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Solution Manual for Prealgebra and Introductory Algebra, 5th Edition

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     I NSTRUCTOR ’ S S OLUTIONS M ANUAL P REALGEBRA & I NTRODUCTORY A LGEBRA F IFTH E DITION Elayn Martin-Gay University of New Orleans

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    Contents Chapter 1 1 Chapter 2 42 Chapter 3 71 Chapter 4 101 Chapter 5 164 Chapter 6 209 Chapter 7 254 Chapter 8 285 Chapter 9 325 Chapter 10 368 Chapter 11 414 Chapter 12 454 Chapter 13 507 Chapter 14 567 Chapter 15 612 Chapter 16 647 Appendix 698 Practice Final Exam 704

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    1 Chapter 1 Section 1.2 Practice Exercises 1. The place value of the 8 in 38,760,005 is millions. 2. The place value of the 8 in 67,890 is hundreds. 3. The place value of the 8 in 481,922 is ten- thousands. 4. 54 is written as fifty-four. 5. 678 is written as six hundred seventy-eight. 6. 93,205 is written as ninety-three thousand, two hundred five. 7. 679,430,105 is written as six hundred seventy- nine million, four hundred thirty thousand, one hundred five. 8. Thirty-seven in standard form is 37. 9. Two hundred twelve in standard form is 212. 10. Eight thousand, two hundred seventy-four in standard form is 8,274 or 8274. 11. Five million, fifty-seven thousand, twenty-six in standard form is 5,057,026. 12. 4,026,301 = 4,000,000 + 20,000 + 6000 + 300 + 1 13. a. Find Australia in the “Country” column. Read from left to right until the “bronze” column is reached. Australia won 10 bronze medals. b. Find the countries for which the entry in the “Total” column is greater than 60. The United States, China, and Great Britain won more than 60 medals. Vocabulary, Readiness & Video Check 1.2 1. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... are called whole numbers. 2. The number 1286 is written in standard form. 3. The number “twenty-one” is written in words. 4. The number 900 + 60 + 5 is written in expanded form. 5. In a whole number, each group of 3 digits is called a period. 6. The place value of the digit 4 in the whole number 264 is ones. 7. hundreds 8. To read (or write) a number, read from left to right. 9. 80,000 10. Boxer Exercise Set 1.2 2. The place value of the 5 in 905 is ones. 4. The place value of the 5 in 6527 is hundreds. 6. The place value of the 5 in 79,050,000 is ten- thousands. 8. The place value of the 5 in 51,682,700 is ten- millions. 10. 316 is written as three hundred sixteen. 12. 5445 is written as five thousand, four hundred forty-five. 14. 42,009 is written as forty-two thousand, nine. 16. 3,204,000 is written as three million, two hundred four thousand. 18. 47,033,107 is written as forty-seven million, thirty-three thousand, one hundred seven. 20. 254 is written as two hundred fifty-four. 22. 119,926 is written as one hundred nineteen thousand, nine hundred twenty-six. 24. 50,400,000,000 is written as fifty billion, four hundred million. 26. 11,239 is written as eleven thousand, two hundred thirty-nine. 28. 202,700 is written as two hundred two thousand, seven hundred.

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 2 30. Four thousand, four hundred sixty-eight in standard form is 4468. 32. Seventy-three thousand, two in standard form is 73,002. 34. Sixteen million, four hundred five thousand, sixteen in standard form is 16,405,016. 36. Two million, twelve in standard form is 2,000,012. 38. Six hundred forty thousand, eight hundred eighty-one in standard form is 640,881. 40. Two hundred thirty-four thousand in standard form is 234,000. 42. One thousand, eight hundred fifteen in standard form is 1815. 44. Two hundred eight million, eight hundred six thousand, two hundred seventy in standard form is 208,806,270. 46. Seven hundred nine in standard form is 709. 48. 789 = 700 + 80 + 9 50. 6040 = 6000 + 40 52. 20,215 = 20,000 + 200 + 10 + 5 54. 99,032 = 90,000 + 9000 + 30 + 2 56. 47,703,029 = 40,000,000 + 7,000,000 + 700,000 + 3000 + 20 + 9 58. Mount Baker erupted in 1792, which is in standard form. 60. Mount Shasta and Mount St. Helens have each had two eruptions listed. 62. Mount St. Helens has an eruption listed in 1980. All other eruptions listed in the table occurred before this one. 64. More German shepherds are registered than Golden retrievers. 66. German shepherds are second in popularity. 26 is written as twenty-six. 68. The maximum height of an average-size standard poodle is 26 inches. 70. The largest number is 77,753. 72. Yes 74. answers may vary 76. A quadrillion in standard form is 1,000,000,000,000,000. Section 1.3 Practice Exercises 1. 4135 252 4387 + 2. 1 1 1 1 47,364 135,898 183, 262 + 3. Notice 12 + 8 = 20 and 4 + 6 = 10. 12 + 4 + 8 + 6 + 5 = 20 + 10 + 5 = 35 4. 1 2 2 6432 789 54 28 7303 + 5. a. 14 − 6 = 8 because 8 + 6 = 14. b. 20 − 8 = 12 because 12 + 8 = 20 c. 93 − 93 = 0 because 0 + 93 = 93. d. 42 − 0 = 42 because 42 + 0 = 42. 6. a. 9143 122 9021 − Check : 9021 122 9143 + b. 978 851 127 − Check: 127 851 978 + 7. a. 8 17 69 7 4 9 64 8 − Check : 648 49 697 +

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 3 b. 2 12 326 245 81 − Check: 81 245 326 + c. 1234 822 412 − Check: 412 822 1234 + 8. a. 9 3 1010 4 0 0 1 6 4 2 3 6 − Check: 236 164 400 + b. 9 91010 10 0 0 7 6 2 2 3 8 − Check: 238 762 1000 + 9. 2 cm + 8 cm + 15 cm + 5 cm = 30 cm The perimeter is 30 centimeters. 10. 647 + 647 + 647 = 1941 The perimeter is 1941 feet. 11. 15, 759 458 15,301 − The radius of Neptune is 15,301 miles. 12. a. The country with the fewest threatened amphibians corresponds to the shortest bar, which is Madagascar. b. To find the total number of threatened amphibians for Madagascar, Peru, and Mexico, we add. 69 102 211 382 + The total number of threatened amphibians for Madagascar, Peru, and Mexico is 382. Calculator Explorations 1. 89 + 45 = 134 2. 76 + 97 = 173 3. 285 + 55 = 340 4. 8773 + 652 = 9425 5. 985 + 1210 + 562 + 77 = 2834 6. 465 + 9888 + 620 + 1550 = 12,523 7. 865 − 95 = 770 8. 76 − 27 = 49 9. 147 − 38 = 109 10. 366 − 87 = 279 11. 9625 − 647 = 8978 12. 10,711 − 8925 = 1786 Vocabulary, Readiness & Video Check 1.3 1. The sum of 0 and any number is the same number. 2. In 35 + 20 = 55, the number 55 is called the sum and 35 and 20 are each called an addend. 3. The difference of any number and that same number is 0. 4. The difference of any number and 0 is the same number. 5. In 37 − 19 = 18, the number 37 is the minuend, the 19 is the subtrahend, and the 18 is the difference. 6. The distance around a polygon is called its perimeter. 7. Since 7 + 10 = 10 + 7, we say that changing the order in addition does not change the sum. This property is called the commutative property of addition. 8. Since (3 + 1) + 20 = 3 + (1 + 20), we say that changing the grouping in addition does not change the sum. This property is called the associative property of addition. 9. To add whole numbers, we line up place values and add from right to left. 10. We cannot take 7 from 2 in the ones place, so we borrow one ten from the tens place and move it over to the ones place to give us 10 + 2 or 12. 11. triangle; 3

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 4 12. To find the sale price, subtract the discount from the regular price. Exercise Set 1.3 2. 27 31 58 + 4. 37 542 579 + 6. 23 45 30 98 + 8. 236 6243 6479 + 10. 1 17, 427 821, 059 838, 486 + 12. 3 5 8 5 7 28 + 14. 2 2 64 28 56 25 32 205 + 16. 1 1 2 16 1056 748 7770 9590 + 18. 1 1 1 1 6789 4321 5555 16, 665 + 20. 1 1 1 26 582 4 763 62,511 67,882 + 22. 1 1 1 2 1 2 504, 218 321,920 38,507 594, 687 1, 459,332 + 24. 957 257 700 − Check: 700 257 957 + 26. 55 29 26 − Check: 1 26 29 55 + 28. 674 299 375 − Check: 1 1 375 299 674 + 30. 300 149 151 − Check: 1 1 151 149 300 + 32. 5349 720 4629 − Check : 1 4629 720 5349 + 34. 724 16 708 − Check: 1 708 16 724 +

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 5 36. 1983 1914 69 − Check: 1 69 1914 1983 + 38. 40, 000 23,582 16, 418 − Check: 1 1 1 1 16, 418 23,582 40, 000 + 40. 6050 1878 4172 − Check: 1 1 1 4172 1878 6050 + 42. 62, 222 39,898 22,324 − Check: 1 1 1 1 22,324 39,898 62, 222 + 44. 986 48 938 − 46. 2 80 93 17 9 2 201 + 48. 10, 000 1786 8214 − 50. 1 1 1 12, 468 3 211 1 988 17, 667 + 52. 3 + 4 + 5 = 12 The perimeter is 12 centimeters. 54. Opposite sides of a rectangle have the same length. 9 + 3 + 9 + 3 = 12 + 12 = 24 The perimeter is 24 miles. 56. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37 The perimeter is 37 inches. 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. 60. “Find the sum” indicates addition. 1 802 6487 7289 + The sum of 802 and 6487 is 7289. 62. “Find the total” indicates addition. 1 2 89 45 2 19 341 496 + The total of 89, 45, 2, 19, and 341 is 496. 64. “Find the difference” indicates subtraction. 16 5 11 − The difference of 16 and 5 is 11. 66. “Increased by” indicates addition. 712 38 750 + 712 increased by 38 is 750. 68. “Less” indicates subtraction. 25 12 13 − 25 less 12 is 13. 70. “Subtracted from” indicates subtraction. 90 86 4 − 86 subtracted from 90 is 4. 72. Subtract 39,136 thousand from 44,126 thousand. 44 126 39 136 4 990 − , , California’s projected population increase is 4990 thousand.

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 6 74. Subtract the discount from the regular price. 547 99 448 − The sale price is $448. 76. 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. 78. 189, 000 75, 000 114, 000 − The Upper Mississippi sub-basin drains 114,000 square miles more than the Lower Mississippi sub-basin. 80. Opposite sides of a rectangle have the same length. 60 + 45 + 60 + 45 = 210 The perimeter is 210 feet. 82. 59,320 55, 492 3 828 − They traveled 3828 miles on their trip. 84. 65 542 49 768 115 310 , , , + The total number of F-Series trucks and Silverados sold that month was 115,310. 86. The shortest bar corresponds to the quietest reading. Leaves rustling is the quietest. 88. 100 70 30 − The difference in sound intensity between live rock music and loud television is 30 dB. 90. 119 99 20 − The difference in volume between the mid-size and a sub-compact car is 20 cubic feet. 92. Opposite sides of a rectangle have the same length. 18 + 12 + 18 + 12 = 60 The perimeter of the puzzle is 60 inches. 94. Indiana has the fewest CVS pharmacies. 96. 356 + 867 + 756 + 313 + 301 + 486 + 313 + 309 + 408 + 659 = 4768 The total number of CVS pharmacies in the ten states listed is 4768. 98. The total number of CVS pharmacies in the states listed in the table is 4768. 4768 3048 7816 + There are 7816 CVS pharmacies in the 50 states. 100. 1 5193 1222 6415 + The total highway mileage in Rhode Island is 6415 miles. 102. The minuend is 2863 and the subtrahend is 1904. 104. The minuend is 86 and the subtrahend is 25. 106. answers may vary 108. 2 1 773 659 481 1913 + The given sum is correct. 110. 1 2 19 214 49 651 933 + The given sum is incorrect, the correct sum is 933. 112. 1 1 389 89 478 + The given difference is correct.

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 7 114. 1 1 7168 547 7715 + The given difference is incorrect. 7615 547 7068 − 116. 10, 244 8 534 1 710 − 118. answers may vary Section 1.4 Practice Exercises 1. a. To round 57 to the nearest ten, observe that the digit in the ones place is 7. Since the digit is at least 5, we add 1 to the digit in the tens place. The number 57 rounded to the nearest ten is 60. b. To round 641 to the nearest ten, observe that the digit in the ones place is 1. Since the digit is less than 5, we do not add 1 to the digit in the tens place. The number 641 rounded to the nearest ten is 640. c. To round 325 to the nearest ten observe that the digit in the ones place is 5. Since the digit is at least 5, we add 1 to the digit in the tens place. The number 325 rounded to the nearest ten is 330. 2. a. To round 72,304 to the nearest thousand, observe that the digit in the hundreds place is 3. Since the digit is less than 5, we do not add 1 to the digit in the thousands place. The number 72,304 rounded to the nearest thousand is 72,000. b. To round 9222 to the nearest thousand, observe that the digit in the hundreds place is 2. Since the digit is less than 5, we do not add 1 to the digit in the thousands place. The number 9222 rounded to the nearest thousand is 9000. c. To round 671,800 to the nearest thousand, observe that the digit in the hundreds place is 8. Since this digit is at least 5, we add 1 to the digit in the thousands place. The number 671,800 rounded to the nearest thousand is 672,000. 3. a. To round 3474 to the nearest hundred, observe that the digit in the tens place is 7. Since this digit is at least 5, we add 1 to the digit in the hundreds place. The number 3474 rounded to the nearest hundred is 3500. b. To round 76,243 to the nearest hundred, observe that the digit in the tens place is 4. Since this digit is less than 5, we do not add 1 to the digit in the hundreds place. The number 76,243 rounded to the nearest hundred is 76,200. c. To round 978,965 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 979,000. 4. 49 rounds to 50 25 rounds to 30 32 rounds to 30 51 rounds to 50 98 rounds to + 100 260 5. 3785 rounds to 4000 2479 rounds to 2000 2000 − − 6. 11 rounds to 10 16 rounds to 20 19 rounds to 20 31 rounds to + 30 80 + The total distance is approximately 80 miles. 7. 2930 rounds to 3000 18,166 rounds to 18,000 189 rounds to + 0 21,000 + In 2015, there were approximately 21,000 reported cases of these diseases. Vocabulary, Readiness & Video Check 1.4 1. To graph a number on a number line, darken the point representing the location of the number. 2. Another word for approximating a whole number is rounding.

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 8 3. The number 65 rounded to the nearest ten is 70, but the number 61 rounded to the nearest ten is 60. 4. An exact number of products is 1265, but an estimate is 1000. 5. 3 is in the place we’re rounding to (tens), and the digit to the right of this place is 5 or greater, so we need to add 1 to the 3. 6. On a number line, 22 is closer to 20 than to 30. Thus, 22 rounded to the nearest ten is 20. 7. Each circled digit is to the right of the place value being rounded to and is used to determine whether or not we add 1 to the digit in the place value being rounded to. Exercise Set 1.4 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. 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. 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 hundreds place. The number 8494 rounded to the nearest hundred is 8500. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 28. To round 171,874 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. Therefore 171,874 miles rounded to the nearest thousand is 172,000 miles. 30. 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.

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 9 32. To round 322,962,019 to the nearest million, observe that the digit in the hundred-thousands place is 9. Since this digit is at least 5, we add 1 to the digit in the millions place. Therefore, 322,962,019 rounded to the nearest million is 323,000,000. 34. To round 2,110,000 to the nearest million, observe that the digit in the hundred-thousands place is 1. Since this digit is less than 5, we do not add 1 to the digit in the millions place. Therefore, $2,110,000 rounded to the nearest million is $2,000,000. 36. To round 15,226,000,000 to the nearest ten- million, observe that the digit in the millions place is 6. Since this digit is at least 5, we add 1 to the digit in the ten-millions place. Therefore, 15,226,000,000 bushels rounded to the nearest ten-million is 15,230,000,000 bushels. 38. 52 rounds to 50 33 rounds to 30 15 rounds to 20 29 rounds to + 30 130 + 40. 555 rounds to 560 235 rounds to 240 320 − − 42. 4050 rounds to 4100 3133 rounds to 3100 1220 rounds to 1200 8400 + + 44. 1989 rounds to 2000 1870 rounds to 1900 100 − − 46. 799 rounds to 800 1655 rounds to 1700 271 rounds to + 300 2800 + 48. 522 + 785 is approximately 520 + 790 = 1310. The answer of 1307 is correct. 50. 542 + 789 + 198 is approximately 540 + 790 + 200 = 1530. The answer of 2139 is incorrect. 52. 5233 + 4988 is approximately 5200 + 5000 = 10,200. The answer of 9011 is incorrect. 54. 89 rounds to 90 97 rounds to 100 100 rounds to 100 79 rounds to 80 75 rounds to 80 82 rounds to + 80 530 + The total score is approximately 530. 56. 588 rounds to 600 689 rounds to 700 277 rounds to 300 143 rounds to 100 59 rounds to 100 802 rounds to + 800 2600 + The total distance is approximately 2600 miles. 58. 1895 rounds to 1900 1524 rounds to 1500 400 − − The difference in price is approximately $400. 60. 64 rounds to 60 41 rounds to 40 133 rounds to + 130 230 + The total distance is approximately 230 miles. 62. 51, 746 rounds to 52,000 49, 713 rounds to 50, 000 2 000 − − The increase is approximately 2000 credit hours. 64. 769 hundred-thousands is 76,900,000 in standard form. 76,900,000 rounded to the nearest million is 77,000,000. 76,900,000 rounded to the nearest ten-million is 80,000,000. 66. 568 hundred-thousands is 56,800,000 in standard form. 56,800,000 rounded to the nearest million is 57,000,000. 56,800,000 rounded to the nearest ten-million is 60,000,000. 68. 5698, for example, rounded to the nearest ten is 5700.

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 10 70. The largest possible number that rounds to 1,500,000 when rounded to the nearest hundred- thousand is 1,549,999. 72. answers may vary 74. 5950 rounds to 6 000 7693 rounds to 7 700 8203 rounds to 8 200 21,900 + + The perimeter is approximately 21,900 miles. Section 1.5 Practice Exercises 1. a. 6 × 0 = 0 b. (1)8 = 8 c. (50)(0) = 0 d. 75 ⋅ 1 = 75 2. a. 6(4 + 5) = 6 ⋅ 4 + 6 ⋅ 5 b. 30(2 + 3) = 30 ⋅ 2 + 30 ⋅ 3 c. 7(2 + 8) = 7 ⋅ 2 + 7 ⋅ 8 3. a. 5 29 6 174 × b. 4 4 648 5 3240 × 4. 306 81 306 24 480 24, 786 × 5. 726 142 1 452 29 040 72 600 103, 092 × 6. Area length width (360 miles)(280 miles) 100,800 square miles = ⋅ = = The area of Wyoming is 100,800 square miles. 7. 16 45 80 640 720 × The printer can print 720 pages in 45 minutes. 8. 8 11 88 5 9 45 × = × = 1 88 45 133 + The total cost is $133. 9. 163 rounds to 200 391 rounds to 400 80,000 × × There are approximately 80,000 words on 391 pages. Calculator Explorations 1. 72 × 48 = 3456 2. 81 × 92 = 7452 3. 163 ⋅ 94 = 15,322 4. 285 ⋅ 144 = 41,040 5. 983(277) = 272,291 6. 1562(843) = 1,316,766 Vocabulary, Readiness & Video Check 1.5 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.

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 11 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. 9. distributive 10. To show that 8649 is actually multiplied by 70 and not by just 7. 11. Area is measured in square units, and here we have meters by meters, or square meters; the answer is 63 square meters, or the correct units are square meters. 12. Multiplication is also an application of addition since it is addition of the same addend. Exercise Set 1.5 2. 55 ⋅ 1 = 55 4. 27 ⋅ 0 = 0 6. 7 ⋅ 6 ⋅ 0 = 0 8. 1 ⋅ 41 = 41 10. 5(8 + 2) = 5 ⋅ 8 + 5 ⋅ 2 12. 6(1 + 4) = 6 ⋅ 1 + 6 ⋅ 4 14. 12(12 + 3) = 12 ⋅ 12 + 12 ⋅ 3 16. 79 3 237 × 18. 638 5 3190 × 20. 882 2 1764 × 22. 9021 3 27, 063 × 24. 91 72 182 6370 6552 × 26. 526 23 1 578 10 520 12, 098 × 28. 708 21 708 14 160 14,868 × 30. 720 80 57, 600 × 32. (593)(47)(0) = 0 34. (240)(1)(20) = (240)(20) = 4800 36. 1357 79 12 213 94 990 107, 203 × 38. 807 127 5 649 16 140 80 700 102, 489 × 40. 1234 567 8 638 74 040 617 000 699, 678 ×

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 12 42. 426 110 4 260 42 600 46,860 × 44. 1876 1407 13 132 750 400 1 876 000 2, 639,532 × 46. Area (length)(width) (13 inches)(3 inches) 39 square inches = = = Perimeter length width length width 13 3 13 3 32 inches = + + + = + + + = 48. Area (length)(width) (25 centimeters)(20 centimeters) 500 square centimeters = = = Perimeter length width length width 25 20 25 20 90 centimeters = + + + = + + + = 50. 982 rounds to 1000 650 rounds to 700 700, 000 × × 52. 111 rounds to 100 999 rounds to 1000 100, 000 × × 54. 2872 × 12 is approximately 2872 × 10, which is 28,720. The best estimate is b. 56. 706 × 409 is approximately 700 × 400, which is 280,000. The best estimate is d. 58. 70 12 (7 10) 12 7 (10 12) 7 120 840 × = × × = × × = × = 60. 9 × 900 = 8100 62. 3310 3 9930 × 64. 14 8 112 × There are 112 grams of fat in 8 ounces of hulled sunflower seeds. 66. 34 14 136 340 476 × There are 476 seats in the room. 68. a. 5 × 4 = 20 There are 20 apartments on one floor. b. 20 3 60 × There are 60 apartments in the building. 70. Area (length)(width) (60 feet)(45 feet) 2700 square feet = = = The area is 2700 square feet. 72. Area (length)(width) (776 meters)(639 meters) 495,864 square meters = = = The area is 495,864 square meters. 74. 700 17 4 900 7 000 11,900 × The 17 discs hold 11,900 MB. 76. 365 3 1095 × A cow eats 1095 pounds of grain each year.

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 13 78. 13 16 78 130 208 × There are 208 grams of fat in 16 ounces. 80. Person Number of persons Cost per person Cost per Category Student 24 $5 $120 Nonstudent 4 $7 $28 Children under 12 5 $2 $10 Total Cost $158 82. 3 × 18 = 54 There are projected to be 54 million “older” Americans in 2020. 84. 126 8 118 − 86. 47 + 26 + 10 + 231 + 50 = 364 88. 19 4 76 × The product of 19 and 4 is 76. 90. 14 9 23 + The total of 14 and 9 is 23. 92. 11 + 11 + 11 + 11 + 11 + 11 = 6 ⋅ 11 or 11 ⋅ 6 94. a. 4 ⋅ 5 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4 b. answers may vary 96. 31 50 1550 × 98. 57 × 3 = 171 57 × 6 = 342 The problem is 57 63 × 100. answers may vary 102. 3 × 87 = 261 2 × 650 = 1300 261 + 1300 + 359 = 1920 LeBron James scored 1920 points during the 2015 − 2016 regular season. Section 1.6 Practice Exercises 1. a. 8 9 72 because 8 ⋅ 9 = 72. b. 40 ÷ 5 = 8 because 8 ⋅ 5 = 40. c. 24 4 6 = because 4 ⋅ 6 = 24. 2. a. 7 1 7 = because 1 ⋅ 7 = 7. b. 5 ÷ 1 = 5 because 5 ⋅ 1 = 5. c. 11 1 11 because 11 ⋅ 1 = 11. d. 4 ÷ 1 = 4 because 4 ⋅ 1 = 4. e. 10 10 1 = because 10 ⋅ 1 = 10. f. 21 ÷ 21 = 1 because 1 ⋅ 21 = 21. 3. a. 0 0 7 = because 0 ⋅ 7 = 0. b. 0 8 0 because 0 ⋅ 8 = 0. c. 7 ÷ 0 is undefined because if 7 ÷ 0 is a number, then the number times 0 would be 7. d. 0 ÷ 14 = 0 because 0 ⋅ 14 = 0.

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 14 4. a. 818 6 4908 48 10 6 48 48 0 − − − Check: 818 6 4908 × b. 553 4 2212 20 21 20 12 12 0 − − − Check: 553 4 2212 × c. 251 3 753 6 15 15 03 3 0 − − − Check: 251 3 753 × 5. a. 304 7 2128 21 02 0 28 28 0 − − − Check: 304 × 7 = 2128 b. 5 100 9 45,900 45 0 9 9 000 − − Check: 5100 × 9 = 45,900 6. a. 234 R 3 4 939 8 13 12 19 16 3 − − − Check: 234 ⋅ 4 + 3 = 939 b. 657 R 2 5 3287 30 28 25 37 35 2 − − − Check: 657 ⋅ 5 + 2 = 3287 7. a. 9067 R 2 9 81, 605 81 0 6 0 60 54 65 63 2 − − − − Check: 9067 ⋅ 9 + 2 = 81,605

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 15 b. 5827 R 2 4 23,310 20 3 3 3 2 11 8 30 28 2 − − − − Check: 5827 ⋅ 4 + 2 = 23,310 8. 524 R 12 17 8920 85 42 34 80 68 12 − − − 9. 49 R 60 678 33, 282 27 12 6 162 6 102 60 − − 10. 57 3 171 15 21 21 0 − − Each student got 57 CDs. 11. 44 12 532 48 52 48 4 − − There will be 44 full boxes and 4 printers left over. 12. Find the sum and divide by 7. 4 7 35 16 9 3 52 126 + 18 7 126 7 56 56 0 − − The average time is 18 minutes. Calculator Explorations 1. 848 ÷ 16 = 53 2. 564 ÷ 12 = 47 3. 5890 ÷ 95 = 62 4. 1053 ÷ 27 = 39 5. 32,886 261 126 = 6. 143, 088 542 264 = 7. 0 ÷ 315 = 0 8. 315 ÷ 0 is an error. Vocabulary, Readiness & Video Check 1.6 1. In 90 ÷ 2 = 45, the answer 45 is called the quotient, 90 is called the dividend, and 2 is called the divisor. 2. The quotient of any number and 1 is the same number. 3. The quotient of any number (except 0) and the same number is 1. 4. The quotient of 0 and any number (except 0) is 0. 5. The quotient of any number and 0 is undefined. 6. The average of a list of numbers is the sum of the numbers divided by the number of numbers. 7. 0

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 16 8. zero; this zero becomes a placeholder in the quotient. 9. 202 ⋅ 102 + 15 = 20,619 10. This tells us we have a division problem since division may be used to separate a quantity into equal parts. 11. addition and division Exercise Set 1.6 2. 72 ÷ 9 = 8 4. 24 ÷ 3 = 8 6. 0 ÷ 4 = 0 8. 38 ÷ 1 = 38 10. 49 1 49 = 12. 45 5 9 = 14. 12 is undefined 0 16. 6 ÷ 6 = 1 18. 7 ÷ 0 is undefined 20. 18 ÷ 3 = 6 22. 17 5 85 5 35 35 0 − − Check: 17 ⋅ 5 = 85 24. 80 8 640 64 00 − Check: 80 ⋅ 8 = 640 26. 526 4 2104 20 10 8 24 24 0 − − − Check: 526 ⋅ 4 = 2104 28. 0 0 30 = Check: 0 ⋅ 30 = 0 30. 7 8 56 56 0 − Check: 7 ⋅ 8 = 56 32. 11 11 121 11 11 11 0 − − Check: 11 ⋅ 11 = 121 34. 60 R 6 7 426 42 06 − Check: 60 ⋅ 7 + 6 = 426 36. 413 R 1 3 1240 12 04 3 10 9 1 − − − Check: 413 ⋅ 3 + 1 = 1240

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 17 38. 55 R 2 3 167 15 17 15 2 − − Check: 55 ⋅ 3 + 2 = 167 40. 833 R 1 4 3333 32 13 12 13 12 1 − − − Check: 833 ⋅ 4 + 1 = 3333 42. 32 23 736 69 46 46 0 − − Check: 32 ⋅ 23 = 736 44. 48 42 2016 168 336 336 0 − − Check: 48 ⋅ 42 = 2016 46. 44 R 2 44 1938 176 178 176 2 − − Check: 44 ⋅ 44 + 2 = 1938 48. 612 R 10 12 7354 72 15 12 34 24 10 − − − Check: 612 ⋅ 12 + 10 = 7354 50. 405 14 5670 56 07 0 70 70 0 − − − Check: 405 ⋅ 14 = 5670 52. 39 R 9 64 2505 192 585 576 9 − − Check: 39 ⋅ 64 + 9 = 2505 54. 47 123 5781 492 861 861 0 − − Check: 47 ⋅ 123 = 5781 56. 96 R 52 240 23, 092 21 60 1 492 1 440 52 − − Check: 96 ⋅ 240 + 52 = 23,092

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 18 58. 201 R 50 203 40,853 40 6 25 0 253 203 50 − − − Check: 201 ⋅ 203 + 50 = 40,853 60. 303 R 63 543 164,592 162 9 1 69 0 1 692 1 629 63 − − − Check: 303 ⋅ 543 + 63 = 164,592 62. 13 8 104 8 24 24 0 − − 64. 603 R 2 5 3017 30 01 0 17 15 2 − − − 66. 1714 R 47 50 85, 747 50 35 7 35 0 74 50 247 200 47 − − − − 68. 3 040 214 650,560 642 8 5 0 8 56 8 56 00 0 0 − − − − 70. 13 R 3 7 94 7 24 21 3 − − The quotient is 13 R 3. 72. 3 R 20 32 116 96 20 − 116 divided by 32 is 3 R 20. 74. 15 R 3 5 78 5 28 25 3 − − The quotient is 15 R 3. 76. 58 85 4930 425 680 680 0 − − There are 58 students in the group.

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 19 78. 252000 21 5292000 42 109 105 42 42 0 − − − Each person received $252,000. 80. 412 14 5768 56 16 14 28 28 0 − − − The truck hauls 412 bushels on each trip. 82. Lane divider = 25 + 25 = 50 105 50 5280 50 28 0 280 250 30 − − − There are 105 whole lane dividers. 84. 23 R 1 8 185 16 25 24 1 − − Yes, there is 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. 86. 14 6 84 6 24 24 0 − − The players each scored 14 touchdowns. 88. 16 320 5280 320 2080 1920 160 − − There are 16 whole feet in 1 rod. 90. 3 37 26 15 29 51 22 180 + 30 6 180 18 00 − 180 Average 30 6 = = 92. 2 1 121 200 185 176 163 845 + 169 5 845 5 34 30 45 45 0 − − − 845 Average 169 5 = = 94. 2 92 96 90 85 92 79 534 + 89 6 534 48 54 54 0 − − 534 Average 89 6 = = 96. 53 40 30 123 + 41 3 123 12 03 3 0 − − The average temperature is 41 ° .

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 20 98. 1 1 23 407 92 7011 7533 + 100. 712 54 2 848 35 600 38, 448 × 102. 712 54 658 − 104. 0 0 23 = because 0 ⋅ 23 = 0 106. 9 R 25 31 304 279 25 − 108. The quotient of 200 and 20 is 200 ÷ 20, which is choice b. 110. 40 divided by 8 is 40 ÷ 8, which is choice c. 112. 3,500, 000, 000 2, 680, 000, 000 2, 250, 000, 000 1,800, 000, 000 10, 230, 000, 000 + 2,557,500, 000 4 10, 230, 000, 000 8 2 2 2 0 23 20 30 28 2 0 2 0 000 000 − − − − − The top four advertisers spent an average of $2,557,500,000. 114. The average will decrease; answers may vary. 116. No; answers may vary Possible answer: The average cannot be less than each of the four numbers. 118. 84 ÷ 21 = 4 The width is 4 inches. 120. answers may vary Possible answer: 2 and 2 122. 86 10 76 10 66 10 56 10 46 − − − − 46 10 36 10 26 10 16 10 6 − − − − Therefore, 86 ÷ 10 = 8 R 6. Integrated Review 1. 1 42 63 89 194 + 2. 7006 451 6555 − 3. 87 52 174 4350 4524 × 4. 562 8 4496 40 49 48 16 16 0 − − − 5. 1 ⋅ 67 = 67 6. 36 0 is undefined. 7. 16 ÷ 16 = 1

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 21 8. 5 ÷ 1 = 5 9. 0 ⋅ 21 = 0 10. 7 ⋅ 0 ⋅ 8 = 0 11. 0 ÷ 7 = 0 12. 12 ÷ 4 = 3 13. 9 ⋅ 7 = 63 14. 45 ÷ 5 = 9 15. 207 69 138 − 16. 1 207 69 276 + 17. 3718 2549 1169 − 18. 1 1 1861 7965 9826 + 19. 182 R 4 7 1278 7 57 56 18 14 4 − − − 20. 1259 63 3 777 75 540 79,317 × 21. 1099 R 2 7 7695 7 06 0 69 63 65 63 2 − − − − 22. 111 R 1 9 1000 9 10 9 10 9 1 − − − 23. 663 R 24 32 21, 240 19 2 2 04 1 92 120 96 24 − − − 24. 1 076 R 60 65 70, 000 65 5 0 0 5 00 4 55 450 390 60 − − − − 25. 4000 2963 1037 − 26. 10, 000 101 9 899 −

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 22 27. 303 101 303 30 300 30,603 × 28. (475)(100) = 47,500 29. 1 62 9 71 + The total of 62 and 9 is 71. 30. 62 9 558 × The product of 62 and 9 is 558. 31. 6 R 8 9 62 54 8 − The quotient of 62 and 9 is 6 R 8. 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. 35. 9735 rounded to the nearest ten is 9740. 9735 rounded to the nearest hundred is 9700. 9735 rounded to the nearest thousand is 10,000. 36. 1429 rounded to the nearest ten is 1430. 1429 rounded to the nearest hundred is 1400. 1429 rounded to the nearest thousand is 1000. 37. 20,801 rounded to the nearest ten is 20,800. 20,801 rounded to the nearest hundred is 20,800. 20,801 rounded to the nearest thousand is 21,000. 38. 432,198 rounded to the nearest ten is 432,200. 432,198 rounded to the nearest hundred is 432,200. 432,198 rounded to the nearest thousand is 432,000. 39. 6 + 6 + 6 + 6 = 24 6 × 6 = 36 The perimeter is 24 feet and the area is 36 square feet. 40. 14 + 7 + 14 + 7 = 42 14 7 98 × The perimeter is 42 inches and the area is 98 square inches. 41. 13 9 6 28 + The perimeter is 28 miles. 42. The unknown vertical side has length 4 + 3 = 7 meters. The unknown horizontal side has length 3 + 3 = 6 meters. 3 4 3 7 6 3 26 + The perimeter is 26 meters. 43. 3 19 15 25 37 24 120 + 24 5 120 10 20 20 0 − − 120 Average 24 5 = =

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 23 44. 1 2 108 131 98 159 496 + 124 4 496 4 09 8 16 16 0 − − − 496 Average 124 4 = = 45. 28,547 26,372 2 175 − The Lake Pontchartrain Bridge is longer by 2175 feet. 46. 309 18 2472 3090 5562 × The amount spent on toys is $5562. Section 1.7 Practice Exercises 1. 4 8 8 8 8 8 ⋅ ⋅ ⋅ = 2. 3 3 3 3 3 ⋅ ⋅ = 3. 5 10 10 10 10 10 10 ⋅ ⋅ ⋅ ⋅ = 4. 2 6 5 5 4 4 4 4 4 4 5 4 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ 5. 2 4 4 4 16 = ⋅ = 6. 3 7 7 7 7 343 = ⋅ ⋅ = 7. 1 11 11 = 8. 2 2 3 2 3 3 18 ⋅ = ⋅ ⋅ = 9. 9 3 8 4 27 8 4 27 2 25 ⋅ − ÷ = − ÷ = − = 10. 2 48 3 2 48 3 4 16 4 64 ÷ ⋅ = ÷ ⋅ = ⋅ = 11. 4 2 4 2 (10 7) 2 3 3 2 3 81 2 9 81 18 99 − + ⋅ = + ⋅ = + ⋅ = + = 12. 3 3 3 36 [20 (4 2)] 4 6 36 [20 8] 4 6 36 12 4 6 36 12 64 6 3 64 6 61 ÷ − ⋅ + − = ÷ − + − = ÷ + − = ÷ + − = + − = 13. 3 25 8 2 3 25 8 2 27 2(3 2) 2(1) 25 16 27 2 14 2 7 + ⋅ − + ⋅ − = − + − = = = 14. 36 6 3 5 6 3 5 18 5 23 ÷ ⋅ + = ⋅ + = + = 15. 2 2 Area (side) (12 centimeters) 144 square centimeters = = = The area of the square is 144 square centimeters. Calculator Explorations 1. 6 4 4096 = 2. 6 5 15, 625 = 3. 5 5 3125 = 4. 6 7 117, 649 = 5. 11 2 2048 = 6. 8 6 1, 679, 616 = 7. 4 3 7 5 2526 + = 8. 4 4 12 8 16,640 − = 9. 63 ⋅ 75 − 43 ⋅ 10 = 4295 10. 8 ⋅ 22 + 7 ⋅ 16 = 288 11. 4(15 ÷ 3 + 2) − 10 ⋅ 2 = 8

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 24 12. 155 − 2(17 + 3) + 185 = 300 Vocabulary, Readiness & Video Check 1.7 1. In 5 2 32, = the 2 is called the base and the 5 is called the exponent. 2. To simplify 8 + 2 ⋅ 6, which operation should be performed first? multiplication 3. To simplify (8 + 2) ⋅ 6, which operation should be performed first? addition 4. To simplify 9(3 − 2) ÷ 3 + 6, which operation should be performed first? subtraction 5. To simplify 8 ÷ 2 ⋅ 6, which operation should be performed first? division 6. exponent; base 7. 1 8. division, multiplication, addition 9. The area of a rectangle is length ⋅ width. A square is a special rectangle where length = width. Thus, the area of a square is side ⋅ side or 2 side) ( . Exercise Set 1.7 2. 4 5 5 5 5 5 ⋅ ⋅ ⋅ = 4. 7 6 6 6 6 6 6 6 6 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = 6. 3 10 10 10 10 ⋅ ⋅ = 8. 2 3 4 4 3 3 3 4 3 ⋅ ⋅ ⋅ ⋅ = ⋅ 10. 3 7 4 4 4 7 4 ⋅ ⋅ ⋅ = ⋅ 12. 4 4 6 6 6 6 4 6 ⋅ ⋅ ⋅ ⋅ = ⋅ 14. 2 4 6 6 2 9 9 9 9 6 2 9 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ 16. 2 6 6 6 36 = ⋅ = 18. 3 6 6 6 6 216 = ⋅ ⋅ = 20. 5 3 3 3 3 3 3 243 = ⋅ ⋅ ⋅ ⋅ = 22. 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = 24. 1 8 8 = 26. 4 5 5 5 5 5 625 = ⋅ ⋅ ⋅ = 28. 3 3 3 3 3 27 = ⋅ ⋅ = 30. 3 4 4 4 4 64 = ⋅ ⋅ = 32. 3 8 8 8 8 512 = ⋅ ⋅ = 34. 2 11 11 11 121 = ⋅ = 36. 3 10 10 10 10 1000 = ⋅ ⋅ = 38. 1 14 14 = 40. 5 4 4 4 4 4 4 1024 = ⋅ ⋅ ⋅ ⋅ = 42. 2 5 3 5 3 3 45 ⋅ = ⋅ ⋅ = 44. 2 2 7 2 7 7 98 ⋅ = ⋅ ⋅ = 46. 24 + 6 ⋅ 3 = 24 + 18 = 42 48. 100 ÷ 10 ⋅ 5 + 4 = 10 ⋅ 5 + 4 = 50 + 4 = 54 50. 42 ÷ 7 − 6 = 6 − 6 = 0 52. 8 32 32 4 36 2 + = + = 54. 3 ⋅ 4 + 9 ⋅ 1 = 12 + 9 = 21 56. 2 6 9 3 6 3 9 1 9 9 3 + ÷ + = = = 58. 2 2 6 (10 8) 6 2 36 2 72 ⋅ − = ⋅ = ⋅ = 60. 3 2 3 3 2 3 5 (10 15) 9 3 5 25 9 3 125 25 81 27 5 81 27 113 ÷ + + + = ÷ + + = ÷ + + = + + = 62. 2 2 40 8 48 48 3 25 9 16 5 3 + = = = − − 64. (9 − 7) ⋅ (12 + 18) = 2 ⋅ 30 = 60

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 25 66. 2 5(12 7) 4 5(5) 4 25 4 21 3 25 18 25 18 7 5 18 − − − − = = = = − − − 68. 18 − 7 ÷ 0 = undefined 70. 3 3 2 3 (100 10) 2 3 10 8 3 10 24 10 14 ⋅ − ÷ = ⋅ − = ⋅ − = − = 72. 5 5 5 [40 (8 2)] 2 [40 6] 2 34 2 34 32 2 − − − = − − = − = − = 74. (18 6) [(3 5) 2] (18 6) (8 2) 3 (8 2) 3 16 19 ÷ + + ⋅ = ÷ + ⋅ = + ⋅ = + = 76. 2 2 2 2 35 [3 (9 7) 2 ] 10 3 35 [3 2 2 ] 10 3 35 [9 2 4] 10 3 35 7 10 3 5 10 3 5 30 35 ÷ + − − + ⋅ = ÷ + − + ⋅ = ÷ + − + ⋅ = ÷ + ⋅ = + ⋅ = + = 78. 2 3 4 5 2 1 25 8 1 18 18 9 10 5 4 1 4 2 4 1 4 8 4 2 − + − + = = = = ÷ ⋅ ⋅ ÷ ⋅ ⋅ ÷ ÷ 80. 2 2 2 3 9 3 81 3(10 6) 2 1 3(4) 2 1 84 3(4) 4 1 84 12 4 1 84 8 1 84 7 12 + + = − − − − − = − − = − − = − = = 82. 3 10 2 3 2 20 10 2 27 2 20 5 27 2 20 5 54 20 39 ÷ + ⋅ − = ÷ + ⋅ − = + ⋅ − = + − = 84. 2 2 2 2 2 2 2 [15 (11 6) 2 ] (5 1) [15 5 2 ] 4 [15 5 4] 4 [3 4] 4 7 4 7 16 23 ÷ − + + − = ÷ + + = ÷ + + = + + = + = + = 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 − + ⋅ − − = − + ⋅ − = − + − = − + − = − = 88. 2 2 Area of a square (side) (9 centimeters) 81 square centimeters = = = Perimeter 4(side) 4(9 centimeters) 36 centimeters = = = 90. 2 2 Area of a square (side) (41 feet) 1681 square feet = = = Perimeter = 4(side) = 4(41 feet) = 164 feet 92. The statement is true. 94. 9 4 4 4 4 4 4 4 4 4 4 = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ The statement is false. 96. (2 + 3) ⋅ (6 − 2) = (5) ⋅ (4) = 20 98. 24 (3 2 2) 5 24 (6 2) 5 24 8 5 3 5 15 ÷ ⋅ + ⋅ = ÷ + ⋅ = ÷ ⋅ = ⋅ = 100. The total perimeter is 1260 feet. 4 × 1260 = 5040 The total charge is $5040. 102. 3 3 3 25 (45 7 5) 5 25 (45 35) 5 25 (10) 5 15, 625 10 5 156, 250 5 781, 250 ⋅ − ⋅ ⋅ = ⋅ − ⋅ = ⋅ ⋅ = ⋅ ⋅ = ⋅ = 104. answers may vary

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 26 Section 1.8 Practice Exercises 1. x − 2 = 7 − 2 = 5 2. y ( x − 3) = 4(8 − 3) = 4(5) = 20 3. 6 18 6 24 4 6 6 y x + + = = = 4. 3 3 25 25 2 1 25 8 1 18 z x − + = − + = − + = 5. 5( 32) 5(41 32) 5(9) 45 5 9 9 9 9 F − − = = = = 6. 3( 6) 6 3(8 6) 6 3(2) 6 6 6 True y − = − =   Yes, 8 is a solution. 7. 5 n + 4 = 34 Let n be 10. 5(10) 4 34 50 4 34 54 34 False + + =   No, 10 is not a solution. Let n be 6. 5(6) 4 34 30 4 34 34 34 True + + =   Yes, 6 is a solution. Let n be 8. 5(8) 4 34 40 4 34 44 34 False + + =   No, 8 is not a solution. 8. a. Twice a number is 2 x . 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, Readiness & Video Check 1.8 1. A combination of operations on letters (variables) and numbers is an expression. 2. A letter that represents a number is a variable.

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    ISM: Prealgebra and Introductory Algebra Chapter 1: The Whole Numbers 27 3. 3 x − 2 y 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 the expression. 5. A statement of the form “expression = expression” is called an equation. 6. A value for the variable that makes an equation a true statement is called a solution. 7. When a letter and a variable are next to each other, the operation is an understood multiplication. 8. When first replacing f with 8, we don’t know if the statement is true or false. 9. decreased by Exercise Set 1.8 2. a b a + b a − b a ⋅ b a ÷ b 24 6 24 + 6 = 30 24 − 6 = 18 24 ⋅ 6 = 144 24 ÷ 6 = 4 4. a b a + b a − b a ⋅ b a ÷ b 298 0 298 + 0 = 298 298 − 0 = 298 298 ⋅ 0 = 0 298 ÷ 0 is undefined. 6. a b a + b a − b a ⋅ b a ÷ b 82 1 82 + 1 = 83 82 − 1 = 81 82 ⋅ 1 = 82 82 ÷ 1 = 82 8. 7 + 3 z = 7 + 3(3) = 7 + 9 = 16 10. 4 yz + 2 x = 4(5)(3) + 2(2) = 60 + 4 = 64 12. x + 5 y − z = 2 + 5(5) − 3 = 2 + 25 − 3 = 24 14. 2 y + 5 z = 2(5) + 5(3) = 10 + 15 = 25 16. 3 3 5 3 125 3 122 y z − = − = − = 18. 2 2 3 1 3(5)(3) 1 3 5 9 1 135 1 136 yz + = + = ⋅ ⋅ + = + = 20. 3 (2 4) 3 (2 5 4) 3 (10 4) 3 6 9 y + − = + ⋅ − = + − = + = 22. 4 4 4 ( ) 2 (5 3) 2 2 16 2 14 x y z − − = − − = − = − =

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    Chapter 1: The Whole Numbers ISM: Prealgebra and Introductory Algebra 28 24. 8 8 5 3 120 8 15 15 15 yz ⋅ ⋅ = = = 26. 6 3 6 3(2) 6 6 12 4 3 3 3 x z + + + = = = = 28. 2 6 2 3 6 6 6 12 4 3 3 3 3 z + ⋅ + + = = = = 30. 70 15 70 15 70 15 7 5 2 2 2 5 3 10 3 y z − = − = − = − = ⋅ 32. 2 2 3 2 5 3 2 2 2 5 3 4 2 2 5 12 4 5 11 x x + − = ⋅ + ⋅ − = ⋅ + ⋅ − = + − = 34. 2 2 2 2 (4 3 ) (4 5 3 3) (20 9) 29 841 y z + = ⋅ + ⋅ = + = = 36. 4 4 4 4 ( 5) (2 3 5) (6 5) 1 1 xz − = ⋅ − = − = = 38. 3 ( ) 3 2(5 3) 3 2(8) 6(8) 48 x y z + = ⋅ + = ⋅ = = 40. (2 ) 2 3(2 5 2 3) 2 3(10 2 3) 2 3(9) 6(9) 54 xz y x z + − = ⋅ ⋅ + − = ⋅ + − = ⋅ = = 42. 6 2 6 3 2 5 4 4 18 10 4 28 4 7 z y + ⋅ + ⋅ = + = = = 44. F 50 59 68 77 5( 32) 9 F − 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 − = =

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