(Solution Manual) Basic College Mathematics with Early Integers

Martin-Gay, 4

Math & Statistics

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SOLUTIONS MANUAL FOR BASIC COLLEGE MATH EMAT ICS WITH EARLY INTEGERS FOURTH EDITION Elayn Martin-Gay Contents Chapter 1 1 Chapter 2 50 Chapter 3 82 Chapter 4 137 Chapter 5 179 Chapter 6 224 Chapter 7 263 Chapter 8 289 Chapter 9 326 Appendix A 350 Appendix B 354 Appendix C 361 Practice Final Exam 364 Copyright © 2020 Pearson Education, Inc. 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. 67 is written as sixty-seven. 5. 395 is written as three hundred ninety-five. 6. 12,804 is written as tw elve thousa nd, eight hundred four. 7. 321,670,200 is written as three hundred twenty- one million, six hundred seventy thousand, two hundred. 8. Twenty-nine in standard form is 29. 9. Seven hundred ten in standard form is 710. 10. Twenty-six thousand, seventy-one in standard form is 26,071. 11. Six million, five hundred seven in standard form is 6,000,507. 12. 1,047,608 = 1,000,000 + 40,000 + 7000 + 600 + 8 13. a. Find “France” in the le ft column. Then read from left to right until the “Literature” column is reached. We find that 11 Literature Nobel Prize winners were born in France. b. Look at the “Total” column. Three countries have more than 60 Nobel Prize winners. The United States has 259, the United Kingdom has 99, and Germany has 77. Vocabulary, Readiness & Vocabulary 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 1,286 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. Boott Spur 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 fort y-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. 22,806 is written as twen ty-two thousand, eight hundred six. 22. 118,049 is written as one hundred eighteen thousand, forty-nine. 24. 11,378,000 is written as eleven million, three hundred seventy-eight thousand. 26. 11,239 is written as eleven thousand, two hundred thirty-nine. 28. 202,700 is written as two hundred two thousand, seven hundred. Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 2 Copyright © 2020 Pearson Education, Inc. 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. Two thousand eighty in standard form is 2080. 44. One hundred seventy-four million, seven hundred fifty-one thousand dollars in standard form is $174,751,000. 46. Two thousand, five hundred forty-four in standard form is 2544. 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. The elevation of Mt. Washington in standard form is 6288. 6288 is written as six thousand, two hundred eighty-eight. 60. 5712 = 5000 + 700 + 10 + 2 62. The second tallest mountain in New England is Mt. Adams. 64. The British Museum in London had more visitors than the Shanghai Science and Technology Museum in Shanghai. 66. The number of visitors to the Louvre was 8,700,000 which is written as eight million, seven hundred thousand. 68. Three of the museums listed were visited by fewer than 6,000,000 people. 70. The largest number is 77,753. 72. Yes 74. answers may vary 76. 5 trillion in the American system is written as 5,000,000,000,000 in standard form. Section 1.3 Practice Exercises 1. 7235 542 7777+ 2. 11 11 27,364 92,977 120,341+ 3. 11 + 7 + 8 + 9 + 13 20 + 8 + 20 48 4. 112 19 5042 638 526 6225+ 5. 2 cm + 8 cm + 15 cm + 5 cm = 30 cm The perimeter is 30 centimeters. 6. 647 + 647 + 647 = 1941 The perimeter is 1941 feet. 7. 70 50 120+ Georgia produces 120 million pounds of freestone peaches. 8. a. The country with the fewest threatened mammal species corresponds to the shortest bar, which is Malaysia. b. To find the total number of threatened mammal species for Brazil, India, and Mexico, we add. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 3 82 92 95 269+ The total number of threatened mammal species for Brazil, India, and Mexico is 269. Calculator Explorations 1. 89 + 45 = 134 2. 76 + 91 = 173 3. 285 + 55 = 340 4. 8773 + 652 = 9425 5. 985 1210 562 77 2834+ 6. 465 9888 620 1550 12,523+ Vocabulary, Readiness & Video Check 1.3 1. The sum of 0 and any number is the same number . 2. The sum of any number and 0 is the same number . 3. In 35 + 20 = 55, the number 55 is called the sum and 35 and 20 are each called an addend . 4. The distance around a polygon is called its perimeter . 5. 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. 6. 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. 7. To add whole numbers, we line up place values and add from left to right . 8. triangle; 3 9. increased by Exercise Set 1.3 2. 27 31 58+ 4. 37 542 579+ 6. 23 45 30 98+ 8. 236 6243 6479+ 10. 1 41 74 115+ 12. 1 35 470 505+ 14. 1 17, 427 821,059 838,486+ 16. 2 3 5 8 5 7 28+ 18. 2 12 4 8 2610 60+ Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 4 Copyright © 2020 Pearson Education, Inc. 20. 22 64 28 56 25 32 205+ 22. 2 23 49 18 90+ 24. 11 90 900 20 1010+ 26. 111 1624 32 976 2632+ 28. 112 16 1056 748 7770 9590+ 30. 111 427 383 229 1039+ 32. 11 11 67 8 9 4 321 55 5 5 16,665+ 34. 111 864 33 356 1253+ 36. 5000 1400 3021 9421+ 38. 11 1 26 582 47 6 3 62,511 67,882+ 40. 1112 12 504, 218 321,920 38,507 594,687 1, 459,332+ 42. 1 3 3 5 5 16+ The perimeter is 16 kilometers. 44. 1 3 4 5 12+ The perimeter is 12 centimeters. 46. 2 8 4 8 4 24+ The perimeter is 24 miles. 48. 1 23 2323 23 92+ The perimeter is 92 centimeters. 50. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37 The perimeter is 37 inches. 52. 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. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 5 54. “Find the sum” indicates addition. 1 802 6487 7289+ The sum of 802 and 6487 is 7289. 56. “Find the total” indicates addition. 12 89 45 2 19 341 496+ The total of 89, 45, 2, 19, and 341 is 496. 58. “Increased by” indicates addition. 712 38 750+ 712 increased by 38 is 750. 60. “Plus” indicates addition. 121 3565 565 70 4200+ 3565 plus 565 plus 70 is 4200. 62. Add 4850 to 39,250. 11 1 39 250 48 5 0 44 100, ,+ California’s projected population in 2030 is 44,100 thousand. 64. 11 285 98 383+ The distance from Kansas City to Colby is 383 miles. 66. 21 60 45 60 45 210+ The perimeter of the home is 210 feet. 68. 1 240 100 355 500 200 500 1895+ The fluid intake of the patient was 1895 cc. 70. Add 992 to 1305. 1 1305 992 2297+ Hank Aaron batted in 2297 total runs during his career in professional baseball. 72. Find the sum of 22,867,835 and 4,573,567. 11 1 1 1 1 22 867 835 4 573 567 27 441 402,, ,, ,,+ The sheep population was 27,441,402. 74. 21 257 182 257 182 878+ The perimeter of the puzzle is 878 millimeters. 76. 1940 45 1985+ Allyson Felix was born in the year 1985. 78. Of the states listed, Indiana had the fewest CVS pharmacies. 80. 356 + 867 + 756 + 313 + 301 + 486 + 313 + 309 + 408 + 659 = 4768 The total number of CVS pharmacies in the ten states listed in the table was 4768. 82. The total number of pharmacies listed in the table is 4768. 11 4768 3048 7816+ There were 7816 CVS pharmacies in the 50 states. Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 6 Copyright © 2020 Pearson Education, Inc. 84. 5260 1225 6485+ The total highway mileage in Rhode Island is 6485 miles. 86. answers may vary 88. answers may vary 90. 11 2 22 1 78,962 129,968,350 36, 462,880 166,510,192+ 92. 121 773 659 481 1913+ The given answer is correct. 94. 12 19 214 49 651 933+ The given answer is incorrect. Section 1.4 Practice Exercises 1. 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. 2. a. 9143 122 9021− Check : 9021 122 9143+ b. 978 851 127− Check: 127 851 978+ 3. a. 81 7 69 7 49 64 8− Check : 648 49 697+ b. 21 2 326 245 81− Check: 81 245 326+ c. 1234 822 412− Check: 412 822 1234+ 4. a. 9 31 0 10 40 0 164 236− Check: 236 164 400+ b. 9 91010 1 000 762 238− Check: 238 762 1000+ 5. 15,759 458 15,301− The radius of Neptune is 15,301 miles. 6. 92 47 45− The sale price of the suit is $45. Calculator Explorations 1. 865 − 95 = 770 2. 76 − 27 = 49 3. 147 − 38 = 109 4. 366 − 87 = 279 5. 9625 − 647 = 8978 6. 10,711 − 8925 = 1786 Vocabulary, Readiness & Video Check 1.4 1. The difference of any number and that same number is 0 . 2. The difference of any number and 0 is the same number . 3. In 37 − 19 = 18, the number 37 is the minuend , and the number 19 is the subtrahend . ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 7 4. In 37 − 19 = 18, the number 18 is called the difference . 5. 6 − 6 = 0 6. 93 − 93 = 0 7. 600 − 0 = 600 8. 5 − 0 = 5 9. 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. 10. Order does not matter when adding , but order does matter when subtracting . Exercise Set 1.4 2. 72 41 31− Check: 31 41 72+ 4. 572 321 251− Check: 251 321 572+ 6. 286 45 241− Check: 241 45 286+ 8. 5766 324 5442− Check: 5442 324 5766+ 10. 4912 2610 2302− Check: 2302 2610 4912+ 12. 257 257 0− Check: 0 257 257+ 14. 55 29 26− Check: 1 26 29 55+ 16. 80 37 43− Check: 1 43 37 80+ 18. 436 275 161− Check: 1 161 275 436+ 20. 674 299 375− Check: 11 375 299 674+ Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 8 Copyright © 2020 Pearson Education, Inc. 22. 300 149 151− Check: 11 151 149 300+ 24. 773 29 744− Check: 1 744 29 773+ 26. 813 227 586− Check: 11 586 227 813+ 28. 5349 720 4629− Check: 1 4629 720 5349+ 30. 724 16 708− Check: 1 708 16 724+ 32. 300 211 89− Check: 11 89 211 300+ 34. 1983 1914 69− Check: 1 69 1914 1983+ 36. 76,652 29,498 47,154− Check: 11 1 47,154 29, 498 76,652+ 38. 40,000 23,582 16,418− Check: 11 11 16, 418 23,582 40,000+ 40. 6050 1878 4172− Check: 111 4172 1878 6050+ 42. 62, 222 39,898 22,324− Check: 11 11 22,324 39,898 62, 222+ 44. 21 9 12− 21 subtract 9 is 12. 46. 16 5 11− The difference of 16 and 5 is 11. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 9 48. 59 41 18− 59 subtract 41 is 18. 50. 25 12 13− 25 less 12 is 13. 52. 90 86 4− 86 subtracted from 90 is 4. 54. 59,320 55, 492 3 828− They traveled 3828 miles on their trip. 56. 197 98 99− Kelp can grow 99 feet taller than bamboo. 58. 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. 60. 189,000 75,000 114,000− The Upper Mississippi sub-basin drains 114,000 square miles more than the Lower Mississippi sub-basin. 62. 68 58 10− The low temperature was 10 ° Fahrenheit. 64. 845 649 196− She will have $196 left in her savings account. 66. 243 185 58− Pat’s blood cholesterol level should be decreased by 58. 68. 547 99 448− The sale price of the stereo is $448. 70. 38 708 62 0 8 32 500, ,− There were 32,500 official participants for the 2017 Boston Marathon. 72. The shortest bar corresponds to the quietest reading. Leaves rustling is the quietest. 74. 100 70 30− The difference in sound intensity between live rock music and loud television is 30 dB. 76. 117,006 83, 424 33,582− The population of Springfield was 33,582 greater than the population of Champaign. 78. 276 27 249− The increase in the number of California condors is 249. 80. New York JFK International and Denver International airports have 60 million or fewer passengers per year. 82. 104 81 23− Hartsfield-Jackson Atlanta International Airport has 23 million more passengers per year than the Los Angeles International Airport. 84. Student A Budget 1 600 200 150120 1070+ 1200 1070 130− Student A would have an excess of $130. Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 10 Copyright © 2020 Pearson Education, Inc. Student B Budget 11 300 400 240170 1110+ 1200 1110 90− Student B would have an excess of $90. 86. 986 48 938− 88. 22 80 93 17 9 2 201+ 90. 10,000 17 8 6 82 1 4− 92. 12,468 3 211 19 8 8 17,667+ 94. In 2863 1904−, 2863 is the minuend and 1904 is the subtrahend. 96. In find 86 decreased by 25, 86 is the minuend and 25 is the subtrahend. 98. 478 89 389− The given answer is correct. Check: 1 389 89 478+ 100. 7615 547 7068− The given answer is incorrect. Check: 7068 547 7615+ 102. 10, 244 85 3 4 17 1 0− 104. answers may vary Section 1.5 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 dig it 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 dig it 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 dig it 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. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 11 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 3 000 18,166 rounds to 18 000 189 rounds to + 0 21,000+ The total number of reported cases of these preventable diseases was 21,000 in 2015. Vocabulary, Readiness & Video Check 1.5 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 . 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 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 1.5 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. Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 12 Copyright © 2020 Pearson Education, Inc. 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 15,667 to the nearest thousand, observe that the digit in the hundreds place is 6. Since this digit is at least 5, we add 1 to the digit in the thousands place. Therefore, 15,667 restaurants rounded to the nearest thousand is 16,000 restaurants. 30. To round 60,149 to the nearest hundred, observe that the digit in the tens place is 4. Since this digit is less than 5, we do not add 1 to the digit in the hundreds place. Therefore, 60,149 days rounded to the nearest hundred is 60,100 days. 32. To round 324,758,293 to the nearest million, observe that the digit in the hundred-thousands place is 7. Since this digit is at least 5, we add 1 to the digit in the millions place. Therefore, 324,758,293 rounded to the nearest million is 325,000,000. 34. To round 2,110,000 to the nearest million, observe that the digit in the hundred-thousands place is 1. Since this dig it 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. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 13 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 was approximately 2000 credit hours. 64. $3370 million written in standard form is $3,370,000,000. $3,370,000,000 rounded to the nearest hundred-million is $3,400,000,000. $3,370,000,000 rounded to the nearest billion is $3,000,000,000. 66. $4670 million written in standard form is $4,670,000,000. $4,670,000,000 rounded to the nearest hundred-million is $4,700,000,000. $4,670,000,000 rounded to the nearest billion is $5,000,000,000. 68. 5698, for example, rounded to the nearest ten is 5700. 70. In 950, the digit in the tens place is 5, which is greater than 5, so to round 950 to the nearest hundred, we add 1 to the digit in the hundreds place. 950 rounded to the nearest hundred is 1000. 72. In 48, the digit in the tens place is 4, which is less than 5, so to round 48 to the nearest hundred, we do not add 1 to the digit in the hundreds place. 48 rounded to the nearest hundred is 0. 74. The largest possible number that rounds to 8600 is 8649. 76. answers may vary 78. 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 1.6 Practice Exercises 1. a. 3 × 0 = 0 b. 4(1) = 4 c. (0)(34) = 0 d. 1 ⋅ 76 = 76 2. a. 5(2 + 3) = 5 ⋅ 2 + 5 ⋅ 3 b. 9(8 + 7) = 9 ⋅ 8 + 9 ⋅ 7 c. 3(6 + 1) = 3 ⋅ 6 = 3 ⋅ 1 3. a. 2 36 4 144× b. 21 132 9 1188× 4. a. 594 72 11 8 8 41 580 42,768× Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 14 Copyright © 2020 Pearson Education, Inc. b. 306 81 306 24 480 24,786× 5. a. 726 142 1 452 29 040 72 600 103,092× b. 288 4 1152× 6. 75 ⋅ 100 = 7500 7. 808 ⋅ 1000 = 808,000 8. 35 3 105× 35 ⋅ 3000 = 105,000 Attach 3 zeros. 9. 600 ⋅ 600 = 360,000 10. Area length width (360 miles)(280 miles) 100,800 square miles=⋅ == The area of Wyoming is 100,800 square miles. 11. 16 45 80 640720× The printer can print 720 pages in 45 minutes. 12. 81 1 8 8 59 4 5×= ×= 1 8845 133+ The total cost is $133. 13. 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 1.6 1. The product of 0 and any number is 0 . 2. The product of 1 and any number is the number . 3. In 8 ⋅ 12 = 96, the 96 is called the product and 8 and 12 are each called a factor . 4. Since 9 ⋅ 10 = 10 ⋅ 9, we say that changing the order in multiplication does not change the product. This property is called the commutative property of multiplication. 5. Since (3 ⋅ 4) ⋅ 6 = 3 ⋅ (4 ⋅ 6), we say that changing the grouping in multiplication does not change the product. This property is called the associative property of multiplication. 6. Area measures the amount of surface of a region. 7. Area of a rectangle = length ⋅ width. 8. We know 9(10 + 8) = 9 ⋅ 10 + 9 ⋅ 8 by the distributive property. 9. distributive property 10. To show that 8649 is actually multiplied by 70 and not by just 7. 11. Think of 50 times 9 and then attach the two zeros from 900, or think of 5 times 9 and then attach the three zeros at the end of 50 and 900. Both approaches give us 45,000. 12. Area is measured in square units, and here we have meters times meters, or square meters; the answer is 63 square meters. 13. Multiplication is also an application of addition since it is addition of the same addend. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 15 Exercise Set 1.6 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 63706552× 26. 526 23 15 7 8 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 56 4 9 16 140 80 700 102,489× 40. 1234 567 86 3 8 74 040 617 000 699,678× 42. 426 110 4 260 42 600 46,860× 44. 1876 1407 13 132 750 400 1 876 000 2,639,532× 46. 6 × 100 = 600 48. 26 × 1000 = 26,000 50. 9054 ⋅ 10 = 90,540 52. 3 ⋅ 9 = 27 3 ⋅ 9000 = 27,000 (attach 3 zeros) Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 16 Copyright © 2020 Pearson Education, Inc. 54. 7 ⋅ 3 = 21 70 ⋅ 300 = 21,000 (attach 3 zeros) 56. 27 ⋅ 5 = 135 27 ⋅ 50,000 = 1,350,000 (attach 4 zeros) 58. Area (length)(width) (13 inches)(3 inches) 39 square inches= == Perimeter length width length width 13 3 13 3 32 inches=+ ++ =+ ++ = 60. Area (length)(width) (25 centimeters)(20 centimeters) 500 square centimeters= == Perimeter length width length width 25 20 25 20 90 centimeters=+ ++ =+++ = 62. 982 rounds to 1000 650 rounds to 700 700,000×× 64. 111 rounds to 100 999 rounds to 1000 100,000×× 66. 2872 × 12 is approximately 2872 × 10, which is 28,720. The best estimate is b. 68. 706 × 409 is approximately 700 × 400, which is 280,000. The best estimate is d. 70. 70 12 (7 10) 12 7 (10 12)71 2 0 840×=× × =× ×=×= 72. 9 × 900 = 8100 74. 3310 3 9930× 76. 14 8 112× There are 112 grams of fat in 8 ounces of hulled sunflower seeds. 78. 34 14 136 340 476× There are 476 seats in the room. 80. a. 5 × 4 = 20 There are 20 apartments on one floor. b. 20 3 60× There are 60 apartments in the building. 82. Area (length)(width) (60 feet)(45 feet) 2700 square feet= == The area is 2700 square feet. 84. Area (length)(width) (776 meters)(639 meters) 495,864 square meters= == The area is 495,864 square meters. 86. 700 17 49 0 0 70 0 0 11,900× The 17 discs hold 11,900 MB. 88. 365 3 1095× A cow eats 1095 pounds of grain each year. 90. 14 16 84 140 224× There are 224 grams of fat in 16 ounces. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 17 92. 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 94. 16 × 3 = 48 There were 48 million “older” Americans in 2016. 96. 126 8 118− 98. 47 + 26 + 10 + 231 + 50 = 364 100. 19 4 76× The product of 19 and 4 is 76. 102. 19 4 23+ The total of 19 and 4 is 23. 104. 11 + 11 + 11 + 11 + 11 + 11 = 6 ⋅ 11 or 11 ⋅ 6 106. a. 4 ⋅ 5 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4 b. answers may vary 108. 31 50 1550× 110. 57 × 3 = 171 57 × 6 = 342 The problem is 57 63× 112. answers may vary 114. 3 × 402 = 1206 2 × 403 = 806 1206 + 806 + 363 = 2375 Stephen Curry scored 2375 points during the 2015 −2016 regular season. Section 1.7 Practice Exercises 1. a. 8 97 2 because 8 ⋅ 9 = 72. b. 40 ÷ 5 = 8 because 8 ⋅ 5 = 40. c. 2446= because 4 ⋅ 6 = 24. 2. a. 717= because 1 ⋅ 7 = 7. b. 5 ÷ 1 = 5 because 5 ⋅ 1 = 5. c. 11 11 1 because 11 ⋅ 1 = 11. d. 4 ÷ 1 = 4 because 4 ⋅ 1 = 4. e. 10101= because 10 ⋅ 1 = 10. f. 21 ÷ 21 = 1 because 1 ⋅ 21 = 21. 3. a. 007= because 0 ⋅ 7 = 0. b. 0 80 because 0 ⋅ 8 = 0. c. 5 ÷ 0 is undefined because if 5 ÷ 0 is a number, then the number times 0 would be 5. d. 0 ÷ 14 = 0 because 0 ⋅ 14 = 0. 4. a. 818 6 4908 48 10 6 48 48 0− − − Check: 818 6 4908× Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 18 Copyright © 2020 Pearson Education, Inc. b. 553 4 2212 20 21 20 12 12 0− − − Check: 553 4 2212× c. 251 37 5 3 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. 51 0 0 94 5 , 9 0 0 45 09 9 000− − Check: 5100 × 9 = 45,900 6. a. 234 R 3 49 3 9 8 13 12 19 16 3− − − Check: 234 ⋅ 4 + 3 = 939 b. 657R 2 53 2 8 7 30 28 25 37 35 2− − − Check: 657 ⋅ 5 + 2 = 3287 7. a. 9067 R 2 98 1 , 6 0 5 81 06 0 60 54 65 63 2− − − − Check: 9067 ⋅ 9 + 2 = 81,605 b. 5827 R 2 42 3 , 3 1 0 20 33 32 11 8 30 28 2− − − − Check: 5827 ⋅ 4 + 2 = 23,310 ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 19 8. 524 R 12 17 8920 85 42 34 80 68 12− − − 9. 49 R 60 678 33,282 27 12 61 6 2 61 0 2 60− − 10. 57 31 7 1 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 71 2 6 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. 32,886261126= 6. 143,088542264= 7. 0 ÷ 315 = 0 8. 315 ÷ 0 is an error. Vocabulary, Readiness & Video Check 1.7 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 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 is used to separate a quantity into equal parts. 11. addition and division Exercise Set 1.7 2. 72 ÷ 9 = 8 4. 24 ÷ 3 = 8 6. 0 ÷ 4 = 0 8. 38 ÷ 1 = 38 Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 20 Copyright © 2020 Pearson Education, Inc. 10. 49149= 12. 4559= 14. 12 is undefined0 16. 6 ÷ 6 = 1 18. 7 ÷ 0 is undefined 20. 18 ÷ 3 = 6 22. 17 58 5 5 35 35 0− − Check: 17 ⋅ 5 = 85 24. 80 86 4 0 64 00− Check: 80 ⋅ 8 = 640 26. 526 4 2104 20 10 8 24 24 0− − − Check: 526 ⋅ 4 = 2104 28. 0030= Check: 0 ⋅ 30 = 0 30. 7 85 6 56 0− Check: 7 ⋅ 8 = 56 32. 11 11 121 11 11 11 0− − Check: 11 ⋅ 11 = 121 34. 60R 6 74 2 6 42 06− Check: 60 ⋅ 7 + 6 = 426 36. 413R 1 3 1240 12 04 3 10 9 1− − − Check: 413 ⋅ 3 + 1 = 1240 38. 55R 2 3 167 15 17 15 2− − Check: 55 ⋅ 3 + 2 = 167 40. 833R 1 43 3 3 3 32 13 12 13 12 1− − − Check: 833 ⋅ 4 + 1 = 3333 42. 32 23 736 69 46 46 0− − Check: 32 ⋅ 23 = 736 ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 21 44. 48 42 2016 168 336 336 0− − Check: 48 ⋅ 42 = 2016 46. 44R 2 44 1938 176 178 176 2− − Check: 44 ⋅ 44 + 2 = 1938 48. 612R 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 14 9 2 14 4 0 52− − Check: 96 ⋅ 240 + 52 = 23,092 58. 201 R 50 203 40,853 40 6 25 0 253 203 50− − − Check: 201 ⋅ 203 + 50 = 40,853 60. 303R 63 543 164,592 162 9 16 9 0 1 692 1 629 63− − − Check: 303 ⋅ 543 + 63 = 164,592 62. 13 81 0 4 8 24 24 0− − Chapter 1: The Whole Numbers ISM: Basic College Mathematics with Early Integers 22 Copyright © 2020 Pearson Education, Inc. 64. 603R 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. 30 4 0 214 650,560 642 85 0 85 6 85 6 00 0 0− − − − 70. 13 R 3 79 4 7 24 21 3− − The quotient is 13 R 3. 72. 3R 20 32 116 9620− 116 divided by 32 is 3 R 20. 74. 15R 3 57 8 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. 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. ISM: Basic College Mathematics with Early Integers Chapter 1: The Whole Numbers Copyright © 2020 Pearson Education, Inc. 23 84. 23R 1 81 8 5 16 25 24 1− − Yes, she has enough for a 22-student class. There is one 8-foot length and 1 additional foot of rope left over. That is, she has 9 feet of extra rope. 86. 20 61 2 0 12 00− David Johnson made 20 touchdowns during 2016. 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 61 8 0 18 00− 180Average 306== 92. 21 121 200 185 176 163 845+ 169 58 4 5 5 34 30 45 45 0− − − 845Average 1695== 94. 2 92 9690 85 92 79 534+ 89 65 3 4 48 54 54 0− − 534Average 896== 96. 53 4030 123+ 41 3 123 12 03 3 0− − The average temperature is 41 °. 98. 11 23 407 92 7011 7533+ 100. 712 54 2 848 35 600 38,448× 102. 712 54 658− 104. 0023= because 0 ⋅ 23 = 0 106. 9R 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.