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Solution Manual for Basic College Mathematics with Early Integers, 3rd edition

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    Contents Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . 35 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . 55 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . 107 Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . 127 Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . 153 Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . 167 Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . 189 Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . 209

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    Chapter 1 Whole Numbers Exercise Set 1.1 RC2. In 615,702, the number 615 is in the thousands period. RC4. The number 721 is written in standard notation. 2. 5 ten thousands 4. 5 hundred thousands 6. 8 8. 1 10. 1 thousand + 7 hundreds + 7 tens + 6 ones 12. 1 thousand + 0 hundreds + 8 tens + 1 one, or 1 thousand + 8 tens + 1 one 14. 3 thousands + 0 hundreds + 9 tens + 7 ones, or 3 thou- sands + 9 tens + 7 ones 16. 3 ten thousands + 8 thousands + 4hundreds + 5 tens + 3 ones 18. 1 billion + 2 hundred millions + 0 ten millions + 5 millions + 0 hundred thousands + 7 ten thousands + 3 thousands + 6 hundreds + 1 ten + 2 ones, or 1 billion + 2 hundred millions + 5 millions + 7 ten thousands + 3 thousands + 6 hundreds + 1 ten + 2 ones 20. 3 hundred millions + 1 ten million + 3 millions + 8 hun- dred thousands + 4ten thousands + 7 thousands + 4 hundreds + 6 tens + 5 ones 22. Forty-eight 24. Forty-five thousand, nine hundred eighty-seven 26. One hundred eleven thousand, thirteen 28. Forty-three billion, five hundred fifty million, six hundred fifty-one thousand, eight hundred eight 30. Ninety-one thousand, two hundred forty-five 32. Eighty-nine million, three hundred thirty-one thousand, six hundred twenty-two 34. 354,702 36. 17,112 38. 19,610,439 40. 700,000,000 42. 26,000,000,000 44. 200,017 46. 2,793,000,000 48. All digits are 9’s. Answers may vary. For an 8-digit read- out, for example, it would be 99,999,999. This number has three periods. Exercise Set 1.2 RC2. In the addition 5 + 2 = 7, the number 7 is the sum. RC4. The distance around an object is its perimeter. 2. 1 5 2 1 + 3 4 8 1 8 6 9 4. 1 7 3 + 6 9 1 4 2 6. 1 7 5 0 3 + 2 6 8 3 1 0 , 1 8 6 8. 1 1 9 9 9 + 1 1 1 0 1 0 10. 1 2 7 1 + 3 3 3 8 3 6 0 9 12. 1 2 8 0 + 3 4 , 9 0 2 3 5 , 1 8 2 14. 1 1 1 1 0 , 1 2 0 1 2 , 9 8 9 + 5 7 3 8 2 8 , 8 4 7 16. 1 3 6 5 4 + 2 7 0 0 6 3 5 4 18. 1 1 1 4 5 , 8 7 9 + 2 1 , 7 8 6 6 7 , 6 6 5 20. 1 1 1 1 9 9 , 9 9 9 + 1 1 2 1 0 0 , 1 1 1

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    2 Chapter 1: Whole Numbers 22. 2 3 8 2 7 3 2 1 4 + 7 6 1 8 7 24. 1 1 1 1 4 2 , 4 8 7 8 3 , 1 4 1 + 3 6 , 7 1 2 1 6 2 , 3 4 0 26. 2 2 9 8 9 5 6 6 8 3 4 9 2 0 + 7 0 3 4 0 1 2 28. Perimeter = 14mi + 13 mi + 8 mi + 10 mi + 4 7 mi + 22 mi We carry out the addition. 2 1 4 1 3 8 1 0 4 7 + 2 2 1 1 4 The perimeter of the figure is 114mi. 30. Perimeter = 62 yd + 39 yd + 54yd + 4 6 yd + 28 yd We carry out the addition. 2 6 2 3 9 5 4 4 6 + 2 8 2 2 9 The perimeter of the figure is 229 yd. 32. 90 ft + 90 ft + 90 ft + 90 ft = Perimeter We carry out the addition. 9 0 9 0 9 0 + 9 0 3 6 0 The batter travels 360 ft when a home run is hit. 34. Nine billion, three hundred forty-six million, three hundred ninety-nine thousand, four hundred sixty-eight Exercise Set 1.3 RC2. subtraction symbol RC4. difference 2. 8 7 − 3 4 5 3 4. 5 2 6 − 3 2 3 2 0 3 6. 6 13 7 / 3 / − 2 8 4 5 8. 5 14 6 / 4 / − 1 9 4 5 10. 18 6 8 / 15 7 / 9 / 5 / − 3 9 8 3 9 7 12. 10 2 0 / 16 3 / 1 / 6 / − 2 4 7 6 9 14. 17 7 7 / 17 8 / 8 / 7 / − 6 9 8 1 8 9 16. 3 12 3 4 / 2 / − 2 1 7 1 2 5 18. 13 12 5 3 / 2 / 11 6 / 4 / 3 / 1 / − 2 8 9 6 3 5 3 5 20. 12 15 7 2 / 5 / 14 8 / 3 / 6 / 4 / − 5 3 7 5 2 9 8 9 22. 11 13 8 1 / 3 / 11 9 / 2 / 4 / 1 / − 5 6 4 3 3 5 9 8

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    Exercise Set 1.4 3 24. 6 15 7 / 5 / 8 3 − 3 6 4 1 3 9 4 2 26. 11 11 5 1 / 1 / 12 1 6 / , 2 / 2 / 2 / − 5 , 8 8 8 1 0 , 3 3 4 28. 11 2 1 / 11 8 14 3 / 2 / , 1 / 9 / 4 / − 2 9 , 2 3 6 2 9 5 8 30. 8 10 9 / 0 / − 7 8 1 2 32. 7 9 13 8 0 3 ✥✥ − 4 1 8 3 8 5 34. 3 9 15 9 4 0 5 / ✥✥ − 2 5 8 9 1 4 7 36. 14 6 4 / 9 10 7 / 5 0 0 / ✥✥ − 3 6 0 4 3 8 9 6 38. 6 9 13 8 4 , 7 0 3 / ✥✥ − 2 9 8 8 4 , 4 0 5 40. 14 4 / 10 0 17 1 / 5 / , 0 / 1 / 7 / − 7 8 0 9 7 2 0 8 42. 7 9 9 13 8 0 0 3 / ✥✥✥ − 5 9 9 7 4 0 4 44. 6 9 9 10 1 7 , 0 0 0 / ✥✥✥ − 1 1 , 5 9 8 5 4 0 2 46. 3 9 9 9 16 4 0 , 0 0 6 / ✭✭✭✭ − 1 4 7 3 9 , 8 5 9 48. 2 9 9 9 14 3 0 , 0 0 4 / ✭✭✭✭ − 6 7 4 9 2 3 , 2 5 5 50. 9 0 1 + 2 3 9 2 4 52. 1 9 9 0 9 + 1 0 1 1 1 0 , 9 2 0 54. 9 thousands + 1 hundred + 0 tens + 3 ones, or 9 thousands + 1 hundred + 3 ones 56. 3 , 928 , 124 − 1 , 098 , 947 Using a calculator to carry out the subtraction, we find that the difference is 2,829,177. Exercise Set 1.4 RC2. In the multiplication 4 × 3 = 12, 12 is the product. RC4. The product of 1 and any number a is a . 2. 2 8 7 × 4 3 4 8 4. 5 7 6 × 9 6 8 4 6. 4 8 0 6 × 7 5 6 4 2 8. 3 2 2 7 8 6 7 × 4 3 1 , 4 6 8 10. 4 7 8 × 6 0 4 6 8 0 12. 2 2 8 7 × 3 4 3 4 8 2 6 1 0 2 9 5 8 14. 2 3 4 0 × 1 0 0 0 2 , 3 4 0 , 0 0 0 16. 8 0 0 × 7 0 0 5 6 0 , 0 0 0

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    4 Chapter 1: Whole Numbers 18. 5 4 5 4 7 7 7 × 7 7 5 4 3 9 5 4 3 9 0 5 9 , 8 2 9 20. 3 7 3 7 5 4 9 × 8 8 4 3 9 2 4 3 9 2 0 4 8 , 3 1 2 22. 2 1 1 1 4 3 2 × 3 7 5 2 1 6 0 3 0 2 4 0 1 2 9 6 0 0 1 6 2 , 0 0 0 24. 2 3 2 3 4 5 3 4 6 × 6 5 9 3 1 1 4 1 7 3 0 0 2 0 7 6 0 0 2 2 8 , 0 1 4 26. 2 2 6 1 5 1 1 8 9 2 8 × 3 1 7 2 1 7 8 5 6 6 2 4 9 6 0 8 9 2 8 0 0 2 6 7 8 4 0 0 0 2 8 , 3 1 9 , 6 1 6 28. 2 4 2 4 1 3 6 4 0 8 × 6 0 6 4 2 5 6 3 2 3 8 4 4 8 0 3 8 4 4 8 0 0 0 3 8 , 8 5 8 , 1 1 2 30. 1 1 4 4 4 4 3 5 5 × 2 9 9 3 1 9 5 3 1 9 5 0 7 1 0 0 0 1 0 6 , 1 4 5 32. 1 2 2 4 1 6 5 2 1 × 3 4 4 9 5 8 6 8 9 2 6 0 8 4 0 2 6 0 8 4 0 0 1 9 5 6 3 0 0 0 2 2 , 4 9 0 , 9 2 9 34. 3 4 4 4 4 5 0 6 × 7 8 0 0 3 6 0 4 8 0 0 3 1 5 4 2 0 0 0 3 5 , 1 4 6 , 8 0 0 36. 1 2 6 0 0 9 × 2 0 0 3 1 8 0 2 7 1 2 0 1 8 0 0 0 1 2 , 0 3 6 , 0 2 7 38. A = l × w = 129 yd × 65 yd = 8385 sq yd 40. A = l × w = 200 ft × 85 ft = 17 , 000 sq ft 42. 1 2 2 9 8 7 6 8 7 6 7 6 + 6 1 0 , 8 3 4 44. 13 2 3 / 10 8 18 3 / 4 / 0 / , 7 9 / 8 / − 8 6 , 6 7 9 2 5 4 , 1 1 9 46. 0 48. Seven million, four hundred thirty-two thousand Exercise Set 1.5 RC2. dividend RC4. divisor 2. 54 ÷ 9 = 6 because 54= 9 · 6. 4. 37 37 = 1 Any nonzero number divided by itself is 1. 6. 56 1 = 56 Any number divided by 1 is that same number. 8. 0 32 = 0 Zero divided by any nonzero number is 0. 10. 74 ÷ 0 is not defined, because division by 0 is not defined. 12. 20 4 = 5 because 20 = 4 · 5.

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    Exercise Set 1.5 5 14. 2 3 3 3 6 9 9 6 9 9 9 9 0 The answer is 233. 16. 1 0 8 8 8 6 9 8 6 9 6 4 5 The answer is 108 R 5. 18. 7 0 8 3 2 1 2 4 2 1 2 4 2 4 0 The answer is 708. 20. 1 0 1 2 9 9 1 1 0 9 1 1 9 2 0 1 8 2 The answer is 1012 R 2. 22. 1 9 4 2 3 8 9 2 1 8 1 8 9 8 1 The answer is 194R 1. 24. 1 4 6 6 8 8 1 6 2 8 2 4 4 1 3 6 5 The answer is 146 R 5. 26. 2 0 0 9 3 6 0 2 7 6 2 7 2 7 0 The answer is 2009. 28. 5 1 7 8 4 1 3 9 4 0 1 3 8 5 9 5 6 3 The answer is 517 R 3. 30. 1 2 7 0 1 0 0 1 2 7 , 0 0 0 1 0 0 2 7 0 2 0 0 7 0 0 7 0 0 0 0 0 The answer is 1270. 32. 4 2 6 1 0 4 2 6 0 4 0 2 6 2 0 6 0 6 0 0 The answer is 426. 34. 2 8 9 2 0 5 7 9 8 4 0 1 7 9 1 6 0 1 9 8 1 8 0 1 8 The answer is 289 R 18. 36. 2 4 4 0 9 8 7 8 0 1 8 7 1 6 0 2 7 The answer is 24R 27.

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    6 Chapter 1: Whole Numbers 38. 4 0 2 3 9 4 2 9 2 2 2 The answer is 40 R 22. 40. 5 0 5 4 2 7 2 9 2 7 0 2 9 The answer is 50 R 29. 42. 5 5 1 0 2 5 6 1 2 5 1 0 5 1 2 5 1 0 2 The answer is 55 R 2. 44. 1 0 7 7 7 4 9 7 4 9 4 9 0 The answer is 107. 46. 8 0 8 9 7 2 7 3 7 2 7 3 7 2 1 The answer is 808 R 1. 48. 1 0 1 0 7 7 0 7 4 7 0 7 7 4 The answer is 1010 R 4. 50. 3 0 1 2 4 7 2 4 2 7 2 4 2 2 4 1 8 The answer is 301 R 18. 52. 1 0 2 4 8 4 8 9 9 4 8 9 9 9 6 3 The answer is 102 R 3. 54. 2 1 0 3 6 7 5 6 3 7 2 3 6 3 6 3 The answer is 210 R 3. 56. 8 0 3 3 6 2 8 , 9 2 9 2 8 8 1 2 9 1 0 8 2 1 The answer is 803 R 21. 58. 9 8 4 9 0 8 8 , 5 6 0 8 1 0 7 5 6 7 2 0 3 6 0 3 6 0 0 The answer is 984. 60. 2 9 0 4 3 0 6 8 8 8 , 8 8 8 6 1 2 2 7 6 8 2 7 5 4 1 4 8 8 1 2 2 4 2 6 4 The answer is 2904R 264 . 62. 7 0 0 2 8 0 3 5 , 6 2 2 , 6 0 6 5 6 2 1 1 6 0 6 1 6 0 6 0 The answer is 7002. 64. 8 8 , 7 7 7 − 2 2 , 3 3 3 6 6 , 4 4 4 66. 2 6 8 × 3 5 1 3 4 0 8 0 4 0 9 3 8 0 68. A = l × w = 11 ft × 9 ft = 99 sq ft

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    Chapter 1 Mid-Chapter Review 7 70. Pairs of factors whose product is 36 are: 1 and 36 2 and 18 3 and 12 4and 9 6 and 6 a) The pair above whose sum is 13 is 4and 9. b) The pair above whose difference is 0 is 6 and 6. c) The pair above whose sum is 20 is 2 and 18. d) The pair above whose difference is 9 is 3 and 12. 72. 34 , 584 , 132 ÷ 76 = 4 , 386 Consider the related multiplication sentence: 4 , 386 · 76 = 34 , 584 , 132 Since the ones digit of the product is 2, the missing ones digit must be either 2 or 7 (6 · 2 = 12 and 6 · 7 = 42). We try 2: 34 , 584 , 132 ÷ 762 = 45 , 386 We see that the missing ones digit is 2 and the missing thousands digit is 5. Chapter 1 Mid-Chapter Review 1. The statement is false. For example, 8 − 5 = 3, but 5 is not equal to 8 + 3. 2. The statement is true. See page 19 in the text. 3. The statement is true. See page 19 in the text. 4. The statement is false. For example, 3 · 0 = 0 and 0 is not greater than 3. Also, 1 · 1 = 1 and 1 is not greater than 1. 5. It is true that zero divided by any nonzero number is 0. 6. The statement is false. Any number divided by 1 is the number itself. For example, 27 1 = 27. 7. 95 ︸︷︷︸ , 4 06 ︸︷︷︸ , 237 ︸︷︷︸ ↑ ↑ ↑ Ninety-five million, four hundred six thousand, two hundred thirty-seven 8. 5 9 14 6 0 4 / ✥✥ − 4 9 7 1 0 7 9. 2 6 9 8 The digit 6 names the number of hundreds. 10. 6 1, 2 0 4 The digit 6 names the number of ten thousands. 11. 1 4 6 , 2 3 7 The digit 6 names the number of thousands. 12. 5 8 6 The digit 6 names the number of ones. 13. 3 0 6, 4 5 8, 1 2 9 The digit 2 names the number of tens. 14. 3 0 6 , 4 5 8, 1 2 9 The digit 6 names the number of millions. 15. 3 0 6, 4 5 8, 1 2 9 The digit 5 names the number of ten thousands. 16. 3 0 6, 4 5 8, 1 2 9 The digit 1 names the number of hundreds. 17. 5602 = 5 thousands + 6 hundreds + 0 tens + 2 ones, or 5 thousands + 6 hundreds + 2 ones 18. 69,345 = 6 ten thousands + 9 thousands + 3 hundreds + 4tens + 5 ones 19. A word name for 136 is one hundred thirty-six. 20. A word name for 64,325 is sixty-four thousand, three hun- dred twenty-five. 21. Standard notation for three hundred eight thousand, seven hundred sixteen is 308,716. 22. Standard notation for four million, five hundred sixty- seven thousand, two hundred ninety-one is 4,567,291. 23. 3 1 6 + 4 8 2 7 9 8 24. 1 1 5 9 3 + 4 3 7 1 0 3 0 25. 1 1 2 6 3 8 + 5 2 8 4 7 9 2 2 26. 1 1 1 4 6 1 7 2 4 3 6 + 4 8 1 7 5 3 4 27. 7 8 6 − 3 2 1 4 6 5 28. 11 5 1 / 14 6 / 2 / 4 / − 2 8 5 3 3 9 29. 15 2 5 / 9 12 3 / 6 0 2 / ✥✥ − 1 7 4 8 1 8 5 4

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    8 Chapter 1: Whole Numbers 30. 4 9 9 14 5 0 0 4 / ✥✥✥ − 6 7 6 4 3 2 8 31. 3 3 6 × 6 2 1 6 32. 1 1 5 5 5 6 7 × 2 8 4 5 3 6 1 1 3 4 0 1 5 , 8 7 6 33. 2 1 3 4 0 7 × 3 2 5 2 0 3 5 8 1 4 0 1 2 2 1 0 0 1 3 2 , 2 7 5 34. 2 2 3 1 9 4 3 5 × 6 0 2 1 8 8 7 0 5 6 6 1 0 0 0 5 , 6 7 9 , 8 7 0 35. 2 5 3 4 1 0 1 2 8 2 1 2 0 1 2 1 2 0 The answer is 253. 36. 1 1 2 3 8 4 2 6 1 3 8 4 6 3 8 8 1 7 6 5 The answer is 112 R 5. 37. 2 3 6 0 1 3 9 9 1 2 0 1 9 9 1 8 0 1 9 The answer is 23 R 19. 38. 1 4 4 5 6 8 0 9 5 5 6 2 4 9 2 2 4 2 5 5 2 2 4 3 1 The answer is 144 R 31. 39. Perimeter = 10 m + 4m + 8 m + 3 m = 25 m 40. A = 4in. × 2 in. = 8 sq in. 41. When numbers are being added, it does not matter how they are grouped. 42. Subtraction is not commutative. For example, 5 − 2 = 3, but 2 − 5  = 3. 43. Answers will vary. Suppose one coat costs $150. Then the multiplication 4 · $150 gives the cost of four coats. Suppose one ream of copy paper costs $4. Then the mul- tiplication $4 · 150 gives the cost of 150 reams. 44. Using the definition of division, 0 ÷ 0 = a such that a · 0 = 0. We see that a could be any number since a · 0 = 0 for any number a . Thus, we cannot say that 0 ÷ 0 = 0. This is why we agree not to allow division by 0. Exercise Set 1.6 RC2. Because the digit in the hundreds place, 5, is 5 or higher, we round up. The statement is false. RC4. The statement is true. See page 40 in the text. 2. 530 4. 8950 6. 50 8. 800 10. 900 12. 700 14. 4600 16. 198,400 18. 5000 20. 2000 22. 736,000 24. 6,713,000 26. 6 2 6 0 9 7 1 0 0 4 6 5 0 + 8 1 + 8 0 2 9 0

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    Exercise Set 1.6 9 28. 6 7 3 6 7 0 − 2 8 − 3 0 6 4 0 30. 4 1 4 0 2 1 2 0 5 5 6 0 + 6 0 + 6 0 1 7 7 1 8 0 32. 8 3 6 8 4 0 3 7 4 3 7 0 7 9 4 7 9 0 + 9 3 8 + 9 4 0 3 9 4 7 2 9 4 0 3947 seems to be incorrect. 34. 5 6 8 6 0 0 4 7 2 5 0 0 9 3 8 9 0 0 + 4 0 2 + 4 0 0 2 4 0 0 36. 9 4 3 8 9 4 0 0 − 2 7 8 7 − 2 8 0 0 6 6 0 0 38. 4 8 1 5 0 0 7 0 2 7 0 0 6 2 3 6 0 0 + 1 0 4 3 + 1 0 0 0 1 8 4 9 2 8 0 0 1849 seems to be incorrect. 40. 3 2 6 3 0 0 2 7 5 3 0 0 7 5 8 8 0 0 + 9 4 3 + 9 0 0 2 3 0 2 2 3 0 0 42. 7 6 4 8 8 0 0 0 9 3 4 8 9 0 0 0 7 8 4 2 8 0 0 0 + 2 2 2 2 + 2 0 0 0 2 7, 0 0 0 44. 8 4 , 8 9 0 8 5, 0 0 0 − 1 1, 1 1 0 − 1 1, 0 0 0 7 4 , 0 0 0 46. 5 1 5 0 × 7 8 × 8 0 4 0 0 0 48. 6 3 6 0 × 5 4 × 5 0 3 0 0 0 50. 3 5 5 4 0 0 × 2 9 9 × 3 0 0 1 2 0, 0 0 0 52. 7 8 9 8 0 0 × 4 3 4 × 4 0 0 3 2 0, 0 0 0 54. 454 ÷ 87 ≈ 450 ÷ 90 = 5 56. 1263 ÷ 29 ≈ 1260 ÷ 30 = 42 58. 3641 ÷ 571 ≈ 3600 ÷ 600 = 6 60. 32 , 854 ÷ 748 ≈ 32 , 900 ÷ 700 = 47 62. $ 6 8 6 $ 7 0 0 9 5 1 0 0 + 1 9 9 + 2 0 0 $ 1 0 0 0 64. $ 5 3 6 $ 5 0 0 2 8 9 3 0 0 9 5 1 0 0 1 3 0 1 0 0 + 1 9 9 + 2 0 0 $ 1 2 0 0 Alyssa’s budget covers her choices. 66. Answers will vary depending on the options chosen. 68. a) Total cost of attending: $250 · 490 = $122 , 500 Total cost of hotel rooms: $170 · 2 · 320 = $108 , 800 Total amount spent: $122 , 500 + $108 , 800 = $231 , 300 b) Total cost of attending: $200 · 500 = $100 , 000 Total cost of hotel rooms: $200 · 2 · 300 = $120 , 000 Total amount spent: $100 , 000 + $120 , 000 = $220 , 000 70. $2211 ÷ $11 ≈ $2200 ÷ $10 = 220 boxes 72. 32 > 0 74. 28 > 18 76. 77 < 117 78. 999 > 997 80. 345 < 456 82. 12 < 32 84. 4 , 134 , 519 > 1 , 532 , 623, or 1 , 532 , 623 < 4 , 134 , 519 86. 82 > 77, or 77 < 82 88. 9 0 0 2 + 4 5 8 7 1 3 , 5 8 9 90. 8 9 9 12 9 0 0 2 / ✥✥✥ − 4 5 8 7 4 4 1 5

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    10 Chapter 1: Whole Numbers 92. 3 4 3 0 6 × 5 8 2 4 4 8 1 5 3 0 0 1 7 , 7 4 8 94. 2 0 8 2 3 4 7 8 4 4 6 1 8 4 1 8 4 0 The answer is 208. 96. 27,060; this is close to the estimated sum found in Exercise 42. 98. 73,780; this is close to the estimated difference found in Exercise 44. Exercise Set 1.7 RC2. (a) RC4. (b) 2. 25 4. 8 6. t = 5678 + 9034= 14 , 712 8. m = 9007 − 5667 = 3340 10. z = 34 · 15 = 510 12. w = 256 ÷ 16 = 16 14. t = 22 − 15 = 7 16. t = 16 − 16 = 0 18. x = 57 − 20 = 37 20. w = 53 − 17 = 36 22. x = 42 6 = 7 24. m = 162 9 = 18 26. y = 96 4 = 24 28. t = 741 3 = 24 7 30. y = 9281 − 8322 = 959 32. p = 92 − 56 = 36 34. y = 23 × 78 = 1794 36. z = 133 − 67 = 66 38. w = 3404 4 = 851 40. x = 807 − 438 = 369 42. q = 10 , 534 ÷ 458 = 23 44. x = 6080 19 = 320 46. x = 1500 20 = 75 48. t = 9281 − 8322 = 959 50. n = 3004 − 1745 = 1259 52. n = 660 12 = 55 54. x = 22 , 135 233 = 95 56. z = 512 − 63 = 449 58. 1 4 2 9 1 2 7 8 9 3 7 3 6 1 8 1 8 0 The answer is 142. 60. 3 3 4 1 7 5 6 8 9 5 1 5 8 5 1 7 9 6 8 1 1 The answer is 334R 11. 62. 342 > 339 64. 0 < 11 66. 6,375,600 68. x = 14 , 332 , 388 48 , 916 = 293 Exercise Set 1.8 RC2. Translate. RC4. Check. 2. Let h = the number of feet by which the height of the Grollo Tower would have exceeded the height of the Miglin- Beitler Skyneedle. Solve: 2001 + h = 2224 h = 223 ft 4. Let h = the height of the Burj Khalifa, in feet. Solve: h + 1883 = 4600 h = 2717 ft

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    Exercise Set 1.8 11 6. Let c = the number of milligrams of caffeine in a 20-oz bottle of Coca Cola. Solve: 25 + 32 = c c = 57 milligrams 8. Let n = the number of entries in each row. Solve: 504 ÷ 36 = n n = 14entries 10. Let r = the number of active rotary oil rigs in 2007. Solve: r + 687 = 984 r = 297 rigs 12. Let n = the number of miles by which the length of the Nile exceeds the length of the Missouri-Mississippi. Solve: 3860 + n = 4135 n = 275 mi 14. Let p = the total number of squares in the puzzle. Solve: 15 · 15 = p p = 225 squares 16. Let m = the number of minutes in a day. Solve: 60 · 24= m m = 1440 minutes 18. Let r = the amount by which the average monthly rent in Atlanta exceeds the average monthly rent in Phoenix. Solve: 625 + r = 84 6 r = $221 per month 20. Let r = the amount of rent each sister pays. Solve: 2 r = 1030 r = $515 per month 22. Let r = the amount of rent a tenant would pay for a one- bedroom apartment, on average, in Seattle during a 6- month period. Solve: 6 · 1303 = r r = $7818 24. Let s = the speed limit for trucks. Solve: s + 10 = 75 s = 65 mph 26. Let q = the number of quires in a ream. Solve: 25 · q = 500 q = 20 quires 28. Let s = the amount by which spending by visitors to the United States exceeded spending by Americans traveling abroad. Solve: 110 , 200 , 000 , 000 + s = 153 , 000 , 000 , 000 s = $4 2 , 800 , 000 , 000 30. Let c = the total cost of the purchase. Solve: 96 · 88 = c c = $8448 32. Let w = the number of full weeks that will pass before the station must begin re-airing episodes. Solve: 5 · w = 208 w = 41 R 3, so 41 full weeks will pass and 3 episodes will be shown the following week before previously aired episodes are rerun. 34. Let l = the number of labels on each sheet. Solve: 25 · l = 750 l = 30 labels 36. Let g = the number of gallons required for 3465 mi of city driving. Solve: 3465 ÷ 21 = g g = 165 gal 38. a) Let A = the area of the court, in square feet. Solve: A = 94 · 50 A = 4700 square feet b) Let P = the perimeter of the court, in feet. Solve: P = 94 + 50 + 94 + 50 P = 288 ft c) Let a = the amount by which the area of a col- lege court exceeds the area of a high school court, in square feet. Solve: 4200 + a = 4700 a = 500 square feet 40. Let c = the number of cartons needed. Solve: 528 ÷ 12 = c c = 44 cartons 42. Let m = the distance on the map, in inches, between two cities that, in reality, are 2016 mi apart. Solve: 2016 ÷ 288 = m m = 7 in. Let r = the distance in miles, in reality, between two cities that are 8 in. apart on the map. Solve: 288 · 8 = r r = 2304mi 44. Let m = the number of months required to pay off the loan. Solve: 7824 ÷ 163 = m m = 48 months 46. Let n = the number of 100’s in 3500. Solve: 3500 ÷ 100 = n n = 35

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    12 Chapter 1: Whole Numbers Let t = the number of minutes you must bicycle in order to lose one pound. Solve: t = 35 · 15 t = 525 min; we could also express this as 8 hr, 45 min. 48. Let n = the number of new jobs that will be created for postsecondary teachers and elementary teachers. n = 305 , 700 + 248 , 800 = 554 , 500 Let s = the number of new jobs that will be created for secondary teachers. Solve: s + 4 84 , 600 = 554 , 500 s = 69 , 900 jobs 50. Let F = the number of seats in first class, E = the number of seats in economy class, and T = the total number of seats. Solve: 3 · 4 = F , 21 · 6 = E , and T = F + E F = 12, E = 126, T = 12 + 126 = 138 seats 52. Let c = the total cost of the 5 video games. Solve: 5 · 64= c c = $320 Then let n = the number of $20 bills required. Solve: 320 ÷ 20 = n n = 16 $20 bills 54. Let b = the new balance. Solve: 749 − 34 − 65 + 123 = b b = $773 56. Let l = the total length of the bookshelves, in feet. Solve: 6 · 3 = l l = 18 ft Since the total length of the bookshelves is greater than 16 ft, the shelves cannot be put side by side on the 16-ft wall. 58. 15 8 5 / 9 12 9 / 6 0 2 / ✥✥ − 1 8 4 3 7 7 5 9 60. 1 4 7 3 2 4 7 0 8 3 2 1 5 0 1 2 8 2 2 8 2 2 4 4 The answer is 147 R 4. 62. A = l × w = 211 ft × 46 ft = 9706 sq ft 64. x = 81 − 15 = 66 66. Consider one student taking one class a “student-class unit.” Then let s = the total number of student-class units and p = the number of students taught by each instructor. Solve: 1200 · 5 = s , 4 · 30 = p s = 6000, p = 120 Now let n = the number of instructors. Solve: 6000 ÷ 120 = n n = 50 instructors Exercise Set 1.9 RC2. The expression 9 2 can be read “nine squared.” RC4. To find the average of 7, 8, and 9, we add the numbers and divide the sum by 3. 2. 2 5 4. 13 3 6. 9 2 8. 1 4 10. 125 12. 64 14. 100,000 16. 64 18. (12 + 6) + 18 = 18 + 18 = 36 20. (52 − 40) − 8 = 12 − 8 = 4 22. (1000 ÷ 100) ÷ 10 = 10 ÷ 10 = 1 24. 256 ÷ (64 ÷ 4) = 256 ÷ 16 = 16 26. 2 2 + 5 2 = 4 + 25 = 29 28. (32 − 27) 3 + (19 + 1) 3 = 5 3 + 20 3 = 125 + 8000 = 8125 30. 23 + 18 · 20 = 23 + 360 = 383 32. 10 · 7 − 4 = 70 − 4 = 66 34. 90 − 5 · 5 · 2 = 90 − 50 = 4 0 36. 8 2 − 8 · 2 = 64 − 8 · 2 = 64 − 16 = 4 8

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    Chapter 1 Summary and Review: Concept Reinforcement 13 38. 1000 ÷ 25 − (15 + 5) = 1000 ÷ 25 − 20 = 4 0 − 20 = 20 40. 3 · 8 + 5 · 8 = 24 + 4 0 = 64 42. 144 ÷ 4 − 2 = 36 − 2 = 34 44. 7 · (10 − 3) 2 − 2 · (3 + 1) 2 = 7 · 7 2 − 2 · 4 2 = 7 · 49 − 2 · 16 = 34 3 − 32 = 311 46. 6 2 − 3 4 ÷ 3 3 = 36 − 81 ÷ 27 = 36 − 3 = 33 48. 7 2 + 20 · 4 − (28 + 9 · 2) = 7 2 + 20 · 4 − (28 + 18) = 7 2 + 20 · 4 − 46 = 4 9 + 20 · 4 − 46 = 4 9 + 80 − 46 = 83 50. 8 × 9 − (12 − 8) ÷ 4 − (10 − 7) = 8 × 9 − 4 ÷ 4 − 3 = 72 − 1 − 3 = 68 52. 80 − 2 4 · 15 ÷ (7 · 5 − 45 ÷ 3) = 80 − 2 4 · 15 ÷ (35 − 15) = 80 − 2 4 · 15 ÷ 20 = 80 − 16 · 15 ÷ 20 = 80 − 240 ÷ 20 = 80 − 12 = 68 54. 2 7 ÷ 2 5 · 2 4 ÷ 2 2 = 128 ÷ 32 · 16 ÷ 4 = 4 · 16 ÷ 4 = 64 ÷ 4 = 16 56. 86 + 92 + 80 + 78 4 = 336 4 = 84 58. $1025 + $775 + $2062 + $942 + $3721 5 = $8525 5 = $1705 60. 72 ÷ 6 − { 2 × [9 − (4 × 2)] } = 72 ÷ 6 − { 2 × [9 − 8] } = 72 ÷ 6 − { 2 × 1 } = 72 ÷ 6 − 2 = 12 − 2 = 10 62. [92 × (6 − 4) ÷ 8] + [7 × (8 − 3)] = [92 × 2 ÷ 8] + [7 × 5] = [184 ÷ 8] + 35 = 23 + 35 = 58 64. (18 ÷ 2) · { [(9 · 9 − 1) ÷ 2] − [5 · 20 − (7 · 9 − 2)] } = 9 · { [(81 − 1) ÷ 2] − [5 · 20 − (63 − 2)] } = 9 · { [80 ÷ 2] − [5 · 20 − 61] } = 9 · { 40 − [100 − 61] } = 9 · { 40 − 39 } = 9 · { 1 } = 9 66. 15(23 − 4 · 2) 3 ÷ (3 · 25) = 15(23 − 8) 3 ÷ 75 Multiplying inside parentheses = 15 · 15 3 ÷ 75 Subtracting inside parentheses = 15 · 3375 ÷ 75 Evaluating the exponential expression = 50 , 625 ÷ 75 Doing all multiplication and = 675 divisions in order from left to right 68. (19 − 2 4 ) 5 − (141 ÷ 47) 2 = (19 − 16) 5 − 3 2 = 3 5 − 3 2 = 24 3 − 9 = 234 70. x = 5032 − 4197 = 835 72. y = 1554 42 = 37 74. t = 10 , 000 100 = 100 76. Let g = the total number of gallons of gasoline purchased. Solve: 23 + 24+ 26 + 25 = g g = 98 gallons 78. 12 ÷ 4 + 2 · 3 − 2 = 3 + 6 − 2 = 7 Correct answer 12 ÷ (4+ 2) · (3 − 2) = 2 80. Answers may vary. One correct answer is 9 · 8 + 7 · 6 − 5 · 4 + 3 · 2 · 1 = 100 . Chapter 1 Vocabulary Reinforcement 1. The distance around an object is its perimeter. 2. The minuend is the number from which another number is being subtracted. 3. For large numbers, digits are separated by commas into groups of three, called periods. 4. In the sentence 28 ÷ 7 = 4, the dividend is 28. 5. In the sentence 10 × 1000 = 10 , 000, 10 and 1000 are called factors and 10,000 is called the product. 6. The number 0 is called the additive identity. 7. The sentence 3 × (6 × 2) = (3 × 6) × 2 illustrates the associative law of multiplication. 8. We can use the following rule to check division: quotient · divisor + remainder = dividend.

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    14 Chapter 1: Whole Numbers Chapter 1 Concept Reinforcement 1. The statement is true. See page 42 in the text. 2. a ÷ a = a a = 1, a  = 0; the statement is true. 3. a ÷ 0 is not defined, so the statement is false. 4. The statement is false. For example, 1 + 2 = 5 is not a true equation. 5. The statement is true. See page 71 in the text. 6. The statement is false. See page 73 in the text. Chapter 1 Study Guide 1. 4 3 2 , 0 7 9 The digit 2 names the number of thousands. 2. 1 1 1 3 6 , 0 4 7 + 2 9 , 2 5 5 6 5 , 3 0 2 3. 7 9 15 4 8 0 5 / ✥✥ − 1 5 6 8 3 2 3 7 4. 2 1 1 7 3 6 8 4 × 3 2 9 6 1 5 6 Multiplying by 9 1 3 6 8 0 Multiplying by 20 2 0 5 2 0 0 Multiplying by 300 2 2 5 , 0 3 6 5. 3 1 5 2 7 8 5 1 9 8 1 4 1 2 7 1 4 9 1 3 5 1 4 The answer is 315 R 14. 6. Round 36,468 to the nearest thousand. 3 6 , 4 6 8 ↑ The digit 6 is in the thousands place. Consider the next digit to the right. Since the digit, 4, is 4 or lower, round down, meaning that 6 thousands stays as 6 thousands. Then change the digits to the right of the thousands digit to zeros. The answer is 36,000. 7. Since 78 is to the left of 81 on the number line, 78 < 81. 8. 24 · x = 864 24 · x 24 = 864 24 Dividing by 24 x = 36 Check: 24 · x = 864 24 · 36 ? 864 864 ∣ ∣ ∣ TRUE The solution is 36. 9. 6 3 = 6 · 6 · 6 = 216 Chapter 1 Review Exercises 1. 4 , 6 7 8 , 9 5 2 The digit 8 means 8 thousands. 2. 1 3 , 7 6 8, 9 4 0 The digit 3 names the number of millions. 3. 2793 = 2 thousands + 7 hundreds + 9 tens + 3 ones 4. 56,078 = 5 ten thousands + 6 thousands + 0 hundreds + 7 tens + 8 ones, or 5 ten thousands + 6 thousands + 7 tens + 8 ones 5. 4,007,101 = 4 millions + 0 hundred thousands + 0 ten thousands + 7 thousands + 1 hundred + 0 tens + 1 one, or 4millions + 7 thousands + 1 hundred + 1 one 6. 67 ︸︷︷︸ , 819 ︸︷︷︸ ↑ ↑ Sixty-seven thousand, eight hundred nineteen 7. 2 ︸︷︷︸ , 781 ︸︷︷︸ , 4 27 ︸︷︷︸ ↑ ↑ ↑ Two million, seven hundred eighty-one thousand, four hundred twenty-seven 8. Four hundred seventy-six thousand, five hundred eighty-eight ↓ ↓ Standard notation is ︷︸︸︷ 476 , ︷︸︸︷ 588 . 9. One billion, six hundred forty million, ↓ ↓ Standard notation is ︷︸︸︷ 1 , ︷︸︸︷ 640 ,000,000. 10. 1 1 7 3 0 4 + 6 9 6 8 1 4 , 2 7 2

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