SOLUTIONS MANUAL C TRIMBLE & ASSOCIATES
PREALGEBRA NINTH EDITION
Elayn Martin-Gay
Contents
Chapter 1
1
Chapter 2
42
Chapter 3
71
Chapter 4
101
Chapter 5
164
Chapter 6
209
Chapter 7
246
Chapter 8
284
Chapter 9
330
Chapter 10
370
Appendices
389
Practice Final Exam
392
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 tenthousands. 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.
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. Dachsund Exercise Set 1.2
7. 679,430,105 is written as six hundred seventynine million, four hundred thirty thousand, one hundred five.
2. The place value of the 5 in 905 is ones.
8. Thirty-seven in standard form is 37.
6. The place value of the 5 in 79,050,000 is tenthousands.
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.
4. The place value of the 5 in 6527 is hundreds.
8. The place value of the 5 in 51,682,700 is tenmillions. 10. 316 is written as three hundred sixteen. 12. 5445 is written as five thousand, four hundred forty-five.
12. 4,026,301 = 4,000,000 + 20,000 + 6000 + 300 + 1
14. 42,009 is written as forty-two thousand, nine.
13. a.
16. 3,204,000 is written as three million, two hundred four thousand.
Find Australia in the “Country” column. Read from left to right until the “bronze” column is reached. Australia won 22 bronze medals.
b. Find the countries for which the entry in the “Total” column is greater than 60. The United States, China, ROC, 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.
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. 105,447 is written as one hundred five thousand, four hundred forty-seven. 24. 1,110,000,000 is written as one billion, one hundred ten 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. 30. Four thousand, four hundred sixty-eight in standard form is 4468.
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Chapter 1: The Whole Numbers
ISM: Prealgebra
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.
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.
47,364 + 135,898 183, 262
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.
1 1 11
42. One thousand, eight hundred fifteen in standard form is 1815. 44. Two hundred sixty million, one hundred thirtyeight thousand, five hundred sixty-nine dollars in standard form is $260,138,569. 46. Seven hundred fifteen in standard form is 715. 48. 789 = 700 + 80 + 9 50. 6040 = 6000 + 40 52. 20,215 = 20,000 + 200 + 10 + 5
3. Notice 12 + 8 = 20 and 4 + 6 = 10. 12 + 4 + 8 + 6 + 5 = 20 + 10 + 5 = 35 12 2
4.
6432 789 54 + 28 7303
5. a.
54. 99,032 = 90,000 + 9000 + 30 + 2
b. 20 − 8 = 12 because 12 + 8 = 20
56. 47,703,029 = 40,000,000 + 7,000,000 + 700,000 + 3000 + 20 + 9
c.
58. Mount Baker erupted in 1792, which is in standard form.
62. Mount St. Helens has an eruption listed in 1980. All other eruptions listed in the table occurred before this one. 64. More Golden retrievers are registered than German shepherds.
6. a.
9143 − 122 9021
Check: 9021 + 122 9143
b.
978 − 851 127
Check:
7. a.
69 7 −49 64 8
70. The largest number is 77,753. 72. Yes
127 + 851 978
8 17
66. French bulldogs are second in popularity. 24 is written as twenty-four. 68. The maximum height of an average-size standard dachsund is 9 inches.
93 − 93 = 0 because 0 + 93 = 93.
d. 42 − 0 = 42 because 42 + 0 = 42.
60. Mount Shasta and Mount St. Helens have each had two eruptions listed.
2
14 − 6 = 8 because 8 + 6 = 14.
Check: 648 + 49 697
2 12
b.
326 − 245 81
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Check:
81 + 245 326
ISM: Prealgebra
c.
1234 − 822 412
Chapter 1: The Whole Numbers
Check:
412 + 822 1234
40 0 −1 6 4 2 3 6
Check:
236 + 164 400
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.
11. 9625 − 647 = 8978
Vocabulary, Readiness & Video Check 1.3
91010
10 0 0 −762 238
10. 366 − 87 = 279
12. 10,711 − 8925 = 1786
9
b.
8. 76 − 27 = 49 9. 147 − 38 = 109
9 3 1010
8. a.
7. 865 − 95 = 770
The country with the fewest threatened amphibians corresponds to the shortest bar, which is Peru.
b. To find the total number of threatened amphibians for Brazil, Peru, and Mexico, we add. 110 78 + 191 379 The total number of threatened amphibians for Brazil, Peru, and Mexico is 379. Calculator Explorations
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.
2. 76 + 97 = 173
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.
3. 285 + 55 = 340
11. triangle; 3
4. 8773 + 652 = 9425
12. To find the additional money needed to purchase, subtract the savings account amount from the purchase price.
1. 89 + 45 = 134
5. 985 + 1210 + 562 + 77 = 2834 6. 465 + 9888 + 620 + 1550 = 12,523
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3
Chapter 1: The Whole Numbers
ISM: Prealgebra
Exercise Set 1.3 2.
27 + 31 58
4.
37 + 542 579
6.
23 45 + 30 98
8.
236 + 6243 6479
111
20.
1 11 2 1 2
1
10.
17, 427 + 821, 059 838, 486
12.
3 5 8 5 +7 28
22.
504, 218 321,920 38,507 + 594, 687 1, 459,332
24.
957 − 257 700
Check:
700 + 257 957
26.
55 − 29 26
Check:
26 + 29 55
28.
674 − 299 375
Check:
375 + 299 674
30.
300 − 149 151
Check:
32.
5349 − 720 4629
Check: 4629 + 720 5349
34.
724 − 16 708
Check: 708 + 16 724
36.
1983 − 1914 69
Check:
1
11
11
22
14.
64 28 56 25 + 32 205 11 2
16.
16 1056 748 + 7770 9590 1 111
18.
4
6789 4321 + 5555 16, 665
26 582 4 763 + 62,511 67,882
151 + 149 300 1
1
1
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69 + 1914 1983
ISM: Prealgebra
Chapter 1: The Whole Numbers
11 11
38.
40, 000 − 23,582 16, 418
Check:
6050 − 1878 4172
Check:
16, 418 + 23,582 40, 000 111
40.
4172 + 1878 6050 11 11
42.
62, 222 − 39,898 22,324
44.
986 − 48 938
Check:
22,324 + 39,898 62, 222
80 93 17 9 +2 201
802 + 6487 7289 The sum of 802 and 6487 is 7289.
62. “Find the total” indicates addition. 12
89 45 2 19 + 341 496 The total of 89, 45, 2, 19, and 341 is 496.
66. “Increased by” indicates addition. 712 + 38 750 712 increased by 38 is 750.
48. 10, 000 − 1786 8214
68. “Less” indicates subtraction. 25 − 12 13 25 less 12 is 13.
1 11
50.
1
64. “Find the difference” indicates subtraction. 16 − 5 11 The difference of 16 and 5 is 11.
2
46.
60. “Find the sum” indicates addition.
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.
70. “Subtracted from” indicates subtraction. 90 − 86 4 86 subtracted from 90 is 4.
56. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37 The perimeter is 37 inches.
72. Subtract 7953 million from 8687 million. 8687 − 7953 734 The world’s projected population increase is 734 million.
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.
74. Subtract the discount from the regular price. 276 − 69 207 The first-year price is $207.
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5
Chapter 1: The Whole Numbers 76.
78.
ISM: Prealgebra
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.
94. North Carolina has the fewest Aldi locations.
189, 000 − 75, 000 114, 000 The Upper Mississippi sub-basin drains 114,000 square miles more than the Lower Mississippi sub-basin.
98. The total number of Aldi locations in the states listed is 1335. 1335 + 923 2258 There are 2258 Aldi locations in the United States.
80. Opposite sides of a rectangle have the same length. 60 + 45 + 60 + 45 = 210 The perimeter is 210 feet. 82.
84.
59,320 − 55, 492 3 828 They traveled 3828 miles on their trip. 299,345 + 259,516 558,861 The total number of F-Series trucks and Silverados sold during the first six months of 2022 was 558,861.
96. 211 + 92 + 203 + 98 + 92 + 123 + 91 + 152 + 146 + 127 = 1335 The total number of Aldi locations in the ten states listed is 1335.
11 1
100.
102. The minuend is 2863 and the subtrahend is 1904. 104. The minuend is 86 and the subtrahend is 25. 106. answers may vary 21
108.
86. The shortest bar corresponds to the quietest reading. Leaves rustling is the quietest. 88.
90.
100 − 70 30 The difference in sound intensity between live rock music and loud television is 30 dB. 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.
6
605 + 9779 10,384 The total highway mileage in Kansas is 10,384 miles.
773 659 + 481 1913 The given sum is correct. 1 2
110.
19 214 49 + 651 933 The given sum is incorrect, the correct sum is 933.
112.
389 + 89 478 The given difference is correct.
11
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ISM: Prealgebra
Chapter 1: The Whole Numbers 3. a.
11
114.
116.
7168 + 547 7715 The given difference is incorrect. 7615 − 547 7068
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.
10, 244 − 8 534 1 710
c.
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.
2. a.
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. 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.
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.
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 25 32 51 98
rounds to rounds to rounds to rounds to rounds to
50 30 30 50 + 100 260
5.
3785 − 2479
rounds to rounds to
4000 − 2000 2000
6.
11 16 19 + 31
10 20 20 + 30 80 The total distance is approximately 80 miles.
7.
18, 617 − 1 607
rounds to rounds to rounds to rounds to
rounds to rounds to
18,600 − 1 600 17, 000 The difference in the reported number of pertussis cases between 2019 and 2021 was 17,000.
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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