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Solution Manual for Developmental Mathematics, 4th Edition

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     S OLUTIONS M ANUAL D EVELOPMENTAL M ATHEMATICS F OURTH E DITION Elayn Martin-Gay University of New Orleans

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    Contents Chapter 1 1 Chapter 2 50 Chapter 3 85 Chapter 4 133 Chapter 5 171 Chapter 6 219 Chapter 7 247 Chapter 8 271 Chapter 9 307 Chapter 10 369 Chapter 11 428 Chapter 12 473 Chapter 13 519 Chapter 14 559 Chapter 15 611 Chapter 16 647 Appendices 702 Practice Final Exam 736

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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. 67 is written as sixty-seven. 5. 395 is written as three hundred ninety-five. 6. 12,804 is written as twelve thousand, 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 left 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 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. 22,806 is written as twenty-two thousand, eight hundred six. 22. 118,049 is written as one hundred eighteen thousand, forty-nine. 24. 347,219 is written as three hundred forty-seven thousand, two hundred nineteen. 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: Developmental Mathematics 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. Two thousand eighty in standard form is 2080. 44. Ninety-one million, seventy-one thousand dollars in standard form is $91,071,000. 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. 1 1 1 1 27,364 92,977 120,341 + 3. 11 + 7 + 8 + 9 + 13 20 + 8 + 20 48 4. 1 1 2 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.

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    ISM: Developmental Mathematics Chapter 1: The Whole Numbers 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 26 10 60 +

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    Chapter 1: The Whole Numbers ISM: Developmental Mathematics 4 20. 2 2 64 28 56 25 32 205 + 22. 2 23 49 18 90 + 24. 1 1 90 900 20 1010 + 26. 1 1 1 1624 32 976 2632 + 28. 1 1 2 16 1056 748 7770 9590 + 30. 1 1 1 427 383 229 1039 + 32. 1 1 1 1 6 789 4 321 5 555 16, 665 + 34. 1 1 1 864 33 356 1253 + 36. 5000 1400 3021 9421 + 38. 1 1 1 26 582 4 763 62,511 67,882 + 40. 1 1 1 2 1 2 504, 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 23 23 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.

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    ISM: Developmental Mathematics Chapter 1: The Whole Numbers 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. 1 2 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. 1 2 1 3565 565 70 4200 + 3565 plus 565 plus 70 is 4200. 62. Add 4850 to 39,250. 1 1 1 39 250 4 850 44 100 , , + California’s projected population in 2030 is 44,100 thousand. 64. 1 1 285 98 383 + The distance from Kansas City to Colby is 383 miles. 66. 2 1 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. 1 1 1 1 1 1 22 867 835 4 573 567 27 441 402 , , , , , , + The sheep population was 27,441,402. 74. 2 1 257 182 257 182 878 + 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. 1 1 4768 3048 7816 + There were 7816 CVS pharmacies in the 50 states.

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    Chapter 1: The Whole Numbers ISM: Developmental Mathematics 6 84. 5260 1225 6485 + The total highway mileage in Rhode Island is 6485 miles. 86. answers may vary 88. answers may vary 90. 1 1 2 2 2 1 78,962 129,968,350 36, 462,880 166,510,192 + 92. 1 2 1 773 659 481 1913 + The given answer is correct. 94. 1 2 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. 8 17 69 7 4 9 64 8 − Check : 648 49 697 + b. 2 12 326 245 81 − Check: 81 245 326 + c. 1234 822 412 − Check: 412 822 1234 + 4. 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 + 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.

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    ISM: Developmental Mathematics Chapter 1: The Whole Numbers 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: 1 1 375 299 674 +

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    Chapter 1: The Whole Numbers ISM: Developmental Mathematics 8 22. 300 149 151 − Check: 1 1 151 149 300 + 24. 773 29 744 − Check: 1 744 29 773 + 26. 813 227 586 − Check: 1 1 586 227 813 + 28. 5349 720 4629 − Check: 1 4629 720 5349 + 30. 724 16 708 − Check: 1 708 16 724 + 32. 300 211 89 − Check: 1 1 89 211 300 + 34. 1983 1914 69 − Check: 1 69 1914 1983 + 36. 76,652 29, 498 47,154 − Check: 1 1 1 47,154 29, 498 76, 652 + 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. 21 9 12 − 21 subtract 9 is 12. 46. 16 5 11 − The difference of 16 and 5 is 11.

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    ISM: Developmental Mathematics Chapter 1: The Whole Numbers 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 6 208 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 1 600 200 150 120 1070 + 1200 1070 130 − Student A would have an excess of $130.

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    Chapter 1: The Whole Numbers ISM: Developmental Mathematics 10 Student B Budget 1 1 300 400 240 170 1110 + 1200 1110 90 − Student B would have an excess of $90. 86. 986 48 938 − 88. 2 2 80 93 17 9 2 201 + 90. 10, 000 1 786 8 214 − 92. 12, 468 3 211 1 988 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 8 534 1 710 − 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 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.

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    ISM: Developmental Mathematics Chapter 1: The Whole Numbers 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.

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    Chapter 1: The Whole Numbers ISM: Developmental Mathematics 12 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 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.

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