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Solution Manual for Prealgebra, 6th Edition

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     S OLUTIONS M ANUAL P REALGEBRA S IXTH E DITION Jamie Blair Orange Coast College Costa Mesa, California John Tobey North Shore Community College Danvers, Massachusetts Jeffrey Slater North Shore Community College Danvers, Massachusetts Jennifer Crawford Normandale Community College Bloomington, Minnesota

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    Contents Chapter 1 1 Chapter 2 34 Chapter 3 59 Chapter 4 84 Chapter 5 108 Chapter 6 142 Chapter 7 160 Chapter 8 202 Chapter 9 239 Chapter 10 259 Practice Final Examination 281

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    1 Chapter 1 1.1 Exercises 2. a. 6 > 3 Six is greater than three. b. 3 < 6 Three is less than six. c. We can use the inequality symbols to show the relationship between 6 and 3 in two different ways. 4. a. 46,362 ↑ ten thousands b. 46,362 ↑ hundreds 6. a. 839,400 ↑ hundred thousands b. 839,400 ↑ ten thousands 8. a. 3,098,269 ↑ hundred thousands b. 3,098,269 ↑ thousands 10. 7632 = 7000 + 600 + 30 + 2 12. 3562 = 3000 + 500 + 60 + 2 14. 913,045 = 900,000 + 10,000 + 3000 + 40 + 5 16. $274 274 = 200 + 70 + 4 2 hundred-dollar bills, 7 ten-dollar bills, and 4 one-dollar bills 18. $96 a. 96 = 90 + 6 9 ten-dollar bills and 6 one-dollar bills; answers may vary. b. 96 = 90 + 5 + 1 9 ten-dollar bills, 1 five-dollar bill, and 1 one-dollar bill; answers may vary. 20. 4032 The number begins with 4 in the thousands place. The word name is four thousand, thirty- two. 22. 33,224 The number begins with 3 in the ten thousands place. The word name is thirty-three thousand, two hundred twenty-four. 24. $379 Write 379.00 in the box following $. Write “Three hundred seventy-nine and 00/100” on the line preceding DOLLARS. 26. 3 ? 1 3 is greater than 1. 3 > 1 28. 9 ? 6 9 is greater than 6. 9 > 6 30. 9 ? 11 9 is less than 11. 9 < 11 32. 0 ? 9 0 is less than 9. 0 < 9 34. 3010 ? 3210 3010 is less than 3210. 3010 < 3210 36. 101,351 ? 101,251 101,351 is greater than 101,251. 101,351 > 101,251 38. Seven is less than ten. ↓ ↓ ↓ 7 < 10 40. Ten is greater than seven. ↓ ↓ ↓ 10 > 7

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    Chapter 1: Whole Numbers and Introduction to Algebra ISM: Prealgebra 2 42. 85 Identify the round-off place digit: 85. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace the digit to the right with a zero. 90 44. 123 Identify the round-off place digit: 123. The digit to the right is less than 5. Do not change the round-off place digit. Replace the digit to the right with a zero. 120 46. 12,790 Identify the round-off place digit: 12,790. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. 12,800 48. 701,529 Identify the round-off place digit: 701,529. The digit to the right is less than 5. Do not change the round-off place digit. Replace all digits to the right with zeros. 701,500 50. 56,212 Identify the round-off place digit: 56,212. The digit to the right is less than 5. Do not change the round-off place digit. Replace all digits to the right with zeros. 56,000 52. 312,540 Identify the round-off place digit: 312,540. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. 313,000 54. 1,395,999 Identify the round-off place digit: 1,395,999. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. 1,400,000 56. 3,116,201 Identify the round-off place digit: 3,116,201. The digit to the right is less than 5. Do not change the round-off place digit. Replace all digits to the right with zeros. 3,100,000 58. $212,875 Identify the round-off place digit: 212, 875. The digit to the right is less than 5. Do not change the round-off place digit. Replace all digits to the right with zeros. $210,000 60. Caravan ? Charger $32,732 ? $32,106 32,732 is greater than 32,106. $32, 732 $32,106 Caravan Charger > > 62. $34,775 Identify the round-off place digit: 34,775. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. $35,000 64. 44,972 Identify the round-off place digit: 44,972. The digit to the right is 5 or more. Increase the round-off place digit by 1. Since the round-off place digit is 9, place a zero in the round-off place and increase the digit in the next place to the left by 1. Replace all digits to the right with zeros. 45,000 66. 5,311,192,809,000 Identify the round-off place digit: 5,311,192,809,000. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. 5,311,193,000,000 68. 5 hours and 40 minutes Since 40 minutes is more than one-half hour, we round up. 6 hours 70. 15 yards, 4 inches Since 4 inches is less than one-half yard, we round down. 15 yards Classroom Quiz 1.1 1. 5301 = 5000 + 300 + 1 2. a. 8 ? 0 8 is greater than 0. 8 > 0

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    ISM: Prealgebra Chapter 1: Whole Numbers and Introduction to Algebra 3 b. 2 ? 11 2 is less than 11. 2 < 11 3. 3571 a. Identify the round-off place digit: 3571. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. 4000 b. Identify the round-off place digit: 3571. The digit to the right is less than 5. Do not change the round-off place digit. Replace all digits to the right with zeros. 3570 1.2 Understanding the Concept Addition Facts Made Simple 1. 8 + 5 = (3 + 5) + 5 = 3 + (5 + 5) = 3 + 10 = 13 2. 6 + 8 = 6 + (6 + 2) = (6 + 6) + 2 = 12 + 2 = 14 1.2 Understanding the Concept Using Inductive Reasoning to Reach a Conclusion 1. 8, 14, 20, 26, 32, 38, ... We observe a pattern that each number is 6 more than the preceding number: 14 = 8 + 6, 20 = 14 + 6, and so on. Therefore, if we add 6 to 38, we conclude that the next number in the sequence is 44. 2. 17, 28, 39, 50, 61, ... We observe a pattern that each number is 11 more than the preceding number: 28 = 17 + 11, 39 = 28 + 11, and so on. Therefore, if we add 11 to 61, we conclude that the next number in the sequence is 72. 1.2 Exercises 2. 7 + x ↓ ↓ ↓ Seven plus a number Answers may vary. 4. Because the commutative property allows us to change the order of addition without changing the value of the sum. 6. ( x + 6) + 3 = (6 + x ) + 3 The order of the addition is changed. This is the commutative property of addition. 8. Two added to a number: m + 2 10. the sum of eight and x : 8 + x or x + 8 12. Twelve more than a number: y + 12 14. A number plus four: y + 4 16. y + 6 = 6 + y 18. 5 + x = x + 5 20. By the commutative property of addition, 8790 + 157 = 157 + 8790, so 157 + 8790 = 8947. 22. By the commutative property of addition, 8 + x = x + 8, so x + 8 = 31. 24. a + 6 + 2 = a + (6 + 2) = a + 8 26. 4 + 4 + y = (4 + 4) + y = 8 + y = y + 8 28. x + 3 + 0 = x + (3 + 0) = x + 3 30. ( x + 5) + 1 = x + (5 + 1) = x + 6 32. 3 + (4 + x ) = (3 + 4) + x = 7 + x 34. ( a + 3) + 7 = a + (3 + 7) = a + 10 36. ( y + 1) + 4 = y + (1 + 4) = y + 5 38. (4 ) 5 ( 4) 5 (4 5) 9 x x x x + + = + + = + + = + 40. 5 (3 ) (5 3) 8 8 a a a a + + = + + = + = + 42. 3 ( 2) 1 (3 ) (2 1) ( 3) 3 (3 3) 6 + + + = + + + = + + = + + = + n n n n n 44. (6 4) 4 ( 6 4) 4 ( 10) 4 (10 4) 14 x x x x x + + + = + + + = + + = + + = + 46. (2 8) 5 ( 2 8) 5 ( 10) 5 (10 5) 15 n n n n n + + + = + + + = + + = + + = + 48. a. Replace n with 4. n + 8 = 4 + 8 = 12 When n is equal to 4, n + 8 is equal to 12.

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    Chapter 1: Whole Numbers and Introduction to Algebra ISM: Prealgebra 4 b. Replace n with 7. n + 8 = 7 + 8 = 15 When n is equal to 7, n + 8 is equal to 15. 50. Replace a with 5 and b with 10. a + b = 5 + 10 = 15 When a is 5 and b is 10, a + b is 15. 52. Replace x with 11, y with 18, and z with 15. x + y + z = 11 + 18 + 15 = 44 When a is 11, b is 18, and c is 15, x + y + z is 44. 54. Replace x with 33 and y with 43. x + y + 21 = 33 + 43 + 21 = 97 When x is 33 and y is 43, x + y + 21 is 97. 56. a. Bonus 250 150 15 250 $415 x y = + + = + + = b. Bonus 250 125 18 250 $393 x y = + + = + + = 58. 71 12 83 + 60. 331 57 388 + 62. 33 11 6 4 54 + 64. 308 7 245 75 635 + 66. 531 217 18 766 + 68. 562 65 133 760 + 70. 3366 152 485 4003 + 72. 836,147 99 2, 413 4, 000 842, 659 + 74. 2, 902 9, 050 12 986,100 998, 064 + 76. a. 3477 4614 8091 + Total deposits were $8091. b. 120 3500 1388 5008 + Total debits were $5008. 78. 562 276 142 495 1475 + Shawnee spent $1475 on her car. 80. 7 in. + 1 in. + 7 in. + 1 in. = 16 in. The perimeter is 16 inches. 82. 8 ft + 8 ft + 8 ft + 8 ft = 32 ft The perimeter is 32 feet. 84. 3 ft + 8 ft + 8 ft = 19 ft The perimeter is 19 feet. 86. The length of the unlabeled side is 3 ft + 21 ft or 24 ft. 23 ft + 3 ft + 5 ft + 21 ft + 18 ft + 24 ft = 94 ft The perimeter is 94 feet. 88. The length of the unlabeled side on the left is 145 in., and the length of the right side of the figure is 145 in. + 15 in. or 160 in. 145 in. + 40 in. + 15 in. + 155 in. + 160 in. + 195 in. = 710 in. The perimeter is 710 inches.

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    ISM: Prealgebra Chapter 1: Whole Numbers and Introduction to Algebra 5 90. 2, 4, 6, 8, 10, 12, ... Each number is 2 more than the preceding number. The next number is 12 + 2 or 14. 92. 24, 31, 38, 45, 52, 59, 66, ... Each number is 7 more than the preceding number. The next number is 66 + 7 or 73. 94. 12, 25, 38, 51, 64, ... Each number is 13 more than the preceding number. The next number is 64 + 13 or 77. Classroom Quiz 1.2 1. a. (5 ) 6 ( 5) 6 (5 6) 11 x x x x + + = + + = + + = + b. 1 (5 6) 1 (5 6 ) 1 (11 ) (1 11) 12 or 12 n n n n n n + + + = + + + = + + = + + = + + 2. Replace a with 13 and b with 29. a + b + 12 = 13 + 29 + 12 = 54 When a is 13 and b is 29, a + b + 12 is equal to 54. 3. The length of the unlabeled side on the left is 14 ft, and the length of the right side of the figure is 14 ft + 13 ft or 27 ft. 14 ft + 14 ft + 13 ft + 115 ft + 27 ft + 129 ft = 312 ft The perimeter is 312 feet. 1.3 Understanding the Concept Money and Borrowing 1. We can borrow only from a place value that has a nonzero whole number. For example, in $400 there are only 100-dollar bills to break down (borrow from). 2. When we change the ten-dollar bill to 10 one- dollar bills, we have 0 ten-dollar bills and 10 one-dollar bills, which is similar to borrowing: 0 10 2 1 0. 1.3 Exercises 2. 10 − 2: Two subtracted from 10 Answers may vary. 4. The English phrase “five less than x ” written using symbols, is 5 − x . This statement is false. 6. 5 − 3 = 2 8. 7 − 2 = 5 10. 4 − 2 = 2 12. 6 − 5 = 1 14. 14 − 0 = 14 16. 12 − 12 = 0 18. 900 − 800 = 100 900 − 801 = 99 900 − 802 = 98 900 − 803 = 97 900 − 804 = 96 900 − 805 = 95 900 − 806 = 94 20. 800 − 700 = 100 800 − 701 = 99 800 − 702 = 98 800 − 703 = 97 800 − 704 = 96 800 − 705 = 95 22. Three decreased by a number: 3 − a 24. The difference of three and a number: 3 − n 26. Seven subtracted from a number: x − 7 28. Eight minus two: 8 − 2 30. Nine less than twelve: 12 − 9 32. Replace n with 6. 9 − n = 9 − 6 = 3 If n is equal to 6, 9 − n is equal to 3. 34. Replace n with 1. 9 − n = 9 − 1 = 8 If n is equal to 1, 9 − n is equal to 8. 36. Replace x with 5. x − 2 = 5 − 2 = 3 If x is equal to 5, x − 2 is equal to 3. 38. Replace x with 10. x − 2 = 10 − 2 = 8 If x is equal to 10, x − 2 is equal to 8. 40. 98 25 73 − Check: 25 73 98 +

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    Chapter 1: Whole Numbers and Introduction to Algebra ISM: Prealgebra 6 42. 76 41 35 − Check: 41 35 76 + 44. 57 38 19 − Check: 38 19 57 + 46. 73 35 38 − Check: 35 38 73 + 48. 764 545 219 − Check: 545 219 764 + 50. 700 29 671 − Check: 671 29 700 + 52. 8711 644 8067 − Check: 8067 644 8711 + 54. 8801 4583 4218 − Check: 4583 4218 8801 + 56. 29, 002 3, 667 25,335 − Check: 3, 667 25,335 29, 002 + 58. 796, 020 68, 431 727, 589 − Check: 68, 431 727, 589 796, 020 + 60. The length of the unlabeled side on the top is 20 in. − 8 in. or 12 in., and the length of the right side of the figure is 18 in. − 7 in. or 11 in. 18 in. + 12 in. + 7 in. + 8 in. + 11 in. + 20 in. = 76 in. The perimeter is 76 inches. 62. The length of the unlabeled side on the right is 20 in. − 9 in. or 11 in., and the length of the unlabeled top side of the figure is 38 in. − 17 in. or 21 in. 20 in. + 17 in. + 9 in. + 21 in. + 11 in. + 38 in. = 116 in. The perimeter is 116 inches. 64. 128 90 38 − The top speed of Intimidator 305 is 38 miles per hour slower than the top speed of Kingda Ka. 66. 328 300 28 − The maximum drop of Superman: Escape from Krypton is 28 feet greater than that of Intimidator 305. 68. 7900 2160 5740 − The difference in diameter of Earth and the moon is 5740 miles. 70. a. Blue: 275,000 − 5000 = 270,000 Bowhead: 60,000 − 8500 = 51,500 Humpback: 150,000 − 20,000 = 130,000 The Blue Whale had the largest decline. b. The total decline is 270,000 + 51,500 + 130,000 = 451,500 72. Six less than x : x − 6 Replace x with 10. x − 6 = 10 − 6 = 4 If x is equal to 10, six less than x is equal to 4. Cumulative Review 73. 5,117,206 > 13,842 74. 2,386,702 > 117,401 75. 120 135 105 360 + Edward worked 360 hours in the three-month period. 76. 430 32 12 28 6 508 + Drew paid $508 for the dog and all the supplies.

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    ISM: Prealgebra Chapter 1: Whole Numbers and Introduction to Algebra 7 Classroom Quiz 1.3 1. a. A number subtracted from 8: 8 − n b. Two less than a number: n − 2 c. Four decreased by a number: 4 − n 2. a. 11, 055 6, 294 4, 761 − Check: 6, 294 4, 761 11, 055 + b. 502, 401 291,632 210, 769 − Check: 291, 632 210, 769 502, 401 + 3. 4822 3788 1034 − The first bid was $1034 greater. 1.4 Understanding the Concept Memorizing Multiplication Facts 1. a. 3(7) = 2(7) + 7 = 14 + 7 = 21 b. 4(8) = 5(8) − 8 = 40 − 8 = 32 c. 6(8) = 5(8) + 8 = 40 + 8 = 48 d. 9(8) = 10(8) − 8 = 80 − 8 = 72 1.4 Exercises 2. a. 9 x : Nine times a number. b. mn : the product of m and n 4. 4 times 3: 6. 8(3 ⋅ 4) = (3 ⋅ 4) ⋅ 8 The order of the multiplication is changed. This is the commutative property of multiplication. 8. 4 ⋅ 5(3 x ) = (4 ⋅ 5 ⋅ 3) ⋅ x = 60 x 10. (4 y ) ⋅ 3 ⋅ 2 = 4 ⋅ y ⋅ 3 ⋅ 2 = (4 ⋅ 3 ⋅ 2) ⋅ y = 24 y

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    Chapter 1: Whole Numbers and Introduction to Algebra ISM: Prealgebra 8 12. a. White Pale Blue Rose Beige Beige White Beige Pale Blue Beige Rose Gray Gray White Gray Pale Blue Gray Rose Blue Blue White Blue Pale Blue Blue Rose Light Brown Light Brown White Light Brown Pale Blue Light Brown Rose b. 4(3) = 12 different combinations 14. 10(5) = 50 different ice cream dishes 16. 4(7) = 28 The factors are 4 and 7. The product is 28. 18. 7 a = 49 The factors are 7 and a . The product is 49. 20. A number times 5: x ⋅ 5 = 5 x 22. Double a number: 2 x 24. The product of a and b : ab 26. If a ⋅ b = 0 and a = 10, then b = 0. 28. By the associative and commutative properties of multiplication, b ( a ⋅ c ) = ( b ⋅ a ) ⋅ c = ( a ⋅ b ) ⋅ c , so ( a ⋅ b ) ⋅ c = 30. 30. (4)(5)(2)(2) = (4)(2)(5)(2) = (4 ⋅ 2)(5 ⋅ 2) = (8)(10) = 80 32. (5)(4)(3)(2) = (4)(3)(5)(2) = (4 ⋅ 3)(5 ⋅ 2) = (12)(10) = 120 34. 9 ⋅ 0 ⋅ 8 ⋅ 6 = 0 36. 3 ⋅ 2 ⋅ 4 ⋅ 5 = (3 ⋅ 4) ⋅ (2 ⋅ 5) = 12 ⋅ 10 = 120 38. 7(5 b ) = (7 ⋅ 5) b = 35 b 40. 3( x ⋅ 8) = 3(8 ⋅ x ) = (3 ⋅ 8) x = 24 x 42. 2( a ⋅ 9) = 2(9 ⋅ a ) = (2 ⋅ 9) a = 18 a 44. 5(8 ⋅ x ) = (5 ⋅ 8) x = 40 x 46. 2(3)(5 ⋅ z ) = 6(5 ⋅ z ) = (6 ⋅ 5) z = 30 z 48. 0(7)( z ⋅ 8) = 0 50. 4(7)( x ⋅ 1) = 28 x

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    ISM: Prealgebra Chapter 1: Whole Numbers and Introduction to Algebra 9 52. 6 ⋅ 4(3 y ) = 24(3 y ) = (24 ⋅ 3) y = 72 y 54. (4 a )5 ⋅ 2 = 4 a (5 ⋅ 2) = 4 a (10) = (4 ⋅ 10) a = 40 a 56. 4(3 a ) ⋅ 5 = (4 ⋅ 3) a ⋅ 5 = 12 a ⋅ 5 = 12 ⋅ 5 ⋅ a = 60 a 58. 926 8 7408 × 60. 405 6 2430 × 62. 578 500 289, 000 × 64. 871 300 261,300 × 66. 81 34 324 243 2754 × 68. 44 68 352 264 2992 × 70. 668 95 3 340 60 12 63, 460 × 72. 322 74 1 288 22 54 23,828 × 74. 632 201 632 126 40 127, 032 × 76. 631 201 631 126 20 126,831 × 78. 4456 578 35 648 311 92 2 228 0 2, 575, 568 × 80. 9002 563 27 006 540 12 4 501 0 5, 068,126 × 82. 23,109 605 115 545 13 865 40 13, 980, 945 × 84. 86, 246 2000 172, 492, 000 × 86. 450 6 2700 × The plane travels 2700 miles. 88. 12 6 72 × John has 72 plants.

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    Chapter 1: Whole Numbers and Introduction to Algebra ISM: Prealgebra 10 90. 116 9 1044 × The player will gain 1044 rushing yards in the season. 92. 12 8 96 × Each wall requires 96 tiles. 96 3 288 × Karen needs 288 tiles for the three walls. 24 11 24 24 264 × Karen bought 264 tiles. No, Karen does not have enough tiles to complete the job because she needs 288 tiles but only bought 264. 94. a. The bar for Boston is labeled 41. The high temperature was 41 ° F. b. The high temperature in Burlington was 30 ° F. 30 3 90 × The high temperature in Newport Beach was 90 ° F. 96. (4 x )(2 y )(6 z ) = (4 ⋅ 2 ⋅ 6)( x ⋅ y ⋅ z ) = 48 xyz 98. 2(3 x )(3 y )(5 z ) = (2 ⋅ 3 ⋅ 3 ⋅ 5)( x ⋅ y ⋅ z ) = 90 xyz 100. 8 a (5 b )2 c = (8 ⋅ 5 ⋅ 2)( a ⋅ b ⋅ c ) = 80 abc Cumulative Review 102. 426,862 2,128 428,990 + 103. 7000 142 6858 − 104. 826,540 Identify the round-off place digit: 826,540. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. 827,000 105. 168,406,000 Identify the round-off place digit: 168,406,000. The digit to the right is 5 or more. Increase the round-off place digit by 1. Replace all digits to the right with zeros. 168,410,000 106. 120 97 23 − The bill was $23 less than the budget allotment. 107. 920 455 465 − Mary Ann must drive 465 miles the second day. Classroom Quiz 1.4 1. The product of four and a number: 4 n 2. 2051 107 14 357 205 10 219, 457 × 3. 2 x (5 y )(4) = (2 ⋅ 5 ⋅ 4)( x ⋅ y ) = 40 xy 1.5 Understanding the Concept The Commutative Property and Division 1. a ÷ b = b ÷ a when a and b are equal. 1.5 Understanding the Concept Conclusions and Inductive Reasoning 1. 1, 1, 2, … Notice that 1 + 0 = 1 and 1 + 1 = 2. If we follow a pattern of adding consecutive whole numbers (0, 1, 2, …) to the preceding number, the next number is 2 + 2 = 4. Notice that 1 ⋅ 1 = 1 and 1 ⋅ 2 = 2. If we follow a pattern of multiplying the preceding number by consecutive counting numbers (1, 2, 3, …), the next number is 2 ⋅ 3 = 6.

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    ISM: Prealgebra Chapter 1: Whole Numbers and Introduction to Algebra 11 1.5 Exercises 2. There are 320 ÷ 20 rows. 4. Each person paid n ÷ 7. 6. (b) and (c) are correct. 8. Eight divided by a number: 8 ÷ a 10. Sixty-three jelly beans divided equally among three children: 63 ÷ 3 12. The quotient of forty-four and eleven: 44 ÷ 11 14. The quotient of eleven and forty-four: 11 ÷ 44 16. 25 ÷ 25 = 1 18. 0 0 99 = 20. 45 ÷ 0 undefined 22. 60 ÷ 9 = 6 R 6 6 9 60 54 6 Check: 6(9) + 6 = 54 + 6 = 60 24. 3726 ÷ 6 = 621 621 6 3726 36 12 12 6 6 0 Check: 6(621) = 3726 26. 4046 ÷ 6 = 674 R 2 674 6 4046 36 44 42 26 24 2 Check: 6(674) + 2 = 4044 + 2 = 4046 28. 1863 ÷ 20 = 93 R 3 93 20 1863 180 63 60 3 Check: 20(93) + 3 = 1860 + 3 = 1863 30. 783 ÷ 20 = 39 R 3 39 20 783 60 183 180 3 Check: 20(39) + 3 = 780 + 3 = 783 32. 6436 ÷ 32 = 201 R 4 201 32 6436 64 36 32 4 Check: 32(201) + 4 = 6432 + 4 = 6436 34. 1301 ÷ 24 = 54 R 5 54 24 1301 120 101 96 5 Check: 24(54) + 5 = 1296 + 5 = 1301 36. 1350 ÷ 16 = 84 R 6 84 16 1350 128 70 64 6 Check: 16(84) + 6 = 1344 + 6 = 1350

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    Chapter 1: Whole Numbers and Introduction to Algebra ISM: Prealgebra 12 38. 12,854 ÷ 42 = 306 R 2 306 42 12854 126 254 252 2 Check: 42(306) + 2 = 12,852 + 2 = 12,854 40. 37,780 ÷ 118 = 320 R 20 320 118 37780 354 238 236 20 Check: 118(320) + 20 = 37,760 + 20 = 37,780 42. 123,264 ÷ 136 = 906 R 48 906 136 123264 1224 864 816 48 Check: 136(906) + 48 = 123,216 + 48 = 123,264 44. 21,945 ÷ 29 = 756 R 21 756 29 21945 203 164 145 195 174 21 Check: 29(756) + 21 = 21,924 + 21 = 21,945 46. 3 21 75 63 12 The remainder is 12, so 12 tickets were donated to the homeless shelter. 48. 23 65 1495 130 195 195 0 The ticket price should be $23. 50. 625 250 156250 1500 625 500 1250 1250 0 The rancher should allow 625 cows on the field. 52. 7 14 98 98 0 The pattern is 7 inches wide. 54. a. 14 15 218 15 68 60 8 He can completely fill 14 cases. b. After filling 14 cases, he will have 8 cars left to give to his brother. 56. 4, 16, 64, 256, ... Each number after the first is the preceding number multiplied by 4. The next number is 4 × 256 or 1024. 58. 0, 2, 6, 12, 20, ... Add 2 to the first number to obtain the second. Add 4 to the second number to obtain the third. Add 6, and then add 8. The next number is 20 + 10 or 30. 60. 1, 6, 8, 13, 15, 20, ... Alternate adding 5 and adding 2 to the preceding number. The next number is 20 + 2 or 22.

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    ISM: Prealgebra Chapter 1: Whole Numbers and Introduction to Algebra 13 62. 1, 4, 8, ... Alternate multiplying the preceding number by 4 and multiplying the preceding number by 2. The next number is 4(8) = 32. Add 3 to the first number to obtain the second. Add 4 to the second number to obtain the third. Add 5 to the third number to obtain the fourth: The next number is 8 + 5 or 13. 64. a. (48 ÷ 6) ÷ 2 = 8 ÷ 2 = 4 b. 48 ÷ (6 ÷ 2) = 48 ÷ 3 = 16 c. The property does not apply to division. Cumulative Review 65. Seven plus x : 7 + x 66. 1060 114 946 − 67. 4031 202 8 062 806 20 814, 262 × 68. 556,432 Identify the round-off place: 556,432. The digit to the right is less than 5. Do not change the round-off digit. Replace all digits to the right with zeros. 556,000 69. 1389 430 959 − 959 495 464 − Leo must drive 464 miles the third day. 70. 29, 599 6, 200 23,399 − 23,399 5, 500 17,899 − The balance is $17,899. Classroom Quiz 1.5 1. a. The quotient of twenty and two: 20 ÷ 2 b. The quotient of two and twenty: 2 ÷ 20 2. 10,577 ÷ 35 = 302 R 7 302 35 10577 105 77 70 7 3. 1245000 5 6225000 5 12 10 22 20 25 25 0 Each investor will pay $1,245,000. 1.6 Exercises 2. What number squared is equal to 81? 4. 4 9 9 9 9 9 ⋅ ⋅ ⋅ = 6. 2 b b b ⋅ = 8. 1 = z z 10. 3 7 7 7 7 ⋅ ⋅ = 12. 2 3 8 8 8 ⋅ ⋅ ⋅ ⋅ = x x x x 14. 2 4 3 3 3 y y y y y ⋅ ⋅ ⋅ ⋅ ⋅ = 16. 2 2 6 6 6 ⋅ ⋅ ⋅ ⋅ = x y y xy 18. 5 2 2 5 7 7 7 or 7 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ x x x x x x x 20. a. 6 7 7 7 7 7 7 7 = ⋅ ⋅ ⋅ ⋅ ⋅ b. 2 x x x = ⋅ 22. 3 3 3 3 3 27 = ⋅ ⋅ = 24. 2 6 6 6 36 = ⋅ =

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