check: 99 ⋅ 103 + 100 = 10,297 96 R 52 56. 240 23, 092 −21 60 1 492 −1 440 52 Check: 405 ⋅ 14 = 5670 Check: 96 ⋅ 240 + 52 = 23,092 27 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 202 R 15 57. 102 20619 −204 21 −0 219 −204 15 13 62. 8 104 −8 24 −24 0 511 R 3 63. 7 3580 −35 08 −7 10 −7 3 Check: 102 ⋅ 202 + 15 = 20,619 201 R 50 58. 203 40,853 −40 6 25 −0 253 −203 50 603 R 2 64. 5 3017 −30 01 −0 17 −15 2 Check: 201 ⋅ 203 + 50 = 40,853 579 R 72 59. 423 244,989 −211 5 33 48 −29 61 3 879 −3 807 72 2132 R 32 65. 40 85312 −80 53 −40 131 −120 112 −80 32 Check: 579 ⋅ 423 + 72 = 244,989 303 R 63 60. 543 164,592 −162 9 1 69 − 0 1 692 −1 629 63 1714 R 47 66. 50 85, 747 −50 35 7 −35 0 74 −50 247 −200 47 Check: 303 ⋅ 543 + 63 = 164,592 17 61. 7 119 −7 49 −49 0 28 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 6 080 67. 142 863,360 −852 11 3 −0 11 36 −11 36 00 −0 0 20 R 2 73. 3 62 −6 02 −0 2 The quotient is 20 R 2. 15 R 3 78 −5 28 −25 3 The quotient is 15 R 3. 74. 5 3 040 68. 214 650,560 −642 85 −0 8 56 −8 56 00 −0 0 33 2145 −195 195 −195 0 There are 33 students in the group. 75. 65 23 R 2 69. 5 117 −10 17 −15 2 The quotient is 23 R 2. 58 76. 85 4930 −425 680 −680 0 There are 58 students in the group. 13 R 3 70. 7 94 −7 24 −21 3 The quotient is 13 R 3. 165 77. 318 52470 −318 2067 −1908 1590 −1590 0 The person weighs 165 pounds on Earth. 5 R 25 71. 35 200 −175 25 200 divided by 35 is 5 R 25. 3 R 20 72. 32 116 −96 20 116 divided by 32 is 3 R 20. 29 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 252000 78. 21 5292000 −42 109 −105 42 −42 0 Each person received $252,000. 10 5280 −492 360 There should be 10 poles, plus the first pole for a total of 11 light poles. 83. 492 23 R 1 185 −16 25 −24 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. 84. 8 310 79. 18 5580 −54 18 −18 0 The distance is 310 yards. 5 85. 5280 26400 −26400 0 Broad Peak is 5 miles tall. 412 80. 14 5768 −56 16 −14 28 −28 0 The truck hauls 412 bushels on each trip. 28 86. 6 168 −12 48 −48 0 Alexander scored 28 touchdowns. 88 R 1 81. 3 265 −24 25 −24 1 There are 88 bridges every 3 miles over the 265 miles, plus the first bridge, for a total of 89 bridges. 1760 87. 3 5280 −3 22 −21 18 −18 0 There are 1760 yards in 1 mile. 82. Lane divider = 25 + 25 = 50 105 50 5280 −50 28 −0 280 −250 30 There are 105 whole lane dividers. 16 88. 320 5280 −320 2080 −1920 160 There are 16 whole feet in 1 rod. 30 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 10 89. 24 35 22 17 + 12 120 Average = Average = Average = Average = 89 534 −48 54 −54 0 534 = 89 6 69 77 + 76 222 74 3 222 −21 12 −12 0 The average temperature is 74°. 96. 169 5 845 −5 34 −30 45 −45 0 121 200 185 176 + 163 845 6 2 95. 1548 = 387 4 21 92. 92 96 90 85 92 + 79 534 Average = 387 4 1548 −12 34 −32 28 −28 0 205 972 210 + 161 1548 395 = 79 5 2 94. 180 = 30 6 1 91. Average = 30 6 180 −18 00 37 26 15 29 51 + 22 180 79 5 395 −35 45 −45 0 86 93. 79 81 69 + 80 395 120 = 20 6 3 90. 2 20 6 120 −12 00 2 53 40 + 30 123 41 3 123 −12 03 −3 0 The average temperature is 41°. 111 97. 845 = 169 5 82 463 29 + 8704 9278 11 98. 23 407 92 + 7011 7533 31 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers 99. × 100. 546 28 4 368 10 920 15, 288 732, 000, 000 2 1, 464, 000, 000 797, 000, 000 111. −1 4 + 667, 000, 000 1, 464, 000, 000 06 −6 04 −4 0 The average amount spent is $732,000,000. 712 × 54 2 848 35 600 38, 448 101. 722 − 43 679 102. 712 − 54 658 103. ISM: Prealgebra 112. 45 is undefined. 0 634, 000, 000 4 2,536, 000, 000 −2 4 13 −12 16 −16 0 The average amount spent is $634,000,000. 797, 000, 000 667, 000, 000 544, 000, 000 + 528, 000, 000 2,536, 000, 000 113. The average will increase; answers may vary. 114. The average will decrease; answers may vary. 0 104. = 0 because 0 ⋅ 23 = 0 23 115. No; answers may vary Possible answer: The average cannot be less than each of the four numbers. 9 R 12 105. 24 228 −216 12 12 116. 5 60 −5 10 −10 0 The length is 12 feet. Notice that Area = length × width = 12 × 5 = 60. 9 R 25 106. 31 304 −279 25 107. The quotient of 40 and 8 is 40 ÷ 8, which is choice c. 117. answers may vary 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. 32 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers Integrated Review 118. 26 −5 21 −5 16 −5 11 −5 6 −5 1 Therefore, 26 ÷ 5 = 5 R 1 1 1. 42 63 + 89 194 2. 7006 − 451 6555 3. 87 × 52 174 4350 4524 The Bigger Picture 1 1. 82 + 39 121 2. 82 − 39 43 3. 82 × 39 738 2460 3198 562 4. 8 4496 −40 49 −48 16 −16 0 5. 1 ⋅ 67 = 67 6. 89 R 11 4. 29 2592 −232 272 −261 11 36 is undefined. 0 7. 16 ÷ 16 = 1 8. 5 ÷ 1 = 5 9. 0 ⋅ 21 = 0 5. 0 ⋅ 15 = 0 10. 7 ⋅ 0 ⋅ 8 = 0 6. 0 ÷ 11 = 0 11. 0 ÷ 7 = 0 7. 26 ⋅ 1 = 26 12. 12 ÷ 4 = 3 8. 36 ÷ 0 is undefined. 13. 9 ⋅ 7 = 63 9. 82 ÷ 1 = 82 14. 45 ÷ 5 = 9 10. 2000 − 156 1844 15. 207 − 69 138 33 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 1 16. 207 + 69 276 17. 3718 − 2549 1169 18. 1861 + 7965 9826 663 R 24 23. 32 21, 240 −19 2 2 04 −1 92 120 −96 24 11 1 076 R 60 24. 65 70, 000 −65 50 −0 5 00 −4 55 450 −390 60 182 R 4 19. 7 1278 −7 57 −56 18 −14 4 20. 25. 1259 63 3 777 75 540 79,317 × 4000 − 2963 1037 26. 10, 000 − 101 9 899 27. 1099 R 2 21. 7 7695 −7 06 −0 69 −63 65 −63 2 303 × 101 303 30 300 30, 603 28. (475)(100) = 47,500 1 111 R 1 22. 9 1000 −9 10 −9 10 −9 1 29. 62 + 9 71 The total of 62 and 9 is 71. 30. 62 × 9 558 The product of 62 and 9 is 558. 34 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 6 R8 31. 9 62 −54 8 The quotient of 62 and 9 is 6 R 8. 41. 32. 62 − 9 53 The difference of 62 and 9 is 53. 33. 200 − 17 183 17 subtracted from 200 is 183. 34. 432 − 201 231 The difference of 432 and 201 is 231. 42. The unknown vertical side has length 4 + 3 = 7 meters. The unknown horizontal side has length 3 + 3 = 6 meters. 3 4 3 7 6 +3 26 The perimeter is 26 meters. 13 9 + 6 28 The perimeter is 28 miles. 3 24 5 120 −10 20 −20 0 19 43. 15 25 37 + 24 120 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. Average = 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. 120 = 24 5 124 4 496 −4 09 −8 16 −16 0 12 44. 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. 108 131 98 + 159 496 Average = 39. 6 + 6 + 6 + 6 = 24 6 × 6 = 36 The perimeter is 24 feet and the area is 36 square feet. 45. 40. 14 + 7 + 14 + 7 = 42 14 × 7 98 The perimeter is 42 inches and the area is 98 square inches. 496 = 124 4 28,547 − 26,372 2 175 The Lake Pontchartrain Bridge is longer by 2175 feet. 35 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers 46. ISM: Prealgebra 14. 36 ÷ 6 ⋅ 3 + 5 = 6 ⋅ 3 + 5 = 18 + 5 = 23 347 × 18 2776 3470 6246 The amount spent on toys is $6246. 15. Area = (side)2 = (12 centimeters)2 = 144 square centimeters The area of the square is 144 square centimeters. Section 1.7 Calculator Explorations Practice Problems 1. 36 = 729 1. 8 ⋅ 8 ⋅ 8 ⋅ 8 = 84 2. 56 = 15, 625 2. 3 ⋅ 3 ⋅ 3 = 33 3. 45 = 1024 3. 10 ⋅10 ⋅10 ⋅10 ⋅10 = 105 4. 76 = 117, 649 4. 5 ⋅ 5 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 = 52 ⋅ 46 5. 211 = 2048 5. 42 = 4 ⋅ 4 = 16 6. 68 = 1, 679, 616 6. 83 = 8 ⋅ 8 ⋅ 8 = 512 7. 7 4 + 53 = 2526 1 7. 11 = 11 8. 124 − 84 = 16, 640 8. 2 ⋅ 32 = 2 ⋅ 3 ⋅ 3 = 18 9. 63 ⋅ 75 − 43 ⋅ 10 = 4295 9. 9 ⋅ 3 − 8 ÷ 4 = 27 − 8 ÷ 4 = 27 − 2 = 25 10. 8 ⋅ 22 + 7 ⋅ 16 = 288 2 10. 48 ÷ 3 ⋅ 2 = 48 ÷ 3 ⋅ 4 = 16 ⋅ 4 = 64 11. 4(15 ÷ 3 + 2) − 10 ⋅ 2 = 8 11. (10 − 7)4 + 2 ⋅ 32 = 34 + 2 ⋅ 32 = 81 + 2 ⋅ 9 = 81 + 18 = 99 3 12. 155 − 2(17 + 3) + 185 = 300 Vocabulary and Readiness Check 1. In 25 = 32, the 2 is called the base and the 5 is called the exponent. 3 12. 36 ÷ [20 − (4 ⋅ 2)] + 4 − 6 = 36 ÷ [20 − 8] + 4 − 6 = 36 ÷ 12 + 43 − 6 = 36 ÷ 12 + 64 − 6 = 3 + 64 − 6 = 61 13. 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 25 + 8 ⋅ 2 − 33 25 + 8 ⋅ 2 − 27 = 2(3 − 2) 2(1) 25 + 16 − 27 = 2 14 = 2 =7 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 36 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers Exercise Set 1.7 24. 81 = 8 1. 4 ⋅ 4 ⋅ 4 = 43 25. 27 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 128 2. 5 ⋅ 5 ⋅ 5 ⋅ 5 = 54 26. 54 = 5 ⋅ 5 ⋅ 5 ⋅ 5 = 625 3. 7 ⋅ 7 ⋅ 7 ⋅ 7 ⋅ 7 ⋅ 7 = 76 27. 28 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 256 4. 6 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 = 67 28. 33 = 3 ⋅ 3 ⋅ 3 = 27 5. 12 ⋅12 ⋅12 = 123 29. 44 = 4 ⋅ 4 ⋅ 4 ⋅ 4 = 256 6. 10 ⋅10 ⋅10 = 103 30. 43 = 4 ⋅ 4 ⋅ 4 = 64 7. 6 ⋅ 6 ⋅ 5 ⋅ 5 ⋅ 5 = 62 ⋅ 53 31. 93 = 9 ⋅ 9 ⋅ 9 = 729 8. 4 ⋅ 4 ⋅ 3 ⋅ 3 ⋅ 3 = 42 ⋅ 33 32. 83 = 8 ⋅ 8 ⋅ 8 = 512 9. 9 ⋅ 8 ⋅ 8 = 9 ⋅ 82 33. 122 = 12 ⋅12 = 144 10. 7 ⋅ 4 ⋅ 4 ⋅ 4 = 7 ⋅ 43 34. 112 = 11 ⋅11 = 121 11. 3 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 3 ⋅ 24 35. 102 = 10 ⋅10 = 100 12. 4 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 = 4 ⋅ 64 36. 103 = 10 ⋅10 ⋅10 = 1000 13. 3 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 = 3 ⋅ 24 ⋅ 55 37. 201 = 20 14. 6 ⋅ 6 ⋅ 2 ⋅ 9 ⋅ 9 ⋅ 9 ⋅ 9 = 62 ⋅ 2 ⋅ 94 38. 141 = 14 15. 82 = 8 ⋅ 8 = 64 39. 36 = 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 729 16. 62 = 6 ⋅ 6 = 36 40. 45 = 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 = 1024 17. 53 = 5 ⋅ 5 ⋅ 5 = 125 41. 3 ⋅ 26 = 3 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 192 18. 63 = 6 ⋅ 6 ⋅ 6 = 216 42. 5 ⋅ 32 = 5 ⋅ 3 ⋅ 3 = 45 19. 25 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 32 43. 2 ⋅ 34 = 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 162 20. 35 = 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 243 44. 2 ⋅ 7 2 = 2 ⋅ 7 ⋅ 7 = 98 21. 110 = 1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 = 1 45. 15 + 3 ⋅ 2 = 15 + 6 = 21 22. 112 = 1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 = 1 46. 24 + 6 ⋅ 3 = 24 + 18 = 42 23. 71 = 7 47. 28 ÷ 7 ⋅ 1 + 3 = 4 ⋅ 1 + 3 = 4 + 3 = 7 48. 100 ÷ 10 ⋅ 5 + 4 = 10 ⋅ 5 + 4 = 50 + 4 = 54 37 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 49. 32 ÷ 4 − 3 = 8 − 3 = 5 66. 50. 42 ÷ 7 − 6 = 6 − 6 = 0 51. 13 + 24 = 13 + 3 = 16 8 52. 32 + 8 = 32 + 4 = 36 2 56. 7 1 6+9÷3 = = 2 3 70. 23 ⋅ 3 − (100 ÷ 10) = 23 ⋅ 3 − 10 = 8 ⋅ 3 − 10 = 24 − 10 = 14 5+3 8 = =8 1 1 6+3 9 = =1 9 9 71. 34 − [35 − (12 − 6)] = 34 − [35 − 6] = 34 − 29 = 81 − 29 = 52 = 32 ÷ 4 ⋅ 23 = 32 ÷ 4 ⋅ 8 = 8⋅8 = 64 72. [40 − (8 − 2)] − 25 = [40 − 6] − 25 = 34 − 25 = 34 − 32 =2 58. 62 ⋅ (10 − 8) = 62 ⋅ 2 = 36 ⋅ 2 = 72 73. (7 ⋅ 5) + [9 ÷ (3 ÷ 3)] = (7 ⋅ 5) + [9 ÷ (1)] = 35 + 9 = 44 59. 52 ⋅ (10 − 8) + 23 + 52 = 52 ⋅ 2 + 23 + 52 = 25 ⋅ 2 + 8 + 25 = 50 + 8 + 25 = 83 74. (18 ÷ 6) + [(3 + 5) ⋅ 2] = (18 ÷ 6) + (8 ⋅ 2) = 3 + (8 ⋅ 2) = 3 + 16 = 19 60. 53 ÷ (10 + 15) + 92 + 33 = 53 ÷ 25 + 92 + 33 = 125 ÷ 25 + 81 + 27 = 5 + 81 + 27 = 113 62. 18 + 6 4 2 −2 2 40 + 8 2 2 5 −3 5(5) − 4 25 − 4 21 = = =3 25 − 18 25 − 18 7 69. 24 ⋅ 4 − (25 ÷ 5) = 24 ⋅ 4 − 5 = 16 ⋅ 4 − 5 = 64 − 5 = 59 57. (7 + 52 ) ÷ 4 ⋅ 23 = (7 + 25) ÷ 4 ⋅ 23 61. 5 − 18 = 68. 18 − 7 ÷ 0 = undefined 54. 3 ⋅ 4 + 9 ⋅ 1 = 12 + 9 = 21 5 + 12 ÷ 4 2 67. 8 ÷ 0 + 37 = undefined 53. 6 ⋅ 5 + 8 ⋅ 2 = 30 + 16 = 46 55. 5(12 − 7) − 4 = 24 24 = =2 16 − 4 12 = 48 48 = =3 25 − 9 16 75. 8 ⋅ [22 + (6 − 1) ⋅ 2] − 50 ⋅ 2 = 8 ⋅ (22 + 5 ⋅ 2) − 50 ⋅ 2 = 8 ⋅ (4 + 5 ⋅ 2) − 50 ⋅ 2 = 8 ⋅ (4 + 10) − 50 ⋅ 2 = 8 ⋅14 − 50 ⋅ 2 = 112 − 50 ⋅ 2 = 112 − 100 = 12 63. (3 + 5) ⋅ (9 − 3) = 8 ⋅ 6 = 48 64. (9 − 7) ⋅ (12 + 18) = 2 ⋅ 30 = 60 65. 7(9 − 6) + 3 2 3 −3 = 7(3) + 3 21 + 3 24 = = =4 9−3 6 6 38 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 82. 10 ÷ 2 + 33 ⋅ 2 − 20 = 10 ÷ 2 + 27 ⋅ 2 − 20 = 5 + 27 ⋅ 2 − 20 = 5 + 54 − 20 = 39 76. 35 ÷ [32 + (9 − 7) − 22 ] + 10 ⋅ 3 = 35 ÷ [32 + 2 − 22 ] + 10 ⋅ 3 = 35 ÷ [9 + 2 − 4] + 10 ⋅ 3 = 35 ÷ 7 + 10 ⋅ 3 = 5 + 10 ⋅ 3 = 5 + 30 = 35 83. [13 ÷ (20 − 7) + 25 ] − (2 + 3)2 = [13 ÷ 13 + 25 ] − 52 = [13 ÷ 13 + 32] − 52 = [1 + 32] − 52 92 + 22 − 12 81 + 4 − 1 77. = 8 ÷ 2 ⋅ 3 ⋅1 ÷ 3 4 ⋅ 3 ⋅1 ÷ 3 85 − 1 = 12 ⋅1 ÷ 3 84 = 12 ÷ 3 84 = 4 = 21 78. 79. 80. = 33 − 52 = 33 − 25 =8 84. [15 ÷ (11 − 6) + 22 ] + (5 − 1) 2 = [15 ÷ 5 + 22 ] + 42 = [15 ÷ 5 + 4] + 42 = [3 + 4] + 42 = 7 + 42 = 7 + 16 = 23 52 − 23 + 14 25 − 8 + 1 18 18 = = = =9 10 ÷ 5 ⋅ 4 ⋅1 ÷ 4 2 ⋅ 4 ⋅1 ÷ 4 8 ÷ 4 2 2+4 2 2 5(20 − 16) − 3 − 5 3 + 92 2 3(10 − 6) − 2 − 1 = = 85. 7 2 − {18 − [40 ÷ (5 ⋅1) + 2] + 52 } 2 + 16 = 7 2 − {18 − [40 ÷ 5 + 2] + 52 } 2 5(4) − 3 − 5 18 = 5(4) − 9 − 5 18 = 20 − 9 − 5 18 = 11 − 5 18 = 6 =3 = 7 2 − {18 − [8 + 2] + 52 } = 7 2 − {18 − 10 + 52 } = 7 2 − {18 − 10 + 25} = 7 2 − 33 = 49 − 33 = 16 86. 29{5 + 3[8 ⋅ (10 − 8)] − 50} = 29 − {5 + 3[8 ⋅ 2] − 50} = 29 − {5 + 3(16) − 50} = 29 − {5 + 48 − 50} = 29 − 3 = 26 3 + 81 3(4) − 22 − 1 84 = 3(4) − 4 − 1 84 = 12 − 4 − 1 84 = 8 −1 84 = 7 = 12 87. Area of a square = (side) 2 = (7 meters)2 = 49 square meters 88. Area of a square = (side) 2 = (9 centimeters)2 = 81 square centimeters 89. Area of a square = (side) 2 81. 9 ÷ 3 + 52 ⋅ 2 − 10 = 9 ÷ 3 + 25 ⋅ 2 − 10 = 3 + 25 ⋅ 2 − 10 = 3 + 50 − 10 = 43 = (23 miles)2 = 529 square miles 39 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra The Bigger Picture 90. Area of a square = (side) 2 = (41 feet) 2 = 1681 square feet 1. 63 = 6 ⋅ 6 ⋅ 6 = 216 91. The statement is true. 2. 23 ⋅ 61 = 2 ⋅ 2 ⋅ 2 ⋅ 6 = 48 92. The statement is true. 3. 8 ⋅ 52 = 8 ⋅ 5 ⋅ 5 = 200 93. 25 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 The statement is false. 4. 1 + 2(3 + 4) = 1 + 2(7) = 1 + 14 = 15 5. 2 + 5(10 − 3) = 2 + 5(7) = 2 + 35 = 37 9 94. 4 = 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 The statement is false. 6. 200 ÷ 2 ⋅ 2 = 100 ⋅ 2 = 200 95. (2 + 3) ⋅ 6 − 2 = 5 ⋅ 6 − 2 = 30 − 2 = 28 7. 978 − 179 799 8. 72 × 30 2160 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) ⋅ 5 = 24 ÷ 8 ⋅ 5 = 3⋅5 = 15 10 R 34 9. 58 614 −58 34 −0 34 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. 3 10. 3[(7 − 3)2 − (25 − 22) 2 ] + 6 = 3[42 − 32 ] + 6 = 3(16 − 9) + 6 = 3(7) + 6 = 21 + 6 = 27 3 100. 25 ⋅ (45 − 7 ⋅ 5) ⋅ 5 = 25 ⋅ (45 − 35) ⋅ 5 = 253 ⋅ (10) ⋅ 5 = 15, 625 ⋅10 ⋅ 5 = 156, 250 ⋅ 5 = 781, 250 Section 1.8 101. (7 + 24 )5 − (35 − 24 )2 = (7 + 16)5 − (243 − 16)2 Practice Problems = 235 − 227 2 = 6, 436,343 − 51,529 = 6,384,814 1. x − 2 = 7 − 2 = 5 2. y(x − 3) = 4(8 − 3) = 4(5) = 20 102. answers may vary 3. 103. answers may vary; possible answer: (20 − 10) ⋅ 5 ÷ 25 + 3 = 10 ⋅ 5 ÷ 25 + 3 = 50 ÷ 25 + 3 = 2+3 =5 y + 6 18 + 6 24 = = =4 x 6 6 4. 25 − z 3 + x = 25 − 23 + 1 = 25 − 8 + 1 = 18 5. 5( F − 32) 5(41 − 32) 5(9) 45 = = = =5 9 9 9 9 40 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 6. 3( y − 6) = 6 3(8 − 6) ⱨ 6 3(2) ⱨ 6 6 = 6 True Yes, 8 is a solution. 7. 5n + 4 = 34 Let n be 10. 5(10) + 4 ⱨ 34 50 + 4 ⱨ 34 54 = 34 False No, 10 is not a solution. Let n be 6. 5(6) + 4 ⱨ 34 30 + 4 ⱨ 34 34 = 34 True Yes, 6 is a solution. Let n be 8. 5(8) + 4 ⱨ 34 40 + 4 ⱨ 34 44 = 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 Vocabulary and Readiness Check 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. 41 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra Exercise Set 1.8 1. 2. a b a+b a−b a⋅b a÷b 21 7 21 + 7 = 28 21 − 7 = 14 21 ⋅ 7 = 147 21 ÷ 7 = 3 a b a+b a−b a⋅b a÷b 24 6 24 + 6 = 30 24 − 6 = 18 24 ⋅ 6 = 144 24 ÷ 6 = 4 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. 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. 3. 4. 5. 6. a b a+b a−b a⋅b a÷b 56 1 56 + 1 = 57 56 − 1 = 55 56 ⋅ 1 = 56 56 ÷ 1 = 56 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. y 3 − 4 x = 53 − 4(2) = 125 − 4(2) = 125 − 8 = 117 16. y 3 − z = 53 − 3 = 125 − 3 = 122 17. 2 xy 2 − 6 = 2(2)(5)2 − 6 = 2 ⋅ 2 ⋅ 25 − 6 = 100 − 6 = 94 42 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 18. 3 yz 2 + 1 = 3(5)(3) 2 + 1 = 3⋅5⋅9 +1 = 135 + 1 = 136 32. 3x 2 + 2 x − 5 = 3 ⋅ 22 + 2 ⋅ 2 − 5 = 3⋅ 4 + 2 ⋅ 2 − 5 = 12 + 4 − 5 = 11 19. 8 − (y − x) = 8 − (5 − 2) = 8 − 3 = 5 33. (4 y − 5 z )3 = (4 ⋅ 5 − 5 ⋅ 3)3 = (20 − 15)3 20. 3 + (2 y − 4) = 3 + (2 ⋅ 5 − 4) = 3 + (10 − 4) = 3+ 6 =9 5 = (5)3 = 125 34. (4 y + 3z )2 = (4 ⋅ 5 + 3 ⋅ 3) 2 5 21. x + ( y − z ) = 2 + (5 − 3) = (20 + 9)2 5 = 2 +2 = 32 + 2 = 34 4 4 = 292 = 841 35. ( xy + 1) 2 = (2 ⋅ 5 + 1) 2 = (10 + 1)2 = 112 = 121 4 22. x − ( y − z ) = 2 − (5 − 3) = 2 − 2 = 16 − 2 = 14 36. ( xz − 5) 4 = (2 ⋅ 3 − 5) 4 = (6 − 5)4 = 14 = 1 6 xy 6 ⋅ 2 ⋅ 5 60 = = = 20 23. 3 3 z 24. 8 yz 8 ⋅ 5 ⋅ 3 120 = = =8 15 15 15 25. 2 y − 2 2(5) − 2 10 − 2 8 = = = =4 2 2 2 x 26. 6 + 3x 6 + 3(2) 6 + 6 12 = = = =4 3 3 3 z 27. x + 2 y 2 + 2 ⋅ 5 2 + 10 12 = = = =4 3 3 3 z 28. 2 z + 6 2 ⋅ 3 + 6 6 + 6 12 = = = =4 3 3 3 3 29. 5 x 10 5(2) 10 10 − = − = −2 = 2−2 = 0 5 5 5 y y 37. 2 y (4 z − x) = 2 ⋅ 5(4 ⋅ 3 − 2) = 2 ⋅ 5(12 − 2) = 2 ⋅ 5(10) = 10(10) = 100 38. 3x( y + z ) = 3 ⋅ 2(5 + 3) = 3 ⋅ 2(8) = 6(8) = 48 39. xy (5 + z − x) = 2 ⋅ 5(5 + 3 − 2) = 2 ⋅ 5(6) = 10(6) = 60 40. xz (2 y + x − z ) = 2 ⋅ 3(2 ⋅ 5 + 2 − 3) = 2 ⋅ 3(10 + 2 − 3) = 2 ⋅ 3(9) = 6(9) = 54 41. 30. 70 15 70 15 70 15 − = − = − = 7−5 = 2 2 y z 2 ⋅ 5 3 10 3 42. 31. 2 y 2 − 4 y + 3 = 2 ⋅ 52 − 4 ⋅ 5 + 3 = 2 ⋅ 25 − 4 ⋅ 5 + 3 = 50 − 20 + 3 = 33 7 x + 2 y 7(2) + 2(5) 14 + 10 24 = = = =4 3x 3(2) 6 6 6z + 2 y 6 ⋅ 3 + 2 ⋅ 5 = 4 4 18 + 10 = 4 28 = 4 =7 43 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers 43. 44. ISM: Prealgebra t 1 2 3 4 16t 2 16 ⋅12 = 16 ⋅1 = 16 16 ⋅ 22 = 16 ⋅ 4 = 64 16 ⋅ 32 = 16 ⋅ 9 = 144 16 ⋅ 42 = 16 ⋅16 = 256 F 50 59 68 77 5( F − 32) 9 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. n −8 = 2 10 − 8 ⱨ 2 2 = 2 True Yes, 10 is a solution. 46. Let n be 9. n−2 = 7 9−2ⱨ 7 7 = 7 True Yes, 9 is a solution. 47. Let n be 3. 24 = 80n 24 ⱨ 80 ⋅ 3 24 = 240 False No, 3 is not a solution. 48. Let n be 50. 250 = 5n 250 ⱨ 5(50) 250 = 250 True Yes, 50 is a solution. 49. Let n be 7. 3n − 5 = 10 3(7) − 5 ⱨ 10 21 − 5 ⱨ 10 16 = 10 False No, 7 is not a solution. 50. Let n be 8. 11n + 3 = 91 11(8) + 3 ⱨ 91 88 + 3 ⱨ 91 91 = 91 True Yes, 8 is a solution. 44 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 58. n + 3 = 16 Let n be 9. 9 + 3 ⱨ 16 12 = 16 False Let n be 11. 11 + 3 ⱨ 16 14 = 16 False Let n be 13. 13 + 3 ⱨ 16 16 = 16 True 13 is a solution. 51. Let n be 20. 2(n − 17) = 6 2(20 − 17) ⱨ 6 2(3) ⱨ 6 6 = 6 True Yes, 20 is a solution. 52. Let n be 0. 5(n + 9) = 40 5(0 + 9) ⱨ 40 5(9) ⱨ 40 45 = 40 False No, 0 is not a solution. 59. 5n = 30 Let n be 6. 5 ⋅ 6 ⱨ 30 30 = 30 True Let n be 25. 5 ⋅ 25 ⱨ 30 125 = 30 False Let n be 30. 5 ⋅ 30 ⱨ 30 150 = 30 False 6 is a solution. 53. Let x be 0. 5 x + 3 = 4 x + 13 5(0) + 3 ⱨ 4(0) + 13 0 + 3 ⱨ 0 + 13 3 = 13 False No, 0 is not a solution. 54. Let x be 2. 3 x − 6 = 5 x − 10 3(2) − 6 ⱨ 5(2) − 10 6 − 6 ⱨ 10 − 10 0 = 0 True Yes, 2 is a solution. 60. 3n = 45 Let n be 15. 3 ⋅15 ⱨ 45 45 = 45 True Let n be 30. 3 ⋅ 30 ⱨ 45 90 = 45 False Let n be 45. 3 ⋅ 45 ⱨ 45 135 = 45 False 15 is a solution. 55. Let f be 8. 7 f = 64 − f 7(8) ⱨ 64 − 8 56 = 56 True Yes, 8 is a solution. 56. Let x be 5. 8 x − 30 = 2 x 8(5) − 30 ⱨ 2(5) 40 − 30 ⱨ 10 10 = 10 True Yes, 5 is a solution. 61. 6n + 2 = 26 Let n be 0. 6(0) + 2 ⱨ 26 0 + 2 ⱨ 26 2 = 26 False Let n be 2. 6(2) + 2 ⱨ 26 12 + 2 ⱨ 26 14 = 26 False Let n be 4. 6(4) + 2 ⱨ 26 24 + 2 ⱨ 26 26 = 26 True 4 is a solution. 57. n − 2 = 10 Let n be 10. 10 − 2 ⱨ 10 8 = 10 False Let n be 12. 12 − 2 ⱨ 10 10 = 10 True Let n be 14. 14 − 2 ⱨ 10 12 = 10 False 12 is a solution. 45 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 7(7) − 9 ⱨ 5(7) + 13 49 − 9 ⱨ 35 + 13 40 = 48 False Let x be 11. 7(11) − 9 ⱨ 5(11) + 13 77 − 9 ⱨ 55 + 13 68 = 68 True 11 is a solution. 62. 4n − 14 = 6 Let n be 0. 4 ⋅ 0 − 14 ⱨ 6 0 − 14 ⱨ 6 −14 = 6 False Let n be 5. 4 ⋅ 5 − 14 ⱨ 6 20 − 14 ⱨ 6 6 = 6 True Let n be 10. 4 ⋅10 − 14 ⱨ 6 40 − 14 ⱨ 6 26 = 6 False 5 is a solution. 66. 9x − 15 = 5x + 1 Let x be 2. 9 ⋅ 2 − 15 ⱨ 5 ⋅ 2 + 1 18 − 15 ⱨ 10 + 1 3 = 11 False Let x be 4. 9 ⋅ 4 − 15 ⱨ 5 ⋅ 4 + 1 36 − 15 ⱨ 20 + 1 21 = 21 True Let x be 11. 9 ⋅11 − 15 ⱨ 5 ⋅11 + 1 99 − 15 ⱨ 55 + 1 84 = 56 False 4 is a solution. 63. 3(n − 4) = 10 Let n be 5. 3(5 − 4) ⱨ 10 3(1) ⱨ 10 3 = 10 False Let n be 7. 3(7 − 4) ⱨ 10 3(3) ⱨ 10 9 = 10 False Let n be 10. 3(10 − 4) ⱨ 10 3(6) ⱨ 10 18 = 10 False None are solutions. 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. 64. 6(n + 2) = 23 Let n be 1. 6(1 + 2) ⱨ 23 6(3) ⱨ 23 18 = 23 False Let n be 3. 6(3 + 2) ⱨ 23 6(5) ⱨ 23 30 = 23 False Let n be 5. 6(5 + 2) ⱨ 23 6(7) ⱨ 23 42 = 23 False None are solutions. 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 76. A number divided by 11 is 65. 7x − 9 = 5x + 13 Let x be 3. 7(3) − 9 ⱨ 5(3) + 13 21 − 9 ⱨ 15 + 13 12 = 28 False Let x be 7. 6 . x x . 11 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. 46 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 80. The quotient of twenty and a number, decreased 20 by three is − 3. x 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. 81. A number subtracted from 11 is 11 − x. 82. Twelve subtracted from a number is x − 12. 3. The position of each digit in a number determines its place value. 83. A number less 5 is x − 5. 4. An exponent is a shorthand notation for repeated multiplication of the same factor. 84. The product of a number and 7 is 7x. 85. 6 divided by a number is 6 ÷ x or 6 . x 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. 86. The sum of a number and 7 is x + 7. 87. Fifty decreased by eight times a number is 50 − 8x. 7. A letter used to represent a number is called a variable. 88. Twenty decreased by twice a number is 20 − 2x. 8. An equation can be written in the form “expression = expression.” 89. x 4 − y 2 = 234 − 722 = 279,841 − 5184 = 274, 657 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. 90. 2( x + y )2 = 2(23 + 72)2 2 = 2(95) = 2(9025) = 18, 050 11. A collection of numbers (or objects) enclosed by braces is called a set. 91. x 2 + 5 y − 112 = 232 + 5(72) − 112 = 529 + 360 − 112 = 777 12. The 21 above is called the sum. 13. The 5 above is called the divisor. 14. The 35 above is called the dividend. 92. 16 y − 20 x + x3 = 16 ⋅ 72 − 20 ⋅ 23 + 233 = 1152 − 460 + 12,167 = 12,859 15. The 7 above is called the quotient. 16. The 3 above is called a factor. 93. 5x is the largest; answers may vary. 17. The 6 above is called the product. x 94. is the smallest; answers may vary. 3 18. The 20 above is called the minuend. 19. The 9 above is called the subtrahend. 95. As t gets larger, 16t 2 gets larger. 20. The 11 above is called the difference. 5( F − 32) 96. As F gets larger, gets larger. 9 21. The 4 above is called an addend. 47 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra Chapter 1 Review 16. 583 − 279 304 17. 428 + 21 449 18. 819 + 21 840 1. The place value of 4 in 7640 is tens. 2. The place value of 4 in 46,200,120 is tenmillions. 3. 7640 is written as seven thousand, six hundred forty. 1 4. 46,200,120 is written as forty-six million, two hundred thousand, one hundred twenty. 5. 3158 = 3000 + 100 + 50 + 8 19. 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. 4000 86 3914 − 8000 92 7908 20. 8. Six billion, three hundred four million in standard form is 6,304,000,000. 121 9. Locate Houston, Texas in the city column and read across to the number in the 2000 column. The population was 1,953,631. 21. 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. 91 3623 + 497 4211 11 22. 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. 82 1647 + 238 1967 11 23. 1 13. − 18 + 49 67 74 342 + 918 1334 The sum of 74, 342, and 918 is 1334. 2 1 14. 28 + 39 67 15. 462 − 397 65 24. 49 529 + 308 886 The sum of 49, 529, and 308 is 886. 25. 25,862 − 7 965 17,897 7965 subtracted from 25,862 is 17,897. 48 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 26. 39, 007 − 4 349 34, 658 4349 subtracted from 39,007 is 34,658. 27. 205 + 7318 7523 The total distance is 7523 miles. 37. To round 43 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 43 rounded to the nearest ten is 40. 1 38. To round 45 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 45 rounded to the nearest ten is 50. 39. To round 876 to the nearest ten, observe that the digit in the ones place is 6. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 876 rounded to the nearest ten is 880. 11 1 28. 62,589 65,340 + 69, 770 197, 699 Her total earnings were $197,699. 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. 29. 40 + 52 + 52 + 72 = 216 The perimeter is 216 feet. 30. 11 + 20 + 35 = 66 The perimeter is 66 kilometers. 31. 32. 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. 1, 256,509 − 1,144, 646 111,863 The population increased by 111,863. 42. To round 57,534 to the nearest thousand, observe that the digit in the hundreds place is 5. Since this digit is at least 5, we add 1 to the digit in the thousands place. The number 57,534 rounded to the nearest thousand is 58,000. 1,517,550 − 1, 463, 281 54, 269 The population decreased by 54,269. 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. 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. 280 − 170 110 The balance decreased by $110 from February to April. 36. 490 − 250 240 The balance increased by $240 from June to August. 44. To round 768,542 to the nearest hundredthousand, observe that the digit in the tenthousands 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 648 + 2866 rounds to rounds to rounds to 49 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall 2 3800 600 + 2900 7300 Chapter 1: The Whole Numbers 46. 5925 − 1787 47. 630 192 271 56 703 454 + 329 rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to rounds to ISM: Prealgebra 5900 − 1800 4100 600 200 300 100 700 500 + 300 2700 They traveled approximately 2700 miles. 48. 1, 461,575 − 1, 213,825 rounds to rounds to 57. 586 × 29 5 274 11 720 16,994 58. 242 × 37 1694 7260 8954 59. 642 177 4 494 44 940 64 200 113, 634 × 1,500,000 − 1,200,000 300,000 The population of Phoenix is approximately 300,000 larger than that of Dallas. 49. 276 × 8 2208 50. 349 × 4 1396 51. 57 × 40 2280 52. 69 × 42 138 2760 2898 60. 347 × 129 3 123 6 940 34 700 44, 763 61. 1026 401 1 026 410 400 411, 426 × 62. 2107 302 4 214 632 100 636,314 × 53. 20(7)(4) = 140(4) = 560 63. “Product” indicates multiplication. 250 × 6 1500 The product of 6 and 250 is 1500. 54. 25(9)(4) = 225(4) = 900 or 25(4)(9) = 100(9) = 900 55. 26 ⋅ 34 ⋅ 0 = 0 56. 62 ⋅ 88 ⋅ 0 = 0 64. “Product” indicates multiplication. 820 × 6 4920 The product of 6 and 820 is 4920. 50 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra 65. Chapter 1: The Whole Numbers 32 × 15 160 320 480 38 × 11 38 380 418 33 R 2 75. 5 167 −15 17 −15 2 480 + 418 898 The total cost is $898. 66. Check: 33 × 5 + 2 = 167 19 R 7 76. 8 159 −8 79 −72 7 4820 × 20 96, 400 The total cost is $96,400. Check: 19 × 8 + 7 = 159 67. Area = (length)(width) = (13 miles)(7 miles) = 91 square miles 77. 26 68. Area = (length)(width) = (25 centimeters)(20 centimeters) = 500 square centimeters 69. 49 =7 7 Check: 7 ×7 49 70. 36 =4 9 Check: 9 ×4 36 24 R 2 626 −52 106 −104 2 Check: 24 × 26 + 2 = 626 78. 19 35 R 15 680 −57 110 −95 15 Check: 35 × 19 + 15 = 680 506 R 10 79. 47 23, 792 −23 5 29 −0 292 −282 10 5 R2 71. 5 27 −25 2 Check: 5 × 5 + 2 = 27 4 R2 72. 4 18 −16 2 Check: 506 × 47 + 10 = 23,792 Check: 4 × 4 + 2 = 18 73. 918 ÷ 0 is undefined. 74. 0 ÷ 668 = 0 Check: 0 ⋅ 668 = 0 51 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers 80. 53 ISM: Prealgebra 907 R 40 48,111 −47 7 41 −0 411 −371 40 21 R 2 86 −8 06 −4 2 The quotient of 86 and 4 is 21 R 2. 84. 4 27 85. 24 648 −48 168 −168 0 27 boxes can be filled with cans of corn. Check: 907 × 53 + 40 = 48,111 2793 R 140 81. 207 578, 291 −414 164 2 −144 9 19 39 −18 63 761 −621 140 13 22,880 −17 60 5 280 −5 280 0 There are 13 miles in 22,880 yards. 86. 1760 Check: 2793 × 207 + 140 = 578,291 2012 R 60 82. 306 615, 732 −612 37 −0 3 73 −3 06 672 −612 60 87. Divide the sum by 4. 76 49 32 + 47 204 The average is 51. 4 51 204 −20 04 −4 0 88. Divide the sum by 4. Check: 2012 × 306 + 60 = 615,732 23 85 62 + 66 236 The average is 59. 18 R 2 83. 5 92 −5 42 −40 2 The quotient of 92 and 5 is 18 R 2. 4 89. 82 = 8 ⋅ 8 = 64 90. 53 = 5 ⋅ 5 ⋅ 5 = 125 91. 5 ⋅ 92 = 5 ⋅ 9 ⋅ 9 = 405 92. 4 ⋅102 = 4 ⋅10 ⋅10 = 400 52 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall 59 236 −20 36 −36 0 ISM: Prealgebra Chapter 1: The Whole Numbers 93. 18 ÷ 2 + 7 = 9 + 7 = 16 106. (7 − 5)3 ⋅ [92 ÷ (2 + 7)] = (7 − 5)3 ⋅ [92 ÷ 9] = (7 − 5)3 ⋅ [81 ÷ 9] 94. 12 − 8 ÷ 4 = 12 − 2 = 10 2 95. 96. 5(6 − 3) 2 3 +2 7(16 − 8) 23 = 5(36 − 3) 5(33) 165 = = = 15 9+2 11 11 = 7(8) 56 = =7 8 8 = 23 ⋅ 9 = 8⋅9 = 72 107. 97. 48 ÷ 8 ⋅ 2 = 6 ⋅ 2 = 12 108. 98. 27 ÷ 9 ⋅ 3 = 3 ⋅ 3 = 9 5⋅ 7 − 3⋅5 2 2(11 − 3 ) 4 ⋅ 8 − 1 ⋅11 3 3(9 − 2 ) = 35 − 15 20 20 = = =5 2(11 − 9) 2(2) 4 = 32 − 11 21 21 = = =7 3(9 − 8) 3(1) 3 109. Area = (side)2 = (7 meters)2 = 49 square meters 99. 2 + 3[15 + (20 − 17) ⋅ 3] + 5 ⋅ 2 = 2 + 3[15 + 3 ⋅ 3] + 5 ⋅ 2 = 2 + 3[1 + 3 ⋅ 3] + 5 ⋅ 2 = 2 + 3[1 + 9] + 5 ⋅ 2 = 2 + 3 ⋅10 + 5 ⋅ 2 = 2 + 30 + 10 = 42 110. Area = (side) 2 = (3 inches) 2 = 9 square inches 111. 2 x 2 ⋅ 5 10 = = =5 2 2 z 112. 4x − 3 = 4 ⋅ 5 − 3 = 20 − 3 = 17 4 100. 21 − [2 − (7 − 5) − 10] + 8 ⋅ 2 = 21 − [24 − 2 − 10] + 8 ⋅ 2 = 21 − [16 − 2 − 10] + 8 ⋅ 2 = 21 − 4 + 8 ⋅ 2 = 21 − 4 + 16 = 33 113. x +7 5+7 is undefined. = 0 y 114. y 0 0 = = =0 5 x 5 ⋅ 5 25 115. x3 − 2 z = 53 − 2 ⋅ 2 = 125 − 2 ⋅ 2 = 125 − 4 = 121 101. 19 − 2(32 − 22 ) = 19 − 2(9 − 4) = 19 − 2(5) = 19 − 10 =9 116. 7 + x 7 + 5 12 = = =2 3z 3⋅ 2 6 117. ( y + z )2 = (0 + 2)2 = 22 = 4 102. 16 − 2(42 − 32 ) = 16 − 2(16 − 9) = 16 − 2(7) = 16 − 14 =2 118. 100 y 100 0 + = + = 20 + 0 = 20 x 3 5 3 103. 4 ⋅ 5 − 2 ⋅ 7 = 10 − 14 = 6 119. Five subtracted from a number is x − 5. 104. 8 ⋅ 7 − 3 ⋅ 9 = 56 − 27 = 29 120. Seven more than a number is x + 7. 105. (6 − 4)3 ⋅ [102 ÷ (3 + 17)] = (6 − 4)3 ⋅ [102 ÷ 20] 121. Ten divided by a number is 10 ÷ x or 3 = (6 − 4) ⋅ [100 ÷ 20] = 23 ⋅ 5 = 8⋅5 = 40 122. The product of 5 and a number is 5x. 53 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall 10 . x Chapter 1: The Whole Numbers ISM: Prealgebra 123. Let n be 5. n + 12 = 20 − 3 5 + 12 ⱨ 20 − 3 17 = 17 True Yes, 5 is a solution. 129. 5(n + 4) = 90 Let n be 14. 5(14 + 4) ⱨ 90 5(18) ⱨ 90 90 = 90 True Let n be 16. 5(16 + 4) ⱨ 90 5(20) ⱨ 90 100 = 90 False Let n be 26. 5(26 + 4) ⱨ 90 5(30) ⱨ 90 150 = 90 False 14 is a solution. 124. Let n be 23. n − 8 = 10 + 6 23 − 8 ⱨ 10 + 6 15 = 16 False No, 23 is not a solution. 125. Let n = 14. 30 = 3(n − 3) 30 ⱨ 3(14 − 3) 30 ⱨ 3(11) 30 = 33 False No, 14 is not a solution. 130. 3n − 8 = 28 Let n be 3. 3(3) − 8 ⱨ 28 9 − 8 ⱨ 28 1 = 28 False Let n be 7. 3(7) − 8 ⱨ 28 21 − 8 ⱨ 28 13 = 28 False Let n be 15. 3(15) − 8 ⱨ 28 45 − 8 ⱨ 28 37 = 28 False None are solutions. 126. Let n be 20. 5(n − 7) = 65 5(20 − 7) ⱨ 65 5(13) ⱨ 65 65 = 65 True Yes, 20 is a solution. 127. 7n = 77 Let n be 6. 7 ⋅ 6 ⱨ 77 42 = 77 False Let n be 11. 7 ⋅11 ⱨ 77 77 = 77 True Let n be 20. 7 ⋅ 20 ⱨ 77 140 = 77 False 11 is a solution. 128. n − 25 = 150 Let n be 125. 125 − 25 ⱨ 150 100 = 150 False Let n be 145. 145 − 25 ⱨ 150 120 = 150 False Let n be 175. 175 − 25 ⱨ 150 150 = 150 True 175 is a solution. 131. 485 − 68 417 132. 729 − 47 682 133. 732 × 3 2196 134. 629 × 4 2516 22 135. 374 29 + 698 1101 54 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 144. To round 258,371 to the nearest hundredthousand, observe that the digit in the tenthousands 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. 21 136. 593 52 + 766 1411 458 R 8 137. 13 5962 −52 76 −65 112 −104 8 145. 24 ÷ 4 ⋅ 2 = 6 ⋅ 2 = 12 146. 1968 × 36 11 808 59 040 70,848 140. 5324 × 18 42 592 53 240 95,832 141. 2000 − 356 1644 142. 9000 − 519 8481 3 2 +1 = (18)(3) 54 = =6 8 +1 9 147. Let n be 9. 5n − 6 = 40 5 ⋅ 9 − 6 ⱨ 40 45 − 6 ⱨ 40 39 = 40 False No, 9 is not a solution. 237 R 1 138. 18 4267 −36 66 −54 127 −126 1 139. (15 + 3) ⋅ (8 − 5) 148. Let n be 3. 2n − 6 = 5n − 15 2(3) − 6 ⱨ 5(3) − 15 6 − 6 ⱨ 15 − 15 0 = 0 True Yes, 3 is a solution. 53 1714 −160 114 −96 18 There are 53 full boxes with 18 left over. 149. 32 150. 27 × 2 54 8 ×4 32 54 + 32 86 The total bill before taxes is $86. Chapter 1 Test 1. 82,426 in words is eighty-two thousand, four hundred twenty-six. 143. To round 842 to the nearest ten, observe that the digit in the ones place is 2. Since this digit is less than 5, we do not add 1 to the digit in the tens place. The number 842 rounded to the nearest ten is 840. 2. Four hundred two thousand, five hundred fifty in standard form is 402,550. 55 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall Chapter 1: The Whole Numbers ISM: Prealgebra 16. Divide the sum by 5. 1 3. 59 + 82 141 4. 600 − 487 113 5. 496 × 30 14,880 6. 69 5 2 62 79 84 90 + 95 410 The average is 82. 82 410 −40 10 −10 0 17. To round 52,369 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. The number 52,369 rounded to the nearest thousand is 52,000. 766 R 42 52,896 −48 3 4 59 −4 14 456 −414 42 7. 23 ⋅ 52 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 = 200 18. 6289 5403 + 1957 rounds to rounds to rounds to 6 300 5 400 + 2 000 13,700 19. 4267 − 2738 rounds to rounds to 4300 − 2700 1600 20. 107 − 15 92 21. 15 + 107 122 22. 107 × 15 535 1070 1605 8. 98 ÷ 1 = 98 9. 0 ÷ 49 = 0 10. 62 ÷ 0 is undefined. 11. (24 − 5) ⋅ 3 = (16 − 5) ⋅ 3 = 11 ⋅ 3 = 33 12. 16 + 9 ÷ 3 ⋅ 4 − 7 = 16 + 3 ⋅ 4 − 7 = 16 + 12 − 7 = 28 − 7 = 21 13. 61 ⋅ 23 = 6 ⋅ 2 ⋅ 2 ⋅ 2 = 48 14. 2[(6 − 4) 2 + (22 − 19)2 ] + 10 = 2[22 + 32 ] + 10 = 2[4 + 9] + 10 = 2[13] + 10 = 26 + 10 = 36 7 R2 23. 15 107 −105 2 15. 5698 ⋅ 1000 = 5,698,000 56 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall ISM: Prealgebra Chapter 1: The Whole Numbers 17 493 −29 203 −203 0 Each can cost $17. 29. Perimeter = (20 + 10 + 20 + 10) yards = 60 yards Area = (length)(width) = (20 yards)(10 yards) = 200 square yards 25. 725 − 599 126 The higher-priced one is $126 more. 31. Let x be 7 and y be 8. 3x − 5 3(7) − 5 21 − 5 16 = = = =1 2y 2 ⋅8 16 16 26. 45 × 8 360 There are 360 calories in 8 tablespoons of white granulated sugar. 32. a. 430 × 16 2580 4300 6880 33. Let n be 6. 5n − 11 = 19 5(6) − 11 ⱨ 19 30 − 11 ⱨ 19 19 = 19 True 6 is a solution. 24. 29 27. 30. Let x be 2. 5( x3 − 2) = 5(23 − 2) = 5(8 − 2) = 5(6) = 30 The quotient of a number and 17 is x ÷ 17 or x . 17 b. Twice a number, decreased by 20 is 2x − 20. 205 × 5 1025 6880 + 1025 7905 The total cost is $7905. 34. n + 20 = 4n − 10 Let n be 0. 0 + 20 ⱨ 4 ⋅ 0 − 10 20 ⱨ 0 − 10 20 = −10 False Let n be 10. 10 + 20 ⱨ 4 ⋅10 − 10 30 ⱨ 40 − 10 30 = 30 True Let n be 20. 20 + 20 ⱨ 4 ⋅ 20 − 10 40 ⱨ 80 − 10 40 = 70 False 10 is a solution. 28. Perimeter = (5 + 5 + 5 + 5) centimeters = 20 centimeters Area = (side) 2 = (5 centimeters)2 = 25 square centimeters 57 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall