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Prealgebra and Introductory Algebra 1st Edition Solution Manual

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    1 Chapter 1 Whole Numbers Are You Prepared? Section 1.1 Study Tips Group Activity: Becoming a Successful Student 1. Answers will vary. 2. Answers will vary. 3. Answers will vary. 4. Answers will vary. 5. Problem Recognition Exercises: page 114 Chapter Summary: page 123 Chapter Review Exercises: page 125 Chapter Test: page 128 Cumulative Review Exercises: page 129 6. Answers will vary. 7. Answers will vary. 8. Answers will vary. 9. Answers will vary. 10. Answers will vary. Section 1.2 Introduction to Whole Numbers Section 1.2 Practice Exercises 1. Answers will vary. 2. (a) A digit is one of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. (b) A number is written in standard form if the position of each digit determines the place value of the digit. (c) Periods are groups of three digits separated by commas in a large number. (d) A number is written in expanded form if each digit is written with its place value units. 3. 8,213,457 7: ones

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    Chapter 1 Whole Numbers 2 5: tens 4: hundreds 3: thousands 1: ten - thousands 2: hundred - thousands 8: millions 4. 103,596 6: ones 9: tens 5: hundreds 3: thousands 0: ten - thousands 1: hundred - thousands 5. 3 2 1 tens 6. 6 8 9 tens 7. 21 4 ones 8. 73 8 ones 9. 8 7 10 hundreds 10. 2 2 93 hundreds 11. 1 430 thousands 12. 3 101 thousands 13. 4 52,723 hundred - thousands 14. 6 55,878 hundred thousands 15. 1 ,023,676,207 billions 16. 3 ,111,901,211 billions 17. 2 2,422 ten - thousands 18. 5 8,106 ten - thousands 19. 5 1 ,033,201 millions 20. 9 3 ,971,224 millions 21. 1 0,677,881 ten - millions 22. 3 1 ,820 mi 2 thousands 23. 7 ,653,468,440 billions 24. 3 1,000 ft ten - thousands 25. 5 tens + 8 ones 26. 7 tens + 1 one 27. 5 hundreds + 3 tens + 9 ones 28. 3 hundreds + 8 tens + 2 ones 29. 5 thousands + 2 hundreds + 3 ones 30. 7 thousands + 8 tens + 9 ones 31. 1 ten - thousand + 2 hundreds + 4 tens + 1 one 32. 2 ten - thousands + 8 hundreds + 7 tens + 3 ones 33. 524 34. 318 35. 150 36. 620 37. 1,906 38. 4,201 39. 85,007 40. 26,002 41. ones, thousands, millions, billions 42. ones, tens, hundreds, thousands 43. Two hundred forty - one 44. Three hundred twenty - seven 45. Six hundred three 46. One hundred eight 47. Thirty - one thousand, five hundred thirty 48. Fifty - two thousand, one hundred sixty 49. One hundred thousand, two hundred thirty - four 50. Four hundred thousand, one hundred ninety - nine

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    Section 1.2 Introduction to Whole Numbers 3 51. Nine thousand, five hundred thirty - five 52. One thousand, three hundred seventy - seven 53. Twenty thousand, three hundred twenty 54. One thousand, eight hundred 55. Five hundred ninety thousand, seven hundred twelve 56. Sixty million 57. 6005 58. 4004 59. 672,000 60. 248,000 61. 1,484,250 62. 2,647,520 63. 64. 65. Counting on a number line, 10 is 4 units to the right of 6. 66. Counting on a number line, 3 is 8 units to the left of 11. 67. Counting on a number line, 4 is 3 units to the left of 7. 68. Counting on a number line, 5 is 5 units to the right of 0. 69. 8 > 2 8 is greater than 2, or 2 is less than 8. 70. 6 < 11 6 is less than 11, or 11 is greater than 6. 71. 3 < 7 3 is less than 7, or 7 is greater than 3. 72. 14 > 12 14 is greater than 12, or 12 is less than 14. 73. 6 < 11 74. 14 > 13 75. 21 > 18 76. 5 < 7 77. 3 < 7 78. 14 < 24 79. 95 > 89 80. 28 < 30 81. 0 < 3 82. 8 > 0 83. 90 < 91 84. 48 > 47 85. False; 12 is made up of the digits 1 and 2. 86. False; 26 is made up of the digits 2 and 6. 87. 99 88. 999 89. There is no greatest whole number. 90. 0 is the least whole number. 91. 10,000,000 7 zeros 92. 100,000,000,000 11 zeros 93. 964 94. 840 Section 1.3 Addition and Subtraction of Whole Numbers and Perimeter

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    Chapter 1 Whole Numbers 4 Section 1.3 Practice Exercises 1. Answers will vary. 2. (a) A sum is the result of an addition problem. (b) The addends are the numbers being added. (c) A polygon is a flat figure formed by line segments connected at their ends. (d) The perimeter of a polygon is the distance around the outside of the figure. (e) The difference is the result of a subtraction problem. (f) The subtrahend is the number being subtracted. (g) The minuend is the number being subtracted from. (h) A variable is a letter or symbol that represents a number. 3. 3 hundreds + 5 tens + 1 one 4. 2004 5. 4012 6. 6206 7. Fill in the table. Use the number line if necessary. + 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18 8. 11 + 10 = 21 Addends: 11, 10 Sum: 21 9. 1 + 13 + 4 = 18 Addends: 1, 13, 4 Sum: 18 10. 5 + 8 + 2 = 15 Addends: 5, 8, 2 Sum: 15 11. 42 4 tens 2 ones 33 3 tens 3 ones 75 7 tens 5 ones = + + = + = + 12. 21 2 tens 1 one 53 5 tens 3 ones 74 7 tens 4 ones = + + = + = + 13. 12 1 ten 2 ones 15 1 ten 5 ones 32 3 tens 2 ones 59 5 tens 9 ones = + = + + = + = + 14. 10 1 ten 0 ones 8 0 tens 8 ones 30 3 tens 0 ones 48 4 tens 8 ones = + = + = + = +

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    Section 1.3 Addition and Subtraction of Whole Numbers and Perimeter 5 15. 890 107 997 + 16. 444 354 798 + 17. 4 13 102 119 + 18. 11 221 5 237 + 19. 1 76 45 121 + 20. 1 25 59 84 + 21. 1 87 24 111 + 22. 1 38 77 115 + 23. 658 231 889 + 24. 1 642 295 937 + 25. 1 1 152 549 701 + 26. 1 1 462 388 850 + 27. 1 1 79 112 12 203 + 28. 1 1 62 907 34 1003 + 29. 11 4980 10223 15, 203 + 30. 1 1 23112 892 24,004 31. 1 1 1 Ź 10 223 25 782 4 980 40,985 32. 11 1 1 92 377 5 622 34 659 132,658 33. 101 + 44 = 44 + 101 34. 8 + 13 = 13 + 8 35. x + y = y + x 36. t + q = q + t 37. (23 + 9) + 10 = 23 + (9 + 10) 38. 7 + (12 + 8) = (7 + 12) + 8 39. r + ( s + t ) = ( r + s ) + t

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    Chapter 1 Whole Numbers 6 40. ( c + d ) + e = c + ( d + e ) 41. The commutative property changes the order of the addends, and the associative property changes the grouping. 42. The sum of any number and 0 is that number. (a) 423 + 0 = 423 (b) 0 + 25 = 25 (c) 67 + 0 = 67 (d) 0 + x = x 43. 12 − 8 = 4 minuend: 12 subtrahend: 8 difference: 4 44. 9 6 3 − minuend: 9 subtrahend: 6 difference: 3 45. 27 − 9 = 18 because 18 + 9 = 27. 46. 20 − 8 = 12 because 12 + 8 = 20. 47. 102 − 75 = 27 because 27 + 75 = 102. 48. 211 − 45 = 166 because 166 + 45 = 211. 49. 8 − 3 = 5 Check : 5 + 3 = 8 50. 7 − 2 = 5 Check : 5 + 2 = 7 51. 4 − 1 = 3 Check : 3 + 1 = 4 52. 9 − 1 = 8 Check : 8 + 1 = 9 53. 1347 221 1126 − Check : 1126 + 221 1347 ✓ 54. 4865 713 4152 − Check : 4152 + 713 4865 ✓ 55. 14,356 13, 253 1,103 − Check : 1 103 + 13 253 14,356 ✓ 56. 34,550 − 31,450 3100 Check : 3 100 + 31 450 34,550 ✓ 57. 6 16 76 59 17 − Check : 1 17 + 59 76 ✓ 58. 5 14 64 48 16 − Check : 1 16 + 48 64 ✓ 59. 10 6 0 10 7 1 0 1 8 9 5 2 1 − Check : 1 1 521 + 189 710 ✓ 60. 4 10 85 0 − 30 3 547 Check : 1 547 + 303 850 ✓ 61. 9 9 5 10 1012 6 0 0 2 1 2 3 8 4 7 6 4 − Check : 1 1 1 4764 + 1238 6002 ✓ 62. 9 9 210 1010 3 0 0 0 2 3 5 6 6 4 4 − Check : 1 1 1 644 + 2356 3000 ✓ 63. 0 10 10 ,425 − 9 022 1, 403 Check : 1 403 + 9 022 10,425 ✓ 64. 9 1 13 8 10 11 2 3, 9 0 1 − 8 0 6 4 15 ,8 3 7 Check : 1 1 1 15 837 + 8 064 23,901 ✓

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    Section 1.3 Addition and Subtraction of Whole Numbers and Perimeter 7 65. 11 5 1 10 62 088 59 871 2, 217 − Check : 11 2 217 + 59 871 62,088 ✓ 66. 11 10 10 2 1 0 012 32 , 1 1 2 − 28, 3 3 4 3 7 7 8 Check : 1 1 1 1 3 778 + 28 334 32,112 ✓ 67. 16 9 2 6 10 10 37 0 0 − 29 8 7 7 1 3 Check : 1 1 1 713 + 2987 3700 ✓ 68. 9 9 7 10 10 10 8 0 0 0 − 3 7 8 8 4 2 1 2 Check : 1 1 1 4212 + 3788 8000 ✓ 69. 13 1 3 13 32 , 4 39 − 1 4 98 30 ,9 41 Check : 1 1 30 941 + 1 498 32,439 ✓ 70. 1 11 21 335 4 123 17, 212 − Check : 1 17 212 + 4 123 21,335 ✓ 71. 9 7 1010 2 14 8, 0 07, 23 4 2, 3 45,11 5 5, 6 62,11 9 − Check : 1 1 1 5 662 119 + 2 345 115 8,007,234 ✓ 72. 9 2 1014 4 16 3 0 45 5 67 1 8 71 4 95 1, 1 74,0 72 − Check : 1 1 1 174 072 + 1 871 495 3,045,567 ✓ 73. The expression 7 − 4 means 7 minus 4, yielding a difference of 3. The expression 4 − 7 means 4 minus 7 which results in a difference of − 3. 74. Subtraction is not associative. For example, 10 − (6 − 2) = 10 − 4 = 6, and (10 − 6) − 2 = 4 − 2 = 2. Therefore 10 − (6 − 2) does not equal (10 − 6) − 2. 75. 13 + 7 1 13 7 20 + 76. 100 + 42 100 42 142 + 77. 7 + 45 1 7 45 52 + 78. 23 + 81 23 81 104 + 79. 18 + 5 1 18 5 23 + 80. 76 + 2 76 2 78 + 81. 1523 + 90 1 Ź 1523 + 90 1613 82. 1320 + 448 1320 + 448 1768 83. 5 + 39 + 81 1 5 39 81 125 +

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    Chapter 1 Whole Numbers 8 84. 78 6 72 − 85. 422 100 322 − 86. 89 42 47 − 87. 8 10 109 0 7 2 101 8 − 88. 0 11 3111 60 3051 − 89. 4 10 5 0 1 3 3 7 − 90. 405 103 302 − 91. 9 13 10 3 − 3 5 6 8 92. 8 11 9 1 − 1 4 7 7 93. 1 2 1 26,548,000 26,930,000 + 20,805,000 74,283,000 The shows had a total of 74,283,000 viewers. 94. 3 3 38 54 44 61 97 103 + 124 521 521 deliveries were made. 95. 11 115 104 93 111 423 + 423 desks were delivered. 96. 1 $60 82 + 58 $200 The total amount is $200. 97. 1 10 211 Ź 10 20, 320 ft − 14, 246 ft 6, 074 ft Denali is 6074 ft higher than White Mountain Peak. 98. 4 15 5 5 3 9 1 6 − 16 DVDs are left. 99. 9 9 7 10 1010 2 398 0 0 0 2 390 2 5 2 7 7 4 8 − The difference is 7748 marriages. 100. 2,398,000 − 2,248,000 150,000 The decrease is 150,000 marriages.

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    Section 1.3 Addition and Subtraction of Whole Numbers and Perimeter 9 101. 13 3 3 13 2 4 4 3 489 2 2 4 8 000 19 5, 489 − The difference is 195,489 marriages. 102. 2,398,000 2,336,000 62,000 − The greatest increase occurred between 1995 − 2000; the increase was 62,000 marriages. 103. 1 1 1 1 1 100,052 675,038 45,934 821,024 + There are 821,024 nonteachers. 104. 1 11 $7 329 9 560 1 248 3 500 $21,637 + The total cost is $21,637. 105. 6288 − 2032 4256 Mt. Washington is 4256 ft higher than the Pinkham Notch Visitor Center. 106. 9 13 3 10 14 13 4 0 4 3 − 2 0 6 4 1 9 7 9 The Lion King had been performed 1979 more times. 107. 1 26,960 2 600 29,560 + Jeannette will pay $29,560 for 1 year. 108. 11 Ź Ź 138 + 96 234 They are 234 miles apart. 109. 1 35 cm 35 cm 34 cm 104 cm + 110. 1 27 in. 13 in. 20 in. 60 in. + 111. 2 6 yd 10 yd 11 yd 3 yd 5 yd 7 yd 42 yd + 112. 2 3 200 yd 136 yd 142 yd 98 yd 58 yd 38 yd 672 yd + 113. 94 ft 94 ft 50 ft 50 ft 288 ft + 114. 90 ft 90 ft 90 ft 90 ft 360 ft + 115. 14 m 12 m 26 m + 39 m 26 m 13 m − The missing length is 13 m.

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    Chapter 1 Whole Numbers 10 116. 11 139 cm 87 cm 201 cm 427 cm + 547 cm 427 cm 120 cm − The missing length is 120 cm. 117. 45, 418 81,990 9 063 + 56,309 192,780 118. 9,300,050 7,803,513 3, 480,009 907,822 21, 491,394 + 119. 3,421,019 822,761 1,003,721 + 9,678 5,257,179 120. 4,905,620 458,318 4, 447,302 − 121. 953, 400, 415 56,341,902 897,058,513 − 122. 82,025,160 − 79,118,705 2,906,455 123. 103, 718 mi 2 − 54,310 mi 2 49,408 mi 2 The difference in land area between Colorado and Wisconsin is 49,408 mi 2 . 124. 41, 217 mi 2 − 24,078 mi 2 17,139 mi 2 Tennessee has 17,139 mi 2 more than West Virginia. 125. 2 2 2 2 1 045 mi 41, 217 mi 54,310 mi 96,572 mi + The combined land area of Rhode Island, Tennessee, and Wisconsin is 96,572 mi 2 . 126. 2 2 2 2 2 2 1 045 mi 41, 217 mi 24,078 mi 54,310 mi 103,718 mi 224,368 mi + The combined land area of the five states is 224,368 mi 2 . Section 1.4 Rounding and Estimating Section 1.4 Practice Exercises 1. Answers will vary 2. Rounding a number allows us to give an approximation of the number to a specific place value. 3. 59 33 26 − 4. 0 12 10 1 3 0 9 8 3 2 −

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    Section 1.4 Rounding and Estimating 11 5. 1 1 1 4 009 + 998 5 007 6. 12,033 23,441 35,474 + 7. Ten - thousands 8. Hundreds 9. If the digit in the tens place is 0, 1, 2, 3, or 4, then change the tens and ones digits to 0. If the digit in the tens place is 5, 6, 7, 8, or 9, increase the digit in the hundreds place by 1 and change the tens and ones digits to 0. 10. If the digit in the ones place is 0, 1, 2, 3, or 4, then change the ones digits to 0. If the digit in the ones place is 5, 6, 7, 8, or 9, increase the digit in the tens place by 1 and change the ones digit to 0. 11. 3 4 2  340 12. 8 3 4  830 13. 7 2 5  730 14. 4 4 5  450 15. 9 3 8 4  9400 16. 8 3 6 3  8400 17. 8 5 3 9  8500 18. 9 8 1 7  9800 19. 3 4 , 9 92  35,000 20. 7 6 , 8 31  77,000 21. 2 5 78  3000 22. 3 5 11  4000 23. 9 9 8 2  10,000 24. 7 9 7 4  8000 25. 10 9 , 3 37  109,000 26. 43 7 , 2 08  437,000 27. 4 8 9 ,090  490,000 28. 3 8 8 ,725  390,000 29. $14 8 4 31,020  $148,000,000 30. $3 3 , 0 50  $33,000 31. 23 8 , 8 63 mi  239,000 mi 32. 4 9 2,000 2 m  500,000 2 m 33. 57 82 21 + → → → 60 80 20 160 + 34. 33 78 41 + → → → 30 80 40 150 + 35. 639 − 422 → → 640 − 420 220 36. 851 − 399 → → 850 − 400 450 37. 892 + 129 → → 900 + 100 1000 38. 347 + 563 → → 300 + 600 900 39. 3412 − 1252 → → 3400 − 1300 2100 40. 9771 − 4544 → → 9800 − 4500 5300

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    Chapter 1 Whole Numbers 12 41. 97,404,576 53,695,428 + → → 1 97,000,000 54,000,000 151,000,000 + $151,000,000 was brought in by Mars. 42. 81,296,784 54,391,268 38,168,580 + → → → 1 81,000,000 54,000,000 38,000,000 173,000,000 + $173,000,000 was brought in by Hershey. 43. 71,339,710 − 59,684,076 → → 71,000,000 − 60,000,000 11,000,000 Neil Diamond earned $11,000,000 more. 44. 4844 1190 − → → 5000 1000 4000 − 4000 more women gave birth. 45. $3,316,897 3,272,028 + 3,360,289 → → → 1 $3,300,000 3,300,000 + 3,400,000 $10,000,000 46. $3,470,295 3,173,050 + 1,970,380 → → → $3,500,000 3,200,000 + 2,000,000 $8,700,000 47. (a) 2003; $3,470,295 → $3,500,000 (b) 2005; $1,970,380 → $2,000,000 48. $3,500,000 − 2,000,000 $1,500,000 49. Massachusetts; 78,815 → 79,000 students 50. Vermont; 8059 → 8000 students 51. 79,000 − 8 000 71,000 The difference is 71,000 students. 52. 45,879 9137 16,756 78,815 17, 422 13,172 8059 + → → → → → → → 4 46,000 9,000 17,000 79,000 17,000 13,000 + 8 000 189,000 The total is 189,000 students. 53. 3045 mm 1892 mm 3045 mm + 1892 mm → → → → 3000 mm 2000 mm 3000 mm + 2000 mm 10,000 mm 54. 1851 cm 1782 cm 1851 cm + 1782 cm → → → → 2000 cm 2000 cm 2000 cm + 2000 cm 8000 cm 55. 105 in. 57 in. 57 in. 105 in. 57 in. + 57 in. → → → → → → 2 110 in. 60 in. 60 in. 110 in. 60 in. + 60 in. 460 in. 56. 182 ft 121 ft 182 ft 169 ft + 169 ft → → → → → 200 ft 100 ft 200 ft 200 ft + 200 ft 900 ft Section 1.5 Multiplication of Whole Numbers and Area Section 1.5 Practice Exercises 1. Answers will vary. 2. (a) Multiplication is repeated addition.

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    Section 1.5 Multiplication of Whole Numbers and Area 13 (b) The numbers that are multiplied are called factors. (c) The result of multiplication is called the product. (d) Area measures the amount of surface contained within a region. (e) The area of a rectangle is the product of the length and the width. 3. 1 869, 240 870,000 34,921 30,000 108,332 110,000 1,010,000 → → + → + 4. 907,801 900,000 413,560 400,000 500,000 → − → − 5. 8821 8800 3401 3400 5400 → − → − 6.  0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 2 0 2 4 6 8 10 12 14 16 18 3 0 3 6 9 12 15 18 21 24 27 4 0 4 8 12 16 20 24 28 32 36 5 0 5 10 15 20 25 30 35 40 45 6 0 6 12 18 24 30 36 42 48 54 7 0 7 14 21 28 35 42 49 56 63 8 0 8 16 24 32 40 48 56 64 72 9 0 9 18 27 36 45 54 63 72 81 7. 5 + 5 + 5 + 5 + 5 + 5 = 6  5 = 30 8. 2 2 2 2 2 2 2 2 2 9 2 18 + + + + + + + + =  = 9. 9 + 9 + 9 = 3  9 = 27 10. 7 + 7 + 7 + 7 = 4  7 = 28 11. 13  42 = 546 factors: 13, 42; product: 546 12. 26  9 = 234 factors: 26, 9; product: 234 13. 3  5  2 = 30 factors: 3, 5, 2; product: 30 14. 4  3  8 = 96 factors: 4, 3, 8; product: 96 15. For example: 5  12; 5  12; 5(12) 16. For example: 23  14; 23  14; 23(14) 17. d 18. a 19. e 20. b 21. c 22. a 23. 14 • 8 = 8 •14 24. 3 • 9 = 9 • 3 25. 6 • (2 • 10) = (6 • 2) • 10

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    Chapter 1 Whole Numbers 14 26. (4 • 15) • 5 = 4 • (15 • 5) 27. 5(7 + 4) = (5 • 7) + (5 • 4) 28. 3(2 + 6) = (3 • 2) + (3 • 6) 29. 24 6 24 Multiply 6 4. Multiply 6 20. 120 Add. 144    + 30. 18 5 40 Multiply 5 8. Multiply 5 10. 50 Add. 90    + 31. 26 2 12 Multiply 2 6. Multiply 2 20. 40 Add. 52    + 32. 71 3 3 Multiply 3 1. Multiply 3 70. 210 Add. 213    + 33. 131 5 5 Multiply 5 1. Multiply 5 30. 150 Multiply 5 100. 500 Add. 655     + 34. 725  3 15 60 + 2100 2175 Multiply 3  5. Multiply 3  20. Multiply 3  700. Add. 35. 344 4 16 Multiply 4 4. Multiply 4 40. 160 Multiply 4 300. 1200 Add. 1376     + 36. 105 9 45 Multiply 9 5. Multiply 9 0. 00 Multiply 9 100. 900 Add. 945     + 37. 3 1410 8 11, 280  38. 3 2016 6 12,096  39. 2 1 3312 7 23,184  40. 4 4801 5 24,005  41. 1 1 3 42,014 9 378,126  42. 4 51,006 8 408,048  43. 32 14 128 320 448  + 44. 41 21 41 820 861  +

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    Section 1.6 Division of Whole Numbers 15 45. 1 3 1 68 24 272 1360 1632  + 46. 2 55 41 55 2200 2255  + 47. 72 12 144 720 864  + 48. 1 1 13 46 78 520 598  + 49. 3 2 143 17 1001 1430 2431  + 50. 1 1 1 1 1 722 28 5 776 14 440 20, 216  + 51. 1 4 8 349 19 3141 3490 6631  + 52. 512 31 512 15 360 15,872  + 53. 1 3 151 127 1 057 3 020 15 100 19,177  + 54. 1 1 1 703 146 4 218 28 120 70 300 102,638  + 55. 11 1 1 1 222 841 222 8 880 177 600 186,702  + 56. 4 3 5 4 387 506 2 322 0 000 193 500 195,822  + 57. 1 1 3 11 2 1 3532 6014 14 128 35 320 000 000 21192 000 21, 241, 448  +

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