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Chapter 1
Section 1.2
4. The number 900 + 60 + 5 is written in expanded
form.
Practice Problems
5. In a whole number, each group of 3 digits is
called a period.
1. The place value of the 8 in 38,760,005 is
millions.
6. The place value of the digit 4 in the whole
number 264 is ones.
2. The place value of the 8 in 67,890 is hundreds.
3. The place value of the 8 in 481,922 is tenthousands.
Exercise Set 1.2
1. The place value of the 5 in 657 is tens.
4. 54 is written as fifty-four.
2. The place value of the 5 in 905 is ones.
5. 678 is written as six hundred seventy-eight.
3. The place value of the 5 in 5423 is thousands.
6. 93,205 is written as ninety-three thousand, two
hundred five.
4. The place value of the 5 in 6527 is hundreds.
5. The place value of the 5 in 43,526,000 is
hundred-thousands.
7. 679,430,105 is written as six hundred seventynine million, four hundred thirty thousand, one
hundred five.
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.
7. The place value of the 5 in 5,408,092 is millions.
10. Eight thousand, two hundred seventy-four in
standard form is 8,274 or 8274.
8. The place value of the 5 in 51,682,700 is tenmillions.
11. Five million, fifty-seven thousand, twenty-six in
standard form is 5,057,026.
9. 354 is written as three hundred fifty-four.
10. 316 is written as three hundred sixteen.
12. 4,026,301
= 4,000,000 + 20,000 + 6000 + 300 + 1
13. a.
11. 8279 is written as eight thousand, two hundred
seventy-nine.
Find Norway in the left-hand column. Read
from left to right until the “gold” column is
reached. Norway won 96 gold medals.
12. 5445 is written as five thousand, four hundred
forty-five.
13. 26,990 is written as twenty-six thousand, nine
hundred ninety.
b. Find the countries for which the entry in the
first column (gold) is greater than 100.
Germany and Russia have won more than
100 gold medals.
14. 42,009 is written as forty-two thousand, nine.
15. 2,388,000 is written as two million, three
hundred eighty-eight thousand.
Vocabulary and Readiness Check
1. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, ... are called whole numbers.
16. 3,204,000 is written as three million, two
hundred four thousand.
2. The number 1,286 is written in standard form.
17. 24,350,185 is written as twenty-four million,
three hundred fifty thousand, one hundred
eighty-five.
3. The number “twenty-one” is written in words.
1
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Chapter 1: The Whole Numbers
ISM: Prealgebra
18. 47,033,107 is written as forty-seven million,
thirty-three thousand, one hundred seven.
37. Two hundred sixty thousand, nine hundred
ninety-seven in standard form is 260,997.
19. 65,773 is written as sixty-five thousand, seven
hundred seventy-three.
38. Six hundred forty thousand, eight hundred
eighty-one in standard form is 640,881.
20. 40,000 is written as forty thousand.
39. Three hundred fifty-three in standard form is
353.
21. 1679 is written as one thousand, six hundred
seventy-nine.
40. Two hundred thirty-four thousand in standard
form is 234,000.
22. 6912 is written as six thousand, nine hundred
twelve.
41. Four hundred eighty-four thousand, two hundred
thirty-five in standard form is 484,235.
23. 2,800,000 is written as two million, eight
hundred thousand.
42. One thousand, eight hundred fifteen in standard
form is 1815.
24. 15,200,000 is written as fifteen million, two
hundred thousand.
43. Fifty-four million, five hundred thousand in
standard form is 54,500,000.
25. 11,239 is written as eleven thousand, two
hundred thirty-nine.
44. Fifty million, thirteen thousand, eight hundred
fifty-nine in standard form is 50,013,859.
26. 14,433 is written as fourteen thousand, four
hundred thirty-three.
45. Seven hundred fourteen in standard form is 714.
46. Seven hundred fifty-five in standard form is 755.
27. 202,700 is written as two hundred two thousand,
seven hundred.
47. 209 = 200 + 9
28. 799,000 is written as seven hundred ninety-nine
thousand.
48. 789 = 700 + 80 + 9
49. 3470 = 3000 + 400 + 70
29. Six thousand, five hundred eighty-seven in
standard form is 6587.
50. 6040 = 6000 + 40
30. Four thousand, four hundred sixty-eight ion
standard form is 4468.
51. 80,774 = 80,000 + 700 + 70 + 4
52. 20,215 = 20,000 + 200 + 10 + 5
31. Fifty-nine thousand, eight hundred in standard
form is 59,800.
53. 66,049 = 60,000 + 6000 + 40 + 9
32. Seventy-three thousand, two in standard form is
73,002.
54. 99,032 = 90,000 + 9000 + 30 + 2
33. Thirteen million, six hundred one thousand,
eleven in standard form is 13,601,011.
55. 39,680,000
= 30,000,000 + 9,000,000 + 600,000 + 80,000
34. Sixteen million, four hundred five thousand,
sixteen in standard form is 16,405,016.
56. 47,703,029 = 40,000,000 + 7,000,000 + 700,000
+ 3000 + 20 + 9
35. Seven million, seventeen in standard form is
7,000,017.
57. The elevation of Mt. Clay is 5532 which is five
thousand, five hundred thirty-two in words.
36. Two million, twelve in standard form is
2,000,012.
58. The elevation of Mt. Washington is 6288 which
is six thousand, two hundred eighty-eight in
words.
2
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
59. The height of Boott Spur is 5492 which is
5000 + 400 + 90 + 2 in expanded form.
1 1 11
2.
60. The height of Mt. Jefferson is 5712 which is
5000 + 700 + 10 + 2 in expanded form.
47,364
+ 135,898
183, 262
61. Mt. Washington is the tallest mountain in New
England.
3. Notice 12 + 8 = 20 and 4 + 6 = 10.
12 + 4 + 8 + 6 + 5 = 20 + 10 + 5 = 35
62. Mt. Adams is the second tallest mountain in
New England.
4.
12 2
63. Chihuahua has fewer dogs registered than
Golden retriever.
64. Beagle has more dogs registered than Yorkshire
terrier.
6432
789
54
+ 28
7303
5. a.
65. Labrador retrievers have the most registrations;
146,714 is written as one hundred forty-six
thousand, seven hundred fourteen.
b. 20 − 8 = 12 because 12 + 8 = 20
c.
66. Chihuahuas have the fewest registrations; 24,853
is written as twenty-four thousand, eight hundred
fifty-three.
93 − 93 = 0 because 0 + 93 = 93.
d. 42 − 0 = 42 because 42 + 0 = 42.
6. a.
9123
− 142
8981
Check: 8981
+ 142
9123
b.
978
− 851
127
Check:
7. a.
69 7
−49
64 8
67. The maximum weight of an average-size
Dachshund is 25 pounds.
68. The maximum height of an average-size
Yorkshire terrier is 9 inches.
69. The largest number is 9861.
127
+ 851
978
8 17
70. The largest number is 77,753.
71. No; 105.00 should be written as one hundred
five.
72. Yes
Check: 648
+ 49
697
2 12
73. answers may vary
b.
326
− 245
81
Check:
81
+ 245
326
c.
1234
− 822
412
Check:
412
+ 822
1234
Check:
236
+ 164
400
74. answers may vary
75. 135.5 trillion in standard form is
135,500,000,000,000.
Section 1.3
Practice Problems
1.
14 − 6 = 8 because 8 + 6 = 14.
4135
+ 252
4387
8. a.
9
31010
40 0
−1 6 4
2 3 6
3
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
Vocabulary and Readiness Check
9
910 10
b.
10 0 0
−762
238
Check:
1. The sum of 0 and any number is the same
number.
238
+ 762
1000
2. In 35 + 20 = 55, the number 55 is called the sum
and 35 and 20 are each called an addend.
9. 2 cm + 8 cm + 15 cm + 5 cm = 30 cm
The perimeter is 30 centimeters.
3. The difference of any number and that same
number is 0.
10. 647 + 647 + 647 = 1941
The perimeter is 1941 feet.
11.
4. The difference of any number and 0 is the same
number.
15, 759
− 458
15,301
The radius of Neptune is 15,301 miles.
12. a.
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.
The model with the fewest seats
corresponds to the shortest bar, which is the
F-100.
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.
b. Add the number of seats for each model.
370
87
+ 141
598
The total number of seats in the B747-400,
F-100, and B737-400 is 598.
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.
Exercise Set 1.3
Calculator Explorations
1. 89 + 45 = 134
1.
14
+ 22
36
2
27
+ 31
58
3.
62
+ 230
292
4.
37
+ 542
579
5.
12
13
+ 24
49
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
4
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
6.
7.
8.
Chapter 1: The Whole Numbers
22
23
45
+ 30
98
14.
5267
+ 132
5399
1 12
15.
236
+ 6243
6479
1 1 1
9.
22, 781
+ 186, 297
209, 078
11.
12.
17, 427
+ 821, 059
838, 486
16
1056
748
+ 7770
9590
11 1
17.
8
9
2
5
+1
25
6 820
4 271
+ 5 626
16, 717
1 111
18.
3
5
8
5
+7
28
6789
4321
+ 5555
16, 665
11 22
19.
22
13.
24
9006
489
+ 2407
11,926
11 2
16.
1
10.
64
28
56
25
+ 32
205
81
17
23
79
+ 12
212
49
628
5 762
+ 29, 462
35,901
111
20.
26
582
4 763
+ 62,511
67,882
5
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
1 22 2 1
21.
1
31.
121, 742
57, 279
26,586
+ 426, 782
632,389
6283
− 560
5723
Check: 5723
+ 560
6283
32.
5349
− 720
4629
Check: 4629
+ 720
5349
33.
533
− 29
504
Check: 504
+ 29
533
34.
724
− 16
708
Check: 708
+ 16
724
35.
1983
− 1904
79
Check:
36.
1983
− 1914
69
Check:
1
1 11 2 1 2
22.
504, 218
321,920
38,507
+ 594, 687
1, 459,332
1
1
23.
62
−37
25
Check:
25
+ 37
62
24.
55
− 29
26
Check:
26
+ 29
55
25.
749
− 149
600
Check:
600
+ 149
749
957
− 257
700
Check:
922
−634
288
Check:
674
− 299
375
Check:
1
1
26.
1
1
700
+ 257
957
37.
50, 000
− 17, 289
32, 711
Check:
32, 711
+ 17, 289
50, 000
288
+ 634
922
38.
40, 000
− 23,582
16, 418
Check:
16, 418
+ 23,582
40, 000
39.
7020
− 1979
5041
Check:
5041
+ 1979
7020
40.
6050
− 1878
4172
Check:
4172
+ 1878
6050
11 11
11
28.
375
+ 299
674
111
11
29.
600
− 432
168
Check:
300
− 149
151
Check:
168
+ 432
600
111
11
30.
69
+ 1914
1983
1 1 11
11
27.
79
+ 1904
1983
151
+ 149
300
6
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
51. 7 + 8 + 10 = 25
The perimeter is 25 feet.
11 11
41.
51,111
− 19,898
31, 213
Check:
31, 213
+ 19,898
51,111
52. 3 + 4 + 5 = 12
The perimeter is 12 centimeters.
11 11
Check:
53. Opposite sides of a rectangle have the same
length.
4 + 8 + 4 + 8 = 12 + 12 = 24
The perimeter is 24 inches.
42.
62, 222
− 39,898
22,324
43.
986
+ 48
1034
54. Opposite sides of a rectangle have the same
length.
8 + 4 + 8 + 4 = 12 + 12 = 24
The perimeter is 24 miles.
44.
986
− 48
938
55. 8 + 3 + 5 + 7 + 5 + 1 = 29
The perimeter is 29 inches.
45.
22,324
+ 39,898
62, 222
56. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37
The perimeter is 37 inches.
76
− 67
9
57. The unknown vertical side has length
12 − 5 = 7 meters. The unknown horizontal side
has length 10 − 5 = 5 meters.
10 + 12 + 5 + 7 + 5 + 5 = 44
The perimeter is 44 meters.
2
46.
47.
80
93
17
9
+2
201
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.
9000
− 482
8518
59. “Find the sum” indicates addition.
111
297
+ 1796
2093
The sum of 297 and 1796 is 2093.
48. 10, 000
− 1786
8214
60. “Find the sum” indicates addition.
11 1
49.
10,962
4 851
+ 7 063
22,876
50.
12, 468
3 211
+ 1 988
17, 667
1
802
+ 6487
7289
The sum of 802 and 6487 is 7289.
1 11
7
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
68. “Less” indicates subtraction.
25
− 12
13
25 less 12 is 13.
61. “Find the total” indicates addition.
13
76
39
8
17
+ 126
266
The total of 76, 39, 8, 17, and 126 is 266.
69. “Subtracted from” indicates subtraction.
100
− 12
88
12 subtracted from 100 is 88.
62. “Find the total” indicates addition.
12
89
45
2
19
+ 341
496
The total of 89, 45, 2, 19, and 341 is 496.
70. “Subtracted from” indicates subtraction.
90
− 86
4
86 subtracted from 90 is 4.
71. Subtract 36,039 thousand from 38,067 thousand.
38, 067
− 36, 039
2 028
California’s projected population increase is
2028 thousand.
63. “Find the difference” indicates subtraction.
41
− 21
20
The difference of 41 and 21 is 20.
72. Subtract 12,699 thousand from 12,917 thousand.
12,917
− 12, 699
218
Illinois’ projected population increase is
218 thousand.
64. “Find the difference” indicates subtraction.
16
− 5
11
The difference of 16 and 5 is 11.
65. “Increased by” indicates addition.
73. Subtract the cost of the DVD player from the
amount in her savings account.
914
− 295
619
She will have $619 left.
1
452
+ 92
544
452 increased by 92 is 544.
66. “Increased by” indicates addition.
712
+ 38
750
712 increased by 38 is 750.
74. Subtract the discount from the regular price.
547
− 99
448
The sale price is $448.
67. “Less” indicates subtraction.
108
− 36
72
108 less 36 is 72.
75.
189, 000
+ 75, 000
264, 000
The total U.S. land area drained by the Upper
Mississippi and Lower Mississippi sub-basins is
264,000 square miles.
8
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
76.
77.
78.
Chapter 1: The Whole Numbers
86. The shortest bar corresponds to the quietest
reading. Leaves rustling is the quietest.
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.
530, 000
− 247, 000
283, 000
The Missouri sub-basin drains 283,000 square
miles more than the Arkansas Red-White subbasin.
189, 000
− 75, 000
114, 000
The Upper Mississippi sub-basin drains 114,000
square miles more than the Lower Mississippi
sub-basin.
87.
88
− 30
58
The sound of snoring is 58 dB louder than
normal conversation.
88.
100
− 70
30
The difference in sound intensity between live
rock music and loud television is 30 dB.
111
5696
89.
+ 3346
9042
There were 9042 stores worldwide.
79. 70 + 78 + 90 + 102 = 340
The homeowner needs 340 feet of fencing.
90.
80. Opposite sides of a rectangle have the same
length.
60 + 45 + 60 + 45 = 210
The perimeter is 210 feet.
81.
82.
83.
91. Each side of a square has the same length.
31 + 31 + 31 + 31 = 124
The perimeter of the playing board is 124 feet.
503
− 239
264
She must read 264 more pages.
92. Opposite sides of a rectangle have the same
length.
18 + 12 + 18 + 12 = 60
The perimeter of the puzzle is 60 inches.
59,320
− 55, 492
3 828
They traveled 3828 miles on their trip.
93. California has the most Target stores.
94. Arizona has the fewest Target stores.
386,119
+ 426,990
813,109
The total number sold in the U.S. in 2005 was
813,109.
11
95.
111 11
84.
119
− 99
20
The difference in volume between the mid-size
and a sub-compact car is 20 cubic feet.
4,141,199
+ 35, 758,801
39,900, 000
The sheep population was 39,900,000.
205
121
+ 95
421
The total number of Target stores in California,
Texas, and Florida is 421 stores.
96. 41 + 205 + 95 + 44 + 75 + 49 + 53 + 64 + 49
+ 121 = 796
The total number in the ten states listed in
796 stores.
85. Live rock music has a decibel level of 100 dB.
9
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
97. Florida and Georgia:
21
108.
1
95
+ 44
139
Michigan and Ohio:
773
659
+ 481
1913
The given sum is correct.
11
22
53
+ 49
102
Florida and Georgia have more Target stores.
109.
98. The total number of stores listed in the table is
796 stores.
796
+ 601
1397
There are 1397 Target stores in the United
States.
1 2
110.
19
214
49
+ 651
933
The given sum is incorrect, the correct sum is
933.
111.
675
+ 56
731
The given difference is incorrect.
741
− 56
685
112.
389
+ 89
478
The given difference is correct.
113.
141
+ 888
1029
The given difference is correct.
1
99.
2029
+ 3865
5894
The total highway mileage in Delaware is
5894 miles.
11
1
100.
14
173
86
+ 257
530
The given sum is incorrect, the correct sum is
530.
5193
+ 1222
6415
The total highway mileage in Rhode Island is
6415 miles.
101. The minuend is 48 and the subtrahend is 1.
11
102. The minuend is 2863 and the subtrahend is 1904.
103. The minuend is 70 and the subtrahend is 7.
104. The minuend is 86 and the subtrahend is 25.
105. answers may vary
106. answers may vary.
1
107.
566
932
+ 871
2369
The given sum is correct.
10
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ISM: Prealgebra
Chapter 1: The Whole Numbers
tens place. The number 325 rounded to the
nearest ten is 330.
11
114.
7168
+ 547
7715
The given difference is incorrect.
7615
− 547
7068
115.
5269
− 2385
2884
116.
10, 244
− 8 534
1 710
2. a.
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.
117. answers may vary
118. answers may vary
121 3 2
119.
3. a.
289, 462
369, 477
218, 287
+ 121, 685
998,911
Since 998,911 is less than one million, they did
not reach their goal.
1, 000, 000
− 998,911
1 089
They need to read 1089 more pages.
c.
Practice Problems
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.
4. 49
25
32
51
98
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 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.
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.
Section 1.4
1. 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.
5.
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
To round 978,865 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
978,900.
rounds to
rounds to
rounds to
rounds to
rounds to
3785
− 2479
50
30
30
50
+ 100
260
rounds to
rounds to
11
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
4000
− 2000
2000
Chapter 1: The Whole Numbers
6.
11
16
19
+ 31
rounds to
rounds to
rounds to
rounds to
ISM: Prealgebra
5. To round 2791 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 2791 rounded to the
nearest hundred is 2800.
10
20
20
+ 30
80
The total distance is approximately 80 miles.
7.
120, 710
22,878
+ 45,974
rounds to
rounds to
rounds to
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 tens
place. The number 8494 rounded to the nearest
hundred is 8500.
120,000
20,000
+ 50,000
190,000
7. To round 495 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 495 rounded to the nearest ten is
500.
The total number of cases is approximately
190,000.
Vocabulary and Readiness Check
1. To graph a number on a number line, darken the
point representing the location of the number.
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.
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.
9. To round 21,094 to the nearest thousand,
observe that the digit in the hundreds place is 0.
Since this digit is less than 5, we do not add 1 to
the digit in the thousands place. The number
21,094 rounded to the nearest thousand is
21,000.
4. An exact number of products is 1265, but an
estimate is 1000.
Exercise Set 1.4
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.
1. To round 423 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 423 rounded to the nearest
ten is 420.
11. To round 33,762 to the nearest thousand,
observe that the digit in the hundreds place is 7.
Since this digit is at least 5, we add 1 to the digit
in the thousands place. The number 33,762
rounded to the nearest thousand is 34,000.
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.
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.
3. To round 635 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 635 rounded to the nearest ten is
640.
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.
13. To round 328,495 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 328,495 rounded to
the nearest hundred is 328,500.
12
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
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.
23. Estimate 9444 to a given place value by
rounding it to that place value. 9444 rounded to
the tens place is 9440, to the hundreds place is
9400, and to the thousands place is 9000.
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.
15. To round 36,499 to the nearest thousand,
observe that the digit in the hundreds place is 4.
Since this digit is less than 5, we do not add 1 to
the digit in the thousands place. The number
36,499 rounded to the nearest thousand is
36,000.
25. Estimate 14,876 to a given place value by
rounding it to that place value. 14,876 rounded
to the tens place is 14,880, to the hundreds place
is 14,900, and to the thousands place is 15,000.
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.
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.
17. To round 39,994 to the nearest ten, observe that
the digit in the ones place is 4. Since this digit is
less than 5, we do not add 1 to the digit in the
tens place. The number 39,994 rounded to the
nearest ten is 39,990.
27. To round 19,264 to the nearest thousand,
observe that the digit in the hundreds place is 2.
Since this digit is less than 5, we do not add 1 to
the digit in the thousands place. Therefore,
19,264 rounded to the nearest thousand is
19,000.
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.
28. To round 85,907,423 to the nearest hundredthousand, observe that the digit in the tenthousands place is 0. Since this digit is less than
5, we do not add 1 to the digit in the hundredthousands place. Therefore 85,907,423
passengers rounded to the nearest hundredthousand is 85,900,000 passengers.
19. To round 29,834,235 to the nearest ten-million,
observe that the digit in the millions place is 9.
Since this digit is at least 5, we add 1 to the digit
in the ten-millions place. The number
29,834,235 rounded to the nearest ten-million is
30,000,000.
29. 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.
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.
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.
21. Estimate 5281 to a given place value by
rounding it to that place value. 5281 rounded to
the tens place is 5280, to the hundreds place is
5300, and to the thousands place is 5000.
31. To round 67,520,000,000 to the nearest billion,
observe that the digit in the hundred-millions
place is 5. Since this digit is at least 5, we add 1
to the digit in the billions place. Therefore,
$67,520,000,000 rounded to the nearest billion is
$68,000,000,000.
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.
13
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
32. To round 281,421,906 to the nearest million,
observe that the digit in the hundred-thousands
place is 4. Since this digit is less than 5, we do
not add 1 to the digit in the millions place.
Therefore, 281,421,906 rounded to the nearest
million is 281,000,000.
33. To round 3,023,894 to the nearest hundredthousand, observe that the digit in the tenthousands place is 2. Since this digit is less than
5, we do not add 1 to the digit in the hundredthousands place. Therefore, $3,023,894 rounded
to the nearest hundred-thousand is $3,000,000.
34. To round 56,720,000,000 to the nearest billion,
observe that the digit in the hundred-millions
place is 7. Since this digit is at least 5, we add 1
to the digit in the billions place. Therefore,
$56,720,000,000 rounded to the nearest billion is
$57,000,000,000.
35. U.S.: To round 207,897,000 to the nearest
million, observe that the digit in the hundredthousands place is 8. Since this digit is at least 5,
we add 1 to the digit in the millions place. The
number 207,897,000 rounded to the nearest
million is 208,000,000.
India: To round 69,193,300 to the nearest
million, observe that the digit in the hundredthousands place is 1. Since this digit is less than
5, we do not add 1 to the digit in the millions
place. The number 69,193,300 rounded to the
nearest million is 69,000,000.
36. To round 114,878,000 to the nearest ten-million,
observe that the digit in the millions place is 4.
Since this digit is less than 5, we do not add 1 to
the digit in the ten-millions place. Therefore,
114,878,000 bushels rounded to the nearest tenmillion is 110,000,000 bushels.
37.
38.
39
45
22
+ 17
rounds to
rounds to
rounds to
rounds to
40
50
20
+ 20
130
52
33
15
+ 29
rounds to
rounds to
rounds to
rounds to
50
30
20
+ 30
130
39.
449
− 373
rounds to
rounds to
450
− 370
80
40.
555
− 235
rounds to
rounds to
560
− 240
320
41.
1913
1886
+ 1925
rounds to
rounds to
rounds to
1900
1900
+ 1900
5700
42.
4050
3133
+ 1220
rounds to
rounds to
rounds to
4100
3100
+ 1200
8400
43.
1774
− 1492
rounds to
rounds to
1800
− 1500
300
44.
1989
− 1870
rounds to
rounds to
2000
− 1900
100
45.
3995
2549
+ 4944
rounds to
rounds to
rounds to
46.
799
1655
+ 271
rounds to
rounds to
rounds to
4000
2500
+ 4900
11, 400
800
1700
+ 300
2800
47. 463 + 219 is approximately 460 + 220 = 680.
The answer of 680 is incorrect because
463 + 219 = 682.
48. 522 + 785 is approximately 520 + 790 = 1310.
The answer of 1307 is correct.
49. 229 + 443 + 606 is approximately
230 + 440 + 600 = 1270.
The answer of 1278 is correct.
50. 542 + 789 + 198 is approximately
540 + 790 + 200 = 1530.
The answer of 2139 is incorrect.
14
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
51. 7806 + 5150 is approximately
7800 + 5200 = 13,000.
The answer of 12,956 is correct.
52. 5233 + 4988 is approximately
5200 + 5000 = 10,200.
The answer of 9011 is incorrect.
53.
54.
55.
56.
57.
58.
899
1499
+ 999
900
1500
+ 1000
3400
The total cost is approximately $3400.
89
97
100
79
75
+ 82
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
60
40
+ 130
230
61.
910, 000
− 907, 000
3 000
The decrease in enrollment is approximately
3000 children.
62.
51, 746
− 49, 713
909, 608
− 906,993
rounds to
rounds to
rounds to
rounds to
52,000
− 50, 000
2 000
The increase is approximately 2000 credit hours.
64. $214 million is $214,000,000 in standard form.
$214,000,000 rounded to the nearest ten-million
is $210,000,000.
$214,000,000 rounded to the nearest hundredmillion is $200,000,000.
65. $179 million is $179,000,000 in standard form.
$179,000,000 rounded to the nearest ten-million
is $180,000,000.
$179,000,000 rounded to the nearest hundredmillion is $200,000,000.
20, 000
− 14, 000
6 000
The difference in elevation is approximately
6000 feet.
1895
− 1524
64
41
+ 133
rounds to
rounds to
63. $339 million is $339,000,000 in standard form.
$339,000,000 rounded to the nearest ten-million
is $340,000,000.
$339,000,000 rounded to the nearest hundredmillion is $300,000,000.
−
600
700
300
100
100
+ 800
2600
The total distance is approximately 2600 miles.
20,320
− 14, 410
60.
782, 623
− 382,894
The total distance is approximately 230 miles.
1400
500
900
Boston in approximately 900 miles farther from
Kansas City than Chicago is.
588
689
277
143
59
+ 802
780, 000
− 380, 000
400, 000
Jacksonville was approximately 400,000 larger
than Miami.
rounds to
rounds to
rounds to
90
100
100
80
80
+ 80
530
The total score is approximately 530.
1429
− 530
59.
rounds to
rounds to
66. $155 million is $155,000,000 in standard form.
$155,000,000 rounded to the nearest ten-million
is $160,000,000.
$155,000,000 rounded to the nearest hundredmillion is $200,000,000.
rounds to
rounds to
1900
− 1500
400
The difference in price is approximately $400.
67. 5723, for example, rounded to the nearest
hundred is 5700.
68. 5698, for example, rounded to the nearest ten is
5700.
15
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
69. a.
ISM: Prealgebra
The smallest possible number that rounds to
8600 is 8550.
4.
b. The largest possible number that rounds to
8600 is 8649.
70. The largest possible number that rounds to
1,500,000 when rounded to the nearest hundredthousand is 1,549,999.
5.
5950
7693
+ 8203
rounds to
rounds to
rounds to
6 000
7 700
+ 8 200
21,900
6. Area = length ⋅ width
= (360 miles)(280 miles)
= 100,800 square miles
The area of Wyoming is 100,800 square miles.
The perimeter is approximately 21,900 miles.
73. 54 rounds to 50
17 rounds to 20
50 + 20 + 50 + 20 = 140
The perimeter is approximately 140 meters.
7.
Section 1.5
Practice Problems
1. a.
6×0=0
(50)(0) = 0
9.
6(4 + 5) = 6 ⋅ 4 + 6 ⋅ 5
163
× 391
rounds to
rounds to
b. 30(2 + 3) = 30 ⋅ 2 + 30 ⋅ 3
c.
3. a.
b.
1
88
+ 45
133
The total cost is $133.
d. 75 ⋅ 1 = 75
2. a.
16
× 45
80
640
720
The printer can print 720 pages in 45 minutes.
8. 8 × 11 = 88
5 × 9 = 45
b. (1)8 = 8
c.
726
142
1 452
29 040
72 600
103, 092
×
71. answers may vary
72.
306
81
306
24 480
24, 786
×
200
× 400
80,000
There are approximately 80,000 words on 391
pages.
7(2 + 8) = 7 ⋅ 2 + 7 ⋅ 8
29
× 6
54
120
174
Calculator Explorations
1. 72 × 48 = 3456
2. 81 × 92 = 7452
3. 163 ⋅ 94 = 15,322
648
× 5
40
200
3000
3240
4. 285 ⋅ 144 = 41,040
5. 983(277) = 272,291
6. 1562(843) = 1,316,766
16
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
Vocabulary and Readiness Check
15.
64
× 8
512
16.
79
× 3
237
17.
613
× 6
3678
18.
638
× 5
3190
19.
277
× 6
1662
20.
882
× 2
1764
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.
Exercise Set 1.5
21. 1074
× 6
6444
1. 1 ⋅ 24 = 24
2. 55 ⋅ 1 = 55
3. 0 ⋅ 19 = 0
22.
9021
×
3
27, 063
23.
89
× 13
267
890
1157
24.
91
× 72
182
6370
6552
25.
421
× 58
3 368
21 050
24, 418
4. 27 ⋅ 0 = 0
5. 8 ⋅ 0 ⋅ 9 = 0
6. 7 ⋅ 6 ⋅ 0 = 0
7. 87 ⋅ 1 = 87
8. 1 ⋅ 41 = 41
9. 6(3 + 8) = 6 ⋅ 3 + 6 ⋅ 8
10. 5(8 + 2) = 5 ⋅ 8 + 5 ⋅ 2
11. 4(3 + 9) = 4 ⋅ 3 + 4 ⋅ 9
12. 6(1 + 4) = 6 ⋅ 1 + 6 ⋅ 4
13. 20(14 + 6) = 20 ⋅ 14 + 20 ⋅ 6
14. 12(12 + 3) = 12 ⋅ 12 + 12 ⋅ 3
17
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
26.
ISM: Prealgebra
37.
526
23
1 578
10 520
12, 098
×
27.
306
81
306
24 480
24, 786
×
28.
38.
708
21
708
14 160
14,868
780
× 20
15, 600
30.
720
× 80
57, 600
39.
1234
567
8 638
74 040
617 000
699, 678
×
31. (495)(13)(0) = 0
32. (593)(47)(0) = 0
41.
589
× 110
5 890
58 900
64, 790
42.
426
× 110
4 260
42 600
46,860
43.
1941
×
2035
9 705
58 230
3 882 000
3,949,935
33. (640)(1)(10) = (640)(10) = 6400
34. (240)(1)(20) = (240)(20) = 4800
36.
8649
274
34 596
605 430
1 729 800
2,369,826
×
40.
35.
807
127
5 649
16 140
80 700
102, 489
×
×
29.
609
234
2 436
18 270
121 800
142,506
×
1234
× 39
11 106
37 020
48,126
1357
×
79
12 213
94 990
107, 203
18
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
44.
Chapter 1: The Whole Numbers
56. 706 × 409 is approximately 700 × 400, which is
280,000.
The best estimate is d.
1876
1407
13 132
750 400
1 876 000
2, 639,532
×
57. 80 × 11 = (8 × 10) × 11
= 8 × (10 × 11)
= 8 × 110
= 880
45. Area = (length)(width)
= (9 meters)(7 meters)
= 63 square meters
58. 70 × 12 = (7 × 10) × 12
= 7 × (10 × 12)
= 7 × 120
= 840
46. Area = (length)(width)
= (13 inches)(3 inches)
= 39 square inches
59. 6 × 700 = 4200
60. 9 × 900 = 8100
47. Area = (length)(width)
= (40 feet)(17 feet)
= 680 square feet
48. Area = (length)(width)
= (25 centimeters)(20 centimeters)
= 500 square centimeters
49.
50.
576
× 354
rounds to
rounds to
600
× 400
240, 000
982
× 650
rounds to
rounds to
1000
× 700
700, 000
51.
604
× 451
rounds to
rounds to
600
× 500
300, 000
52.
111
× 999
rounds to
rounds to
100
× 1000
100, 000
61.
2240
× 2
4480
62.
3310
× 3
9930
63.
125
× 3
375
There are 375 calories in 3 tablespoons of olive
oil.
64.
14
× 8
112
There are 112 grams of fat in 8 ounces of hulled
sunflower seeds.
65.
94
× 35
470
2820
3290
The total cost is $3290.
66.
34
× 14
136
340
476
There are 476 seats in the room.
53. 38 × 42 is approximately 40 × 40, which is 1600.
The best estimate is c.
54. 2872 × 12 is approximately 2872 × 10, which is
28,720.
The best estimate is b.
55. 612 × 29 is approximately 600 × 30, which is
18,000.
The best estimate is c.
19
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
67. a.
4 × 5 = 20
There are 20 boxes in one layer.
74.
700
× 17
4 900
7 000
11,900
The 17 discs hold 11,900 MB.
75.
5 × 4 = 20
There are 20 apartments on one floor.
60
× 35
300
1 800
2 100
There are 2100 characters in 35 lines.
76.
20
× 3
60
There are 60 apartments in the building.
365
× 3
1095
A cow eats 1095 pounds of grain each year.
77.
160
× 8
1280
There are 1280 calories in 8 ounces.
78.
13
× 16
78
130
208
There are 208 grams of fat in 16 ounces.
b.
20
× 5
100
There are 100 boxes on the pallet.
c.
100
× 20
2000
The weight of the cheese on the pallet is
2000 pounds.
68. a.
b.
ISM: Prealgebra
69. Area = (length)(width)
= (110 feet)(80 feet)
= 8800 square feet
The area is 8800 square feet.
70. Area = (length)(width)
= (60 feet)(45 feet)
= 2700 square feet
The area is 2700 square feet.
71. Area = (length)(width)
= (350 feet)(160 feet)
= 56, 000 square feet
The area is 56,000 square feet.
79.
TShirt
Size
Number
of Shirts
Ordered
Cost
per
Shirt
Cost per
Size
Ordered
72. Area = (length)(width)
= (776 meters)(639 meters)
= 495,864 square meters
The area is 495,864 square meters.
S
4
$10
$40
M
6
$10
$60
L
20
$10
$200
73.
XL
3
$12
$36
XXL
3
$12
$36
94
× 62
188
5640
5828
There are 5828 pixels on the screen.
Total Cost
20
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
$372
ISM: Prealgebra
Chapter 1: The Whole Numbers
90.
Person
Number
of
persons
Cost per
person
Student
24
$5
$120
19
+ 4
23
The total of 19 and 4 is 23.
Nonstudent
4
$7
$28
91. 6 + 6 + 6 + 6 + 6 = 5 ⋅ 6 or 6 ⋅ 5
Children
under 12
5
$2
$10
80.
Total Cost
Cost per
Category
92. 11 + 11 + 11 + 11 + 11 + 11 = 6 ⋅ 11 or 11 ⋅ 6
93. a.
$158
3⋅5=5+5+5=3+3+3+3+3
b. answers may vary
94. a.
81. There are 31 days in March.
31× 700, 000 = 31× 7 × 100, 000
= 217 × 100, 000
= 21, 700, 000
They would use 21,700,000 quarts in March.
b. answers may vary
95.
203
× 14
812
2030
2842
96.
31
× 50
1550
82. 3 × 2,641,000 = 7,923,000
There were 7,923,000 widows in 2005.
83.
+
128
7
135
−
126
8
118
84.
85.
4 ⋅ 5 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4
97. 42 × 3 = 126
42 × 9 = 378
The problem is
134
× 16
804
1340
2144
98. 57 × 3 = 171
57 × 6 = 342
The problem is
42
× 93
57
× 63
86. 47 + 26 + 10 + 231 + 50 = 364
87.
99. answers may vary
19
+ 4
23
The sum of 19 and 4 is 23.
88.
19
× 4
76
The product of 19 and 4 is 76.
89.
19
−4
15
The difference of 19 and 4 is 15.
100. 3 × 110 = 330
2 × 641 = 1282
330 + 1282 + 539 = 2151
Nowitzki scored 2151 points during the
2005−2006 regular season.
21
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
101. On a side with 7 windows per row, there are
7 × 23 = 161 windows. On a side with 4
windows per row, there are
4 × 23 = 92 windows.
161 + 161 + 92 + 92 = 506
There are 506 windows on the building.
4. a.
Section 1.6
Practice Problems
1. a.
8
9 72 because 8 ⋅ 9 = 72.
b. 40 ÷ 5 = 8 because 8 ⋅ 5 = 40.
c.
2. a.
b.
24
= 4 because 4 ⋅ 6 = 24.
6
7
= 1 because 1 ⋅ 7 = 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 because 10 ⋅ 1 = 10.
1
f.
21 ÷ 21 = 1 because 1 ⋅ 21 = 21.
3. a.
b.
c.
c.
0
= 0 because 0 ⋅ 5 = 0.
5
0
8 0 because 0 ⋅ 8 = 0.
5. a.
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.
818
6 4908
−48
10
−6
48
−48
0
Check: 818
× 6
4908
553
4 2212
−20
21
−20
12
−12
0
Check: 553
× 4
2212
251
753
−6
15
−15
03
−3
0
Check: 251
× 3
753
3
7
304
2128
−21
02
−0
28
−28
0
Check: 304 × 7 = 2128
22
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
b.
Chapter 1: The Whole Numbers
5 100
9 45,900
−45
09
−9
000
b.
Check: 5100 × 9 = 45,900
6. a.
4
234 R 3
939
−8
13
−12
19
−16
3
524 R 12
8. 17 8920
−85
42
−34
80
−68
12
657 R 2
5 3287
−30
28
−25
37
−35
2
49 R 60
9. 678 33, 282
−27 12
6 162
−6 102
60
Check: 657 ⋅ 5 + 2 = 3287
7. a.
5827 R 2
23,310
−20
33
−3 2
11
−8
30
−28
2
Check: 5827 ⋅ 4 + 2 = 23,310
Check: 234 ⋅ 4 + 3 = 939
b.
4
9067 R 2
9 81, 605
−81
06
−0
60
−54
65
−63
2
57
10. 3 171
−15
21
−21
0
Each student got 57 CDs.
44
532
−48
52
−48
4
There will be 44 full boxes and 4 printers left
over.
11. 12
Check: 9067 ⋅ 9 + 2 = 81,605
23
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
12. Find the sum and divide by 7.
18
4
7 126
7
−7
56
35
−56
16
9
0
3
+ 52
126
The average time is 18 minutes.
Exercise Set 1.6
1. 54 ÷ 9 = 6
2. 72 ÷ 9 = 8
3. 36 ÷ 3 = 12
4. 24 ÷ 3 = 8
5. 0 ÷ 8 = 0
6. 0 ÷ 4 = 0
Calculator Explorations
7. 31 ÷ 1 = 31
1. 848 ÷ 16 = 53
8. 38 ÷ 1 = 38
2. 564 ÷ 12 = 47
3. 5890 ÷ 95 = 62
4. 1053 ÷ 27 = 39
5.
6.
32,886
= 261
126
143, 088
= 542
264
9.
18
=1
18
10.
49
=1
49
11.
24
=8
3
12.
45
=5
9
7. 0 ÷ 315 = 0
13. 26 ÷ 0 = undefined.
8. 315 ÷ 0 is an error.
Vocabulary and Readiness Check
14.
1. In 90 ÷ 2 = 45, the answer 45 is called the
quotient, 90 is called the dividend, and 2 is
called the divisor.
12
= undefined
0
15. 26 ÷ 26 = 1
16. 6 ÷ 6 = 1
2. The quotient of any number and 1 is the same
number.
17. 0 ÷ 14 = 0
3. The quotient of any number (except 0) and the
same number is 1.
18. 7 ÷ 0 = undefined
19. 18 ÷ 2 = 9
4. The quotient of 0 and any number (except 0) is
0.
20. 18 ÷ 3 = 6
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.
24
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
29
21. 3 87
−6
27
−27
0
27.
28.
Check: 3 ⋅ 29 = 87
30
is undefined.
0
0
=0
30
Check: 0 ⋅ 30 = 0
9
29. 7 63
−63
0
17
22. 5 85
−5
35
−35
0
Check: 7 ⋅ 9 = 63
7
30. 8 56
−56
0
Check: 17 ⋅ 5 = 85
74
23. 3 222
−21
12
−12
0
Check: 7 ⋅ 8 = 56
31. 6
Check: 74 ⋅ 3 = 222
24. 8
80
640
−64
00
25
150
−12
30
−30
0
Check: 25 ⋅ 6 = 150
11
32. 11 121
−11
11
−11
0
Check: 80 ⋅ 8 = 640
338
25. 3 1014
−9
11
−9
24
−24
0
Check: 11 ⋅ 11 = 121
68 R 3
33. 7 479
−42
59
−56
3
Check: 3 ⋅ 338 = 1014
526
26. 4 2104
−20
10
−8
24
−24
0
Check: 7 ⋅ 68 + 3 = 479
34. 7
60 R 6
426
−42
06
Check: 60 ⋅ 7 + 6 = 426
Check: 526 ⋅ 4 = 2104
25
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
236 R 5
35. 6 1421
−12
22
−18
41
−36
5
833 R 1
40. 4 3333
−32
13
−12
13
−12
1
Check: 236 ⋅ 6 + 5 = 1421
Check: 833 ⋅ 4 + 1 = 3333
413 R 1
36. 3 1240
−12
04
−3
10
−9
1
13
41. 55 715
−55
165
−165
0
Check: 55 ⋅ 13 = 715
32
42. 23 736
−69
46
−46
0
Check: 413 ⋅ 3 + 1 = 1240
37. 8
38 R 1
305
−24
65
−64
1
Check: 32 ⋅ 23 = 736
49
43. 23 1127
−92
207
−207
0
Check: 8 ⋅ 38 + 1 = 305
55 R 2
38. 3 167
−15
17
−15
2
Check: 49 ⋅ 23 = 1127
Check: 55 ⋅ 3 + 2 = 167
39. 7
44. 42
326 R 4
2286
−21
18
−14
46
−42
4
48
2016
−168
336
−336
0
Check: 48 ⋅ 42 = 2016
97 R 8
45. 97 9417
−873
687
−679
8
Check: 326 ⋅ 7 + 4 = 2286
Check: 97 ⋅ 97 + 8 = 9417
26
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
46. 44
Chapter 1: The Whole Numbers
202 R 7
51. 46 9299
−92
09
−0
99
−92
7
44 R 2
1938
−176
178
−176
2
Check: 44 ⋅ 44 + 2 = 1938
209 R 11
47. 15 3146
−30
14
−0
146
−135
11
Check: 202 ⋅ 46 + 7 = 9299
39 R 9
52. 64 2505
−192
585
−576
9
Check: 209 ⋅ 15 + 11 = 3146
Check: 39 ⋅ 64 + 9 = 2505
612 R 10
48. 12 7354
−72
15
−12
34
−24
10
53. 236
54
12744
−1180
944
−944
0
Check: 236 ⋅ 54 = 12,744
47
54. 123 5781
−492
861
−861
0
Check: 612 ⋅ 12 + 10 = 7354
506
49. 13 6578
−65
07
−0
78
−78
0
Check: 47 ⋅ 123 = 5781
99 R 100
55. 103 10, 297
−9 27
1 027
−927
100
Check: 13 ⋅ 506 = 6578
405
50. 14 5670
−56
07
−0
70
−70
0
Check: 99 ⋅ 103 + 100 = 10,297
96 R 52
56. 240 23, 092
−21 60
1 492
−1 440
52
Check: 405 ⋅ 14 = 5670
Check: 96 ⋅ 240 + 52 = 23,092
27
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
202 R 15
57. 102 20619
−204
21
−0
219
−204
15
13
62. 8 104
−8
24
−24
0
511 R 3
63. 7 3580
−35
08
−7
10
−7
3
Check: 102 ⋅ 202 + 15 = 20,619
201 R 50
58. 203 40,853
−40 6
25
−0
253
−203
50
603 R 2
64. 5 3017
−30
01
−0
17
−15
2
Check: 201 ⋅ 203 + 50 = 40,853
579 R 72
59. 423 244,989
−211 5
33 48
−29 61
3 879
−3 807
72
2132 R 32
65. 40 85312
−80
53
−40
131
−120
112
−80
32
Check: 579 ⋅ 423 + 72 = 244,989
303 R 63
60. 543 164,592
−162 9
1 69
− 0
1 692
−1 629
63
1714 R 47
66. 50 85, 747
−50
35 7
−35 0
74
−50
247
−200
47
Check: 303 ⋅ 543 + 63 = 164,592
17
61. 7 119
−7
49
−49
0
28
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
6 080
67. 142 863,360
−852
11 3
−0
11 36
−11 36
00
−0
0
20 R 2
73. 3 62
−6
02
−0
2
The quotient is 20 R 2.
15 R 3
78
−5
28
−25
3
The quotient is 15 R 3.
74. 5
3 040
68. 214 650,560
−642
85
−0
8 56
−8 56
00
−0
0
33
2145
−195
195
−195
0
There are 33 students in the group.
75. 65
23 R 2
69. 5 117
−10
17
−15
2
The quotient is 23 R 2.
58
76. 85 4930
−425
680
−680
0
There are 58 students in the group.
13 R 3
70. 7 94
−7
24
−21
3
The quotient is 13 R 3.
165
77. 318 52470
−318
2067
−1908
1590
−1590
0
The person weighs 165 pounds on Earth.
5 R 25
71. 35 200
−175
25
200 divided by 35 is 5 R 25.
3 R 20
72. 32 116
−96
20
116 divided by 32 is 3 R 20.
29
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
252000
78. 21 5292000
−42
109
−105
42
−42
0
Each person received $252,000.
10
5280
−492
360
There should be 10 poles, plus the first pole for a
total of 11 light poles.
83. 492
23 R 1
185
−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.
84. 8
310
79. 18 5580
−54
18
−18
0
The distance is 310 yards.
5
85. 5280 26400
−26400
0
Broad Peak is 5 miles tall.
412
80. 14 5768
−56
16
−14
28
−28
0
The truck hauls 412 bushels on each trip.
28
86. 6 168
−12
48
−48
0
Alexander scored 28 touchdowns.
88 R 1
81. 3 265
−24
25
−24
1
There are 88 bridges every 3 miles over the
265 miles, plus the first bridge, for a total of
89 bridges.
1760
87. 3 5280
−3
22
−21
18
−18
0
There are 1760 yards in 1 mile.
82. Lane divider = 25 + 25 = 50
105
50 5280
−50
28
−0
280
−250
30
There are 105 whole lane dividers.
16
88. 320 5280
−320
2080
−1920
160
There are 16 whole feet in 1 rod.
30
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
10
89.
24
35
22
17
+ 12
120
Average =
Average =
Average =
Average =
89
534
−48
54
−54
0
534
= 89
6
69
77
+ 76
222
74
3 222
−21
12
−12
0
The average temperature is 74°.
96.
169
5 845
−5
34
−30
45
−45
0
121
200
185
176
+ 163
845
6
2
95.
1548
= 387
4
21
92.
92
96
90
85
92
+ 79
534
Average =
387
4 1548
−12
34
−32
28
−28
0
205
972
210
+ 161
1548
395
= 79
5
2
94.
180
= 30
6
1
91.
Average =
30
6 180
−18
00
37
26
15
29
51
+ 22
180
79
5 395
−35
45
−45
0
86
93.
79
81
69
+ 80
395
120
= 20
6
3
90.
2
20
6 120
−12
00
2
53
40
+ 30
123
41
3 123
−12
03
−3
0
The average temperature is 41°.
111
97.
845
= 169
5
82
463
29
+ 8704
9278
11
98.
23
407
92
+ 7011
7533
31
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
99.
×
100.
546
28
4 368
10 920
15, 288
732, 000, 000
2 1, 464, 000, 000
797, 000, 000
111.
−1 4
+ 667, 000, 000
1, 464, 000, 000
06
−6
04
−4
0
The average amount spent is $732,000,000.
712
× 54
2 848
35 600
38, 448
101.
722
− 43
679
102.
712
− 54
658
103.
ISM: Prealgebra
112.
45
is undefined.
0
634, 000, 000
4 2,536, 000, 000
−2 4
13
−12
16
−16
0
The average amount spent is $634,000,000.
797, 000, 000
667, 000, 000
544, 000, 000
+ 528, 000, 000
2,536, 000, 000
113. The average will increase; answers may vary.
114. The average will decrease; answers may vary.
0
104.
= 0 because 0 ⋅ 23 = 0
23
115. No; answers may vary
Possible answer: The average cannot be less than
each of the four numbers.
9 R 12
105. 24 228
−216
12
12
116. 5 60
−5
10
−10
0
The length is 12 feet.
Notice that Area = length × width = 12 × 5 = 60.
9 R 25
106. 31 304
−279
25
107. The quotient of 40 and 8 is 40 ÷ 8, which is
choice c.
117. answers may vary
108. The quotient of 200 and 20 is 200 ÷ 20, which is
choice b.
109. 200 divided by 20 is 200 ÷ 20, which is choice b.
110. 40 divided by 8 is 40 ÷ 8, which is choice c.
32
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
Integrated Review
118. 26
−5
21
−5
16
−5
11
−5
6
−5
1
Therefore, 26 ÷ 5 = 5 R 1
1
1.
42
63
+ 89
194
2.
7006
− 451
6555
3.
87
× 52
174
4350
4524
The Bigger Picture
1
1.
82
+ 39
121
2.
82
− 39
43
3.
82
× 39
738
2460
3198
562
4. 8 4496
−40
49
−48
16
−16
0
5. 1 ⋅ 67 = 67
6.
89 R 11
4. 29 2592
−232
272
−261
11
36
is undefined.
0
7. 16 ÷ 16 = 1
8. 5 ÷ 1 = 5
9. 0 ⋅ 21 = 0
5. 0 ⋅ 15 = 0
10. 7 ⋅ 0 ⋅ 8 = 0
6. 0 ÷ 11 = 0
11. 0 ÷ 7 = 0
7. 26 ⋅ 1 = 26
12. 12 ÷ 4 = 3
8. 36 ÷ 0 is undefined.
13. 9 ⋅ 7 = 63
9. 82 ÷ 1 = 82
14. 45 ÷ 5 = 9
10.
2000
− 156
1844
15.
207
− 69
138
33
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
1
16.
207
+ 69
276
17.
3718
− 2549
1169
18.
1861
+ 7965
9826
663 R 24
23. 32 21, 240
−19 2
2 04
−1 92
120
−96
24
11
1 076 R 60
24. 65 70, 000
−65
50
−0
5 00
−4 55
450
−390
60
182 R 4
19. 7 1278
−7
57
−56
18
−14
4
20.
25.
1259
63
3 777
75 540
79,317
×
4000
− 2963
1037
26. 10, 000
− 101
9 899
27.
1099 R 2
21. 7 7695
−7
06
−0
69
−63
65
−63
2
303
× 101
303
30 300
30, 603
28. (475)(100) = 47,500
1
111 R 1
22. 9 1000
−9
10
−9
10
−9
1
29.
62
+ 9
71
The total of 62 and 9 is 71.
30.
62
× 9
558
The product of 62 and 9 is 558.
34
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
6 R8
31. 9 62
−54
8
The quotient of 62 and 9 is 6 R 8.
41.
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.
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.
13
9
+ 6
28
The perimeter is 28 miles.
3
24
5 120
−10
20
−20
0
19
43.
15
25
37
+ 24
120
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.
Average =
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.
120
= 24
5
124
4 496
−4
09
−8
16
−16
0
12
44.
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.
108
131
98
+ 159
496
Average =
39. 6 + 6 + 6 + 6 = 24
6 × 6 = 36
The perimeter is 24 feet and the area is 36 square
feet.
45.
40. 14 + 7 + 14 + 7 = 42
14
× 7
98
The perimeter is 42 inches and the area is
98 square inches.
496
= 124
4
28,547
− 26,372
2 175
The Lake Pontchartrain Bridge is longer by
2175 feet.
35
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
46.
ISM: Prealgebra
14. 36 ÷ 6 ⋅ 3 + 5 = 6 ⋅ 3 + 5 = 18 + 5 = 23
347
× 18
2776
3470
6246
The amount spent on toys is $6246.
15. Area = (side)2
= (12 centimeters)2
= 144 square centimeters
The area of the square is 144 square centimeters.
Section 1.7
Calculator Explorations
Practice Problems
1. 36 = 729
1. 8 ⋅ 8 ⋅ 8 ⋅ 8 = 84
2. 56 = 15, 625
2. 3 ⋅ 3 ⋅ 3 = 33
3. 45 = 1024
3. 10 ⋅10 ⋅10 ⋅10 ⋅10 = 105
4. 76 = 117, 649
4. 5 ⋅ 5 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 = 52 ⋅ 46
5. 211 = 2048
5. 42 = 4 ⋅ 4 = 16
6. 68 = 1, 679, 616
6. 83 = 8 ⋅ 8 ⋅ 8 = 512
7. 7 4 + 53 = 2526
1
7. 11 = 11
8. 124 − 84 = 16, 640
8. 2 ⋅ 32 = 2 ⋅ 3 ⋅ 3 = 18
9. 63 ⋅ 75 − 43 ⋅ 10 = 4295
9. 9 ⋅ 3 − 8 ÷ 4 = 27 − 8 ÷ 4 = 27 − 2 = 25
10. 8 ⋅ 22 + 7 ⋅ 16 = 288
2
10. 48 ÷ 3 ⋅ 2 = 48 ÷ 3 ⋅ 4 = 16 ⋅ 4 = 64
11. 4(15 ÷ 3 + 2) − 10 ⋅ 2 = 8
11. (10 − 7)4 + 2 ⋅ 32 = 34 + 2 ⋅ 32
= 81 + 2 ⋅ 9
= 81 + 18
= 99
3
12. 155 − 2(17 + 3) + 185 = 300
Vocabulary and Readiness Check
1. In 25 = 32, the 2 is called the base and the 5 is
called the exponent.
3
12. 36 ÷ [20 − (4 ⋅ 2)] + 4 − 6 = 36 ÷ [20 − 8] + 4 − 6
= 36 ÷ 12 + 43 − 6
= 36 ÷ 12 + 64 − 6
= 3 + 64 − 6
= 61
13.
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
25 + 8 ⋅ 2 − 33 25 + 8 ⋅ 2 − 27
=
2(3 − 2)
2(1)
25 + 16 − 27
=
2
14
=
2
=7
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
36
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
Exercise Set 1.7
24. 81 = 8
1. 4 ⋅ 4 ⋅ 4 = 43
25. 27 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 128
2. 5 ⋅ 5 ⋅ 5 ⋅ 5 = 54
26. 54 = 5 ⋅ 5 ⋅ 5 ⋅ 5 = 625
3. 7 ⋅ 7 ⋅ 7 ⋅ 7 ⋅ 7 ⋅ 7 = 76
27. 28 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 256
4. 6 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 = 67
28. 33 = 3 ⋅ 3 ⋅ 3 = 27
5. 12 ⋅12 ⋅12 = 123
29. 44 = 4 ⋅ 4 ⋅ 4 ⋅ 4 = 256
6. 10 ⋅10 ⋅10 = 103
30. 43 = 4 ⋅ 4 ⋅ 4 = 64
7. 6 ⋅ 6 ⋅ 5 ⋅ 5 ⋅ 5 = 62 ⋅ 53
31. 93 = 9 ⋅ 9 ⋅ 9 = 729
8. 4 ⋅ 4 ⋅ 3 ⋅ 3 ⋅ 3 = 42 ⋅ 33
32. 83 = 8 ⋅ 8 ⋅ 8 = 512
9. 9 ⋅ 8 ⋅ 8 = 9 ⋅ 82
33. 122 = 12 ⋅12 = 144
10. 7 ⋅ 4 ⋅ 4 ⋅ 4 = 7 ⋅ 43
34. 112 = 11 ⋅11 = 121
11. 3 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 3 ⋅ 24
35. 102 = 10 ⋅10 = 100
12. 4 ⋅ 6 ⋅ 6 ⋅ 6 ⋅ 6 = 4 ⋅ 64
36. 103 = 10 ⋅10 ⋅10 = 1000
13. 3 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 = 3 ⋅ 24 ⋅ 55
37. 201 = 20
14. 6 ⋅ 6 ⋅ 2 ⋅ 9 ⋅ 9 ⋅ 9 ⋅ 9 = 62 ⋅ 2 ⋅ 94
38. 141 = 14
15. 82 = 8 ⋅ 8 = 64
39. 36 = 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 729
16. 62 = 6 ⋅ 6 = 36
40. 45 = 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 = 1024
17. 53 = 5 ⋅ 5 ⋅ 5 = 125
41. 3 ⋅ 26 = 3 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 192
18. 63 = 6 ⋅ 6 ⋅ 6 = 216
42. 5 ⋅ 32 = 5 ⋅ 3 ⋅ 3 = 45
19. 25 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 32
43. 2 ⋅ 34 = 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 162
20. 35 = 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 243
44. 2 ⋅ 7 2 = 2 ⋅ 7 ⋅ 7 = 98
21. 110 = 1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 = 1
45. 15 + 3 ⋅ 2 = 15 + 6 = 21
22. 112 = 1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 ⋅1 = 1
46. 24 + 6 ⋅ 3 = 24 + 18 = 42
23. 71 = 7
47. 28 ÷ 7 ⋅ 1 + 3 = 4 ⋅ 1 + 3 = 4 + 3 = 7
48. 100 ÷ 10 ⋅ 5 + 4 = 10 ⋅ 5 + 4 = 50 + 4 = 54
37
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
49. 32 ÷ 4 − 3 = 8 − 3 = 5
66.
50. 42 ÷ 7 − 6 = 6 − 6 = 0
51. 13 +
24
= 13 + 3 = 16
8
52. 32 +
8
= 32 + 4 = 36
2
56.
7
1
6+9÷3
=
=
2
3
70. 23 ⋅ 3 − (100 ÷ 10) = 23 ⋅ 3 − 10
= 8 ⋅ 3 − 10
= 24 − 10
= 14
5+3 8
= =8
1
1
6+3 9
= =1
9
9
71. 34 − [35 − (12 − 6)] = 34 − [35 − 6]
= 34 − 29
= 81 − 29
= 52
= 32 ÷ 4 ⋅ 23
= 32 ÷ 4 ⋅ 8
= 8⋅8
= 64
72. [40 − (8 − 2)] − 25 = [40 − 6] − 25
= 34 − 25
= 34 − 32
=2
58. 62 ⋅ (10 − 8) = 62 ⋅ 2 = 36 ⋅ 2 = 72
73. (7 ⋅ 5) + [9 ÷ (3 ÷ 3)] = (7 ⋅ 5) + [9 ÷ (1)]
= 35 + 9
= 44
59. 52 ⋅ (10 − 8) + 23 + 52 = 52 ⋅ 2 + 23 + 52
= 25 ⋅ 2 + 8 + 25
= 50 + 8 + 25
= 83
74. (18 ÷ 6) + [(3 + 5) ⋅ 2] = (18 ÷ 6) + (8 ⋅ 2)
= 3 + (8 ⋅ 2)
= 3 + 16
= 19
60. 53 ÷ (10 + 15) + 92 + 33 = 53 ÷ 25 + 92 + 33
= 125 ÷ 25 + 81 + 27
= 5 + 81 + 27
= 113
62.
18 + 6
4
2 −2
2
40 + 8
2
2
5 −3
5(5) − 4 25 − 4 21
=
=
=3
25 − 18 25 − 18 7
69. 24 ⋅ 4 − (25 ÷ 5) = 24 ⋅ 4 − 5
= 16 ⋅ 4 − 5
= 64 − 5
= 59
57. (7 + 52 ) ÷ 4 ⋅ 23 = (7 + 25) ÷ 4 ⋅ 23
61.
5 − 18
=
68. 18 − 7 ÷ 0 = undefined
54. 3 ⋅ 4 + 9 ⋅ 1 = 12 + 9 = 21
5 + 12 ÷ 4
2
67. 8 ÷ 0 + 37 = undefined
53. 6 ⋅ 5 + 8 ⋅ 2 = 30 + 16 = 46
55.
5(12 − 7) − 4
=
24
24
=
=2
16 − 4 12
=
48
48
=
=3
25 − 9 16
75. 8 ⋅ [22 + (6 − 1) ⋅ 2] − 50 ⋅ 2 = 8 ⋅ (22 + 5 ⋅ 2) − 50 ⋅ 2
= 8 ⋅ (4 + 5 ⋅ 2) − 50 ⋅ 2
= 8 ⋅ (4 + 10) − 50 ⋅ 2
= 8 ⋅14 − 50 ⋅ 2
= 112 − 50 ⋅ 2
= 112 − 100
= 12
63. (3 + 5) ⋅ (9 − 3) = 8 ⋅ 6 = 48
64. (9 − 7) ⋅ (12 + 18) = 2 ⋅ 30 = 60
65.
7(9 − 6) + 3
2
3 −3
=
7(3) + 3 21 + 3 24
=
=
=4
9−3
6
6
38
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
82. 10 ÷ 2 + 33 ⋅ 2 − 20 = 10 ÷ 2 + 27 ⋅ 2 − 20
= 5 + 27 ⋅ 2 − 20
= 5 + 54 − 20
= 39
76. 35 ÷ [32 + (9 − 7) − 22 ] + 10 ⋅ 3
= 35 ÷ [32 + 2 − 22 ] + 10 ⋅ 3
= 35 ÷ [9 + 2 − 4] + 10 ⋅ 3
= 35 ÷ 7 + 10 ⋅ 3
= 5 + 10 ⋅ 3
= 5 + 30
= 35
83. [13 ÷ (20 − 7) + 25 ] − (2 + 3)2 = [13 ÷ 13 + 25 ] − 52
= [13 ÷ 13 + 32] − 52
= [1 + 32] − 52
92 + 22 − 12 81 + 4 − 1
77.
=
8 ÷ 2 ⋅ 3 ⋅1 ÷ 3 4 ⋅ 3 ⋅1 ÷ 3
85 − 1
=
12 ⋅1 ÷ 3
84
=
12 ÷ 3
84
=
4
= 21
78.
79.
80.
= 33 − 52
= 33 − 25
=8
84. [15 ÷ (11 − 6) + 22 ] + (5 − 1) 2 = [15 ÷ 5 + 22 ] + 42
= [15 ÷ 5 + 4] + 42
= [3 + 4] + 42
= 7 + 42
= 7 + 16
= 23
52 − 23 + 14
25 − 8 + 1
18
18
=
=
=
=9
10 ÷ 5 ⋅ 4 ⋅1 ÷ 4 2 ⋅ 4 ⋅1 ÷ 4 8 ÷ 4 2
2+4
2
2
5(20 − 16) − 3 − 5
3 + 92
2
3(10 − 6) − 2 − 1
=
=
85. 7 2 − {18 − [40 ÷ (5 ⋅1) + 2] + 52 }
2 + 16
= 7 2 − {18 − [40 ÷ 5 + 2] + 52 }
2
5(4) − 3 − 5
18
=
5(4) − 9 − 5
18
=
20 − 9 − 5
18
=
11 − 5
18
=
6
=3
= 7 2 − {18 − [8 + 2] + 52 }
= 7 2 − {18 − 10 + 52 }
= 7 2 − {18 − 10 + 25}
= 7 2 − 33
= 49 − 33
= 16
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
3 + 81
3(4) − 22 − 1
84
=
3(4) − 4 − 1
84
=
12 − 4 − 1
84
=
8 −1
84
=
7
= 12
87. Area of a square = (side) 2
= (7 meters)2
= 49 square meters
88. Area of a square = (side) 2
= (9 centimeters)2
= 81 square centimeters
89. Area of a square = (side) 2
81. 9 ÷ 3 + 52 ⋅ 2 − 10 = 9 ÷ 3 + 25 ⋅ 2 − 10
= 3 + 25 ⋅ 2 − 10
= 3 + 50 − 10
= 43
= (23 miles)2
= 529 square miles
39
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
The Bigger Picture
90. Area of a square = (side) 2
= (41 feet) 2
= 1681 square feet
1. 63 = 6 ⋅ 6 ⋅ 6 = 216
91. The statement is true.
2. 23 ⋅ 61 = 2 ⋅ 2 ⋅ 2 ⋅ 6 = 48
92. The statement is true.
3. 8 ⋅ 52 = 8 ⋅ 5 ⋅ 5 = 200
93. 25 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2
The statement is false.
4. 1 + 2(3 + 4) = 1 + 2(7) = 1 + 14 = 15
5. 2 + 5(10 − 3) = 2 + 5(7) = 2 + 35 = 37
9
94. 4 = 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4
The statement is false.
6. 200 ÷ 2 ⋅ 2 = 100 ⋅ 2 = 200
95. (2 + 3) ⋅ 6 − 2 = 5 ⋅ 6 − 2 = 30 − 2 = 28
7.
978
− 179
799
8.
72
× 30
2160
96. (2 + 3) ⋅ (6 − 2) = (5) ⋅ (4) = 20
97. 24 ÷ (3 ⋅ 2) + 2 ⋅ 5 = 24 ÷ 6 + 2 ⋅ 5 = 4 + 10 = 14
98. 24 ÷ (3 ⋅ 2 + 2) ⋅ 5 = 24 ÷ (6 + 2) ⋅ 5
= 24 ÷ 8 ⋅ 5
= 3⋅5
= 15
10 R 34
9. 58 614
−58
34
−0
34
99. The unknown vertical length is
30 − 12 = 18 feet. The unknown horizontal
length is 60 − 40 = 20 feet.
Perimeter = 60 + 30 + 40 + 18 + 20 + 12 = 180
The total perimeter of seven homes is
7(180) = 1260 feet.
3
10. 3[(7 − 3)2 − (25 − 22) 2 ] + 6
= 3[42 − 32 ] + 6
= 3(16 − 9) + 6
= 3(7) + 6
= 21 + 6
= 27
3
100. 25 ⋅ (45 − 7 ⋅ 5) ⋅ 5 = 25 ⋅ (45 − 35) ⋅ 5
= 253 ⋅ (10) ⋅ 5
= 15, 625 ⋅10 ⋅ 5
= 156, 250 ⋅ 5
= 781, 250
Section 1.8
101. (7 + 24 )5 − (35 − 24 )2 = (7 + 16)5 − (243 − 16)2
Practice Problems
= 235 − 227 2
= 6, 436,343 − 51,529
= 6,384,814
1. x − 2 = 7 − 2 = 5
2. y(x − 3) = 4(8 − 3) = 4(5) = 20
102. answers may vary
3.
103. answers may vary; possible answer:
(20 − 10) ⋅ 5 ÷ 25 + 3 = 10 ⋅ 5 ÷ 25 + 3
= 50 ÷ 25 + 3
= 2+3
=5
y + 6 18 + 6 24
=
=
=4
x
6
6
4. 25 − z 3 + x = 25 − 23 + 1 = 25 − 8 + 1 = 18
5.
5( F − 32) 5(41 − 32) 5(9) 45
=
=
=
=5
9
9
9
9
40
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
6. 3( y − 6) = 6
3(8 − 6) ⱨ 6
3(2) ⱨ 6
6 = 6 True
Yes, 8 is a solution.
7. 5n + 4 = 34
Let n be 10.
5(10) + 4 ⱨ 34
50 + 4 ⱨ 34
54 = 34 False
No, 10 is not a solution.
Let n be 6.
5(6) + 4 ⱨ 34
30 + 4 ⱨ 34
34 = 34 True
Yes, 6 is a solution.
Let n be 8.
5(8) + 4 ⱨ 34
40 + 4 ⱨ 34
44 = 34 False
No, 8 is not a solution.
8. a.
Twice a number is 2x.
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 and Readiness Check
1. A combination of operations on letters (variables) and numbers is an expression.
2. A letter that represents a number is a variable.
3. 3x − 2y 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 an expression.
5. A statement of the form
“expression = expression” is called an equation.
6. A value for the variable that makes the equation a true statement is called a solution.
41
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
Exercise Set 1.8
1.
2.
a
b
a+b
a−b
a⋅b
a÷b
21
7
21 + 7 = 28
21 − 7 = 14
21 ⋅ 7 = 147
21 ÷ 7 = 3
a
b
a+b
a−b
a⋅b
a÷b
24
6
24 + 6 = 30
24 − 6 = 18
24 ⋅ 6 = 144
24 ÷ 6 = 4
a
b
a+b
a−b
a⋅b
a÷b
152
0
152 + 0 = 152
152 − 0 = 152
152 ⋅ 0 = 0
152 ÷ 0 is undefined.
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.
3.
4.
5.
6.
a
b
a+b
a−b
a⋅b
a÷b
56
1
56 + 1 = 57
56 − 1 = 55
56 ⋅ 1 = 56
56 ÷ 1 = 56
a
b
a+b
a−b
a⋅b
a÷b
82
1
82 + 1 = 83
82 − 1 = 81
82 ⋅ 1 = 82
82 ÷ 1 = 82
7. 3 + 2z = 3 + 2(3) = 3 + 6 = 9
8. 7 + 3z = 7 + 3(3) = 7 + 9 = 16
9. 3xz − 5x = 3(2)(3) − 5(2) = 18 − 10 = 8
10. 4yz + 2x = 4(5)(3) + 2(2) = 60 + 4 = 64
11. z − x + y = 3 − 2 + 5 = 1 + 5 = 6
12. x + 5y − z = 2 + 5(5) − 3 = 2 + 25 − 3 = 24
13. 4x − z = 4(2) − 3 = 8 − 3 = 5
14. 2y + 5z = 2(5) + 5(3) = 10 + 15 = 25
15. y 3 − 4 x = 53 − 4(2) = 125 − 4(2) = 125 − 8 = 117
16. y 3 − z = 53 − 3 = 125 − 3 = 122
17. 2 xy 2 − 6 = 2(2)(5)2 − 6
= 2 ⋅ 2 ⋅ 25 − 6
= 100 − 6
= 94
42
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
18. 3 yz 2 + 1 = 3(5)(3) 2 + 1
= 3⋅5⋅9 +1
= 135 + 1
= 136
32. 3x 2 + 2 x − 5 = 3 ⋅ 22 + 2 ⋅ 2 − 5
= 3⋅ 4 + 2 ⋅ 2 − 5
= 12 + 4 − 5
= 11
19. 8 − (y − x) = 8 − (5 − 2) = 8 − 3 = 5
33. (4 y − 5 z )3 = (4 ⋅ 5 − 5 ⋅ 3)3
= (20 − 15)3
20. 3 + (2 y − 4) = 3 + (2 ⋅ 5 − 4)
= 3 + (10 − 4)
= 3+ 6
=9
5
= (5)3
= 125
34. (4 y + 3z )2 = (4 ⋅ 5 + 3 ⋅ 3) 2
5
21. x + ( y − z ) = 2 + (5 − 3)
= (20 + 9)2
5
= 2 +2
= 32 + 2
= 34
4
4
= 292
= 841
35. ( xy + 1) 2 = (2 ⋅ 5 + 1) 2 = (10 + 1)2 = 112 = 121
4
22. x − ( y − z ) = 2 − (5 − 3) = 2 − 2 = 16 − 2 = 14
36. ( xz − 5) 4 = (2 ⋅ 3 − 5) 4 = (6 − 5)4 = 14 = 1
6 xy 6 ⋅ 2 ⋅ 5 60
=
=
= 20
23.
3
3
z
24.
8 yz 8 ⋅ 5 ⋅ 3 120
=
=
=8
15
15
15
25.
2 y − 2 2(5) − 2 10 − 2 8
=
=
= =4
2
2
2
x
26.
6 + 3x 6 + 3(2) 6 + 6 12
=
=
=
=4
3
3
3
z
27.
x + 2 y 2 + 2 ⋅ 5 2 + 10 12
=
=
=
=4
3
3
3
z
28.
2 z + 6 2 ⋅ 3 + 6 6 + 6 12
=
=
=
=4
3
3
3
3
29.
5 x 10 5(2) 10 10
− =
− = −2 = 2−2 = 0
5
5
5
y
y
37. 2 y (4 z − x) = 2 ⋅ 5(4 ⋅ 3 − 2)
= 2 ⋅ 5(12 − 2)
= 2 ⋅ 5(10)
= 10(10)
= 100
38. 3x( y + z ) = 3 ⋅ 2(5 + 3) = 3 ⋅ 2(8) = 6(8) = 48
39. xy (5 + z − x) = 2 ⋅ 5(5 + 3 − 2)
= 2 ⋅ 5(6)
= 10(6)
= 60
40. xz (2 y + x − z ) = 2 ⋅ 3(2 ⋅ 5 + 2 − 3)
= 2 ⋅ 3(10 + 2 − 3)
= 2 ⋅ 3(9)
= 6(9)
= 54
41.
30.
70 15 70 15 70 15
− =
− =
− = 7−5 = 2
2 y z 2 ⋅ 5 3 10 3
42.
31. 2 y 2 − 4 y + 3 = 2 ⋅ 52 − 4 ⋅ 5 + 3
= 2 ⋅ 25 − 4 ⋅ 5 + 3
= 50 − 20 + 3
= 33
7 x + 2 y 7(2) + 2(5) 14 + 10 24
=
=
=
=4
3x
3(2)
6
6
6z + 2 y 6 ⋅ 3 + 2 ⋅ 5
=
4
4
18 + 10
=
4
28
=
4
=7
43
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
43.
44.
ISM: Prealgebra
t
1
2
3
4
16t 2
16 ⋅12 = 16 ⋅1 = 16
16 ⋅ 22 = 16 ⋅ 4 = 64
16 ⋅ 32 = 16 ⋅ 9 = 144
16 ⋅ 42 = 16 ⋅16 = 256
F
50
59
68
77
5( F − 32)
9
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
45. Let n be 10.
n −8 = 2
10 − 8 ⱨ 2
2 = 2 True
Yes, 10 is a solution.
46. Let n be 9.
n−2 = 7
9−2ⱨ 7
7 = 7 True
Yes, 9 is a solution.
47. Let n be 3.
24 = 80n
24 ⱨ 80 ⋅ 3
24 = 240 False
No, 3 is not a solution.
48. Let n be 50.
250 = 5n
250 ⱨ 5(50)
250 = 250 True
Yes, 50 is a solution.
49. Let n be 7.
3n − 5 = 10
3(7) − 5 ⱨ 10
21 − 5 ⱨ 10
16 = 10 False
No, 7 is not a solution.
50. Let n be 8.
11n + 3 = 91
11(8) + 3 ⱨ 91
88 + 3 ⱨ 91
91 = 91 True
Yes, 8 is a solution.
44
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
58. n + 3 = 16
Let n be 9.
9 + 3 ⱨ 16
12 = 16 False
Let n be 11.
11 + 3 ⱨ 16
14 = 16 False
Let n be 13.
13 + 3 ⱨ 16
16 = 16 True
13 is a solution.
51. Let n be 20.
2(n − 17) = 6
2(20 − 17) ⱨ 6
2(3) ⱨ 6
6 = 6 True
Yes, 20 is a solution.
52. Let n be 0.
5(n + 9) = 40
5(0 + 9) ⱨ 40
5(9) ⱨ 40
45 = 40 False
No, 0 is not a solution.
59. 5n = 30
Let n be 6.
5 ⋅ 6 ⱨ 30
30 = 30 True
Let n be 25.
5 ⋅ 25 ⱨ 30
125 = 30 False
Let n be 30.
5 ⋅ 30 ⱨ 30
150 = 30 False
6 is a solution.
53. Let x be 0.
5 x + 3 = 4 x + 13
5(0) + 3 ⱨ 4(0) + 13
0 + 3 ⱨ 0 + 13
3 = 13 False
No, 0 is not a solution.
54. Let x be 2.
3 x − 6 = 5 x − 10
3(2) − 6 ⱨ 5(2) − 10
6 − 6 ⱨ 10 − 10
0 = 0 True
Yes, 2 is a solution.
60. 3n = 45
Let n be 15.
3 ⋅15 ⱨ 45
45 = 45 True
Let n be 30.
3 ⋅ 30 ⱨ 45
90 = 45 False
Let n be 45.
3 ⋅ 45 ⱨ 45
135 = 45 False
15 is a solution.
55. Let f be 8.
7 f = 64 − f
7(8) ⱨ 64 − 8
56 = 56 True
Yes, 8 is a solution.
56. Let x be 5.
8 x − 30 = 2 x
8(5) − 30 ⱨ 2(5)
40 − 30 ⱨ 10
10 = 10 True
Yes, 5 is a solution.
61. 6n + 2 = 26
Let n be 0.
6(0) + 2 ⱨ 26
0 + 2 ⱨ 26
2 = 26 False
Let n be 2.
6(2) + 2 ⱨ 26
12 + 2 ⱨ 26
14 = 26 False
Let n be 4.
6(4) + 2 ⱨ 26
24 + 2 ⱨ 26
26 = 26 True
4 is a solution.
57. n − 2 = 10
Let n be 10.
10 − 2 ⱨ 10
8 = 10 False
Let n be 12.
12 − 2 ⱨ 10
10 = 10 True
Let n be 14.
14 − 2 ⱨ 10
12 = 10 False
12 is a solution.
45
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
7(7) − 9 ⱨ 5(7) + 13
49 − 9 ⱨ 35 + 13
40 = 48 False
Let x be 11.
7(11) − 9 ⱨ 5(11) + 13
77 − 9 ⱨ 55 + 13
68 = 68 True
11 is a solution.
62. 4n − 14 = 6
Let n be 0.
4 ⋅ 0 − 14 ⱨ 6
0 − 14 ⱨ 6
−14 = 6 False
Let n be 5.
4 ⋅ 5 − 14 ⱨ 6
20 − 14 ⱨ 6
6 = 6 True
Let n be 10.
4 ⋅10 − 14 ⱨ 6
40 − 14 ⱨ 6
26 = 6 False
5 is a solution.
66. 9x − 15 = 5x + 1
Let x be 2.
9 ⋅ 2 − 15 ⱨ 5 ⋅ 2 + 1
18 − 15 ⱨ 10 + 1
3 = 11 False
Let x be 4.
9 ⋅ 4 − 15 ⱨ 5 ⋅ 4 + 1
36 − 15 ⱨ 20 + 1
21 = 21 True
Let x be 11.
9 ⋅11 − 15 ⱨ 5 ⋅11 + 1
99 − 15 ⱨ 55 + 1
84 = 56 False
4 is a solution.
63. 3(n − 4) = 10
Let n be 5.
3(5 − 4) ⱨ 10
3(1) ⱨ 10
3 = 10 False
Let n be 7.
3(7 − 4) ⱨ 10
3(3) ⱨ 10
9 = 10 False
Let n be 10.
3(10 − 4) ⱨ 10
3(6) ⱨ 10
18 = 10 False
None are solutions.
67. Eight more than a number is x + 8.
68. The sum of three and a number is 3 + x.
69. The total of a number and 8 is x + 8.
70. The difference of a number and five hundred is
x − 500.
64. 6(n + 2) = 23
Let n be 1.
6(1 + 2) ⱨ 23
6(3) ⱨ 23
18 = 23 False
Let n be 3.
6(3 + 2) ⱨ 23
6(5) ⱨ 23
30 = 23 False
Let n be 5.
6(5 + 2) ⱨ 23
6(7) ⱨ 23
42 = 23 False
None are solutions.
71. Twenty decreased by a number is 20 − x.
72. A number less thirty is x − 30.
73. The product of 512 and a number is 512x.
74. A number times twenty is 20x.
75. The quotient of six and a number is
76. A number divided by 11 is
65. 7x − 9 = 5x + 13
Let x be 3.
7(3) − 9 ⱨ 5(3) + 13
21 − 9 ⱨ 15 + 13
12 = 28 False
Let x be 7.
6
.
x
x
.
11
77. The sum of seventeen and a number added to the
product of five and the number is 5x + (17 + x).
78. The difference of twice a number, and four is
2x − 4.
79. The product of five and a number is 5x.
46
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
80. The quotient of twenty and a number, decreased
20
by three is
− 3.
x
Chapter 1 Vocabulary Check
1. The whole numbers are 0, 1, 2, 3, ...
2. The perimeter of a polygon is its distance around
or the sum of the lengths of its sides.
81. A number subtracted from 11 is 11 − x.
82. Twelve subtracted from a number is x − 12.
3. The position of each digit in a number
determines its place value.
83. A number less 5 is x − 5.
4. An exponent is a shorthand notation for repeated
multiplication of the same factor.
84. The product of a number and 7 is 7x.
85. 6 divided by a number is 6 ÷ x or
6
.
x
5. To find the area of a rectangle, multiply length
times width.
6. The digits used to write numbers are 0, 1, 2, 3, 4,
5, 6, 7, 8, and 9.
86. The sum of a number and 7 is x + 7.
87. Fifty decreased by eight times a number is
50 − 8x.
7. A letter used to represent a number is called a
variable.
88. Twenty decreased by twice a number is 20 − 2x.
8. An equation can be written in the form
“expression = expression.”
89. x 4 − y 2 = 234 − 722
= 279,841 − 5184
= 274, 657
9. A combination of operations on variables and
numbers is called an expression.
10. A solution of an equation is a value of the
variable that makes the equation a true
statement.
90. 2( x + y )2 = 2(23 + 72)2
2
= 2(95)
= 2(9025)
= 18, 050
11. A collection of numbers (or objects) enclosed by
braces is called a set.
91. x 2 + 5 y − 112 = 232 + 5(72) − 112
= 529 + 360 − 112
= 777
12. The 21 above is called the sum.
13. The 5 above is called the divisor.
14. The 35 above is called the dividend.
92. 16 y − 20 x + x3 = 16 ⋅ 72 − 20 ⋅ 23 + 233
= 1152 − 460 + 12,167
= 12,859
15. The 7 above is called the quotient.
16. The 3 above is called a factor.
93. 5x is the largest; answers may vary.
17. The 6 above is called the product.
x
94.
is the smallest; answers may vary.
3
18. The 20 above is called the minuend.
19. The 9 above is called the subtrahend.
95. As t gets larger, 16t 2 gets larger.
20. The 11 above is called the difference.
5( F − 32)
96. As F gets larger,
gets larger.
9
21. The 4 above is called an addend.
47
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
Chapter 1 Review
16.
583
− 279
304
17.
428
+ 21
449
18.
819
+ 21
840
1. The place value of 4 in 7640 is tens.
2. The place value of 4 in 46,200,120 is tenmillions.
3. 7640 is written as seven thousand, six hundred
forty.
1
4. 46,200,120 is written as forty-six million, two
hundred thousand, one hundred twenty.
5. 3158 = 3000 + 100 + 50 + 8
19.
6. 403,225,000 = 400,000,000 + 3,000,000
+ 200,000 + 20,000 + 5000
7. Eighty-one thousand, nine hundred in standard
form is 81,900.
4000
86
3914
−
8000
92
7908
20.
8. Six billion, three hundred four million in
standard form is 6,304,000,000.
121
9. Locate Houston, Texas in the city column and
read across to the number in the 2000 column.
The population was 1,953,631.
21.
10. Locate Los Angeles, California in the city
column and read across to the number in the
2005 column. the population was 3,844,829.
91
3623
+ 497
4211
11
22.
11. Locate the smallest number in the 2005 column.
San Jose, CA had the smallest population in
2005.
12. Locate the largest number in the 2005 column.
New York, NY had the largest population in
2005.
82
1647
+ 238
1967
11
23.
1
13.
−
18
+ 49
67
74
342
+ 918
1334
The sum of 74, 342, and 918 is 1334.
2
1
14.
28
+ 39
67
15.
462
− 397
65
24.
49
529
+ 308
886
The sum of 49, 529, and 308 is 886.
25.
25,862
− 7 965
17,897
7965 subtracted from 25,862 is 17,897.
48
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
26.
39, 007
− 4 349
34, 658
4349 subtracted from 39,007 is 34,658.
27.
205
+ 7318
7523
The total distance is 7523 miles.
37. To round 43 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 43 rounded to the nearest ten
is 40.
1
38. To round 45 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 45 rounded to the nearest ten is 50.
39. To round 876 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 876 rounded to the nearest ten is
880.
11 1
28.
62,589
65,340
+ 69, 770
197, 699
Her total earnings were $197,699.
40. To round 493 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 493 rounded to the
nearest hundred is 500.
29. 40 + 52 + 52 + 72 = 216
The perimeter is 216 feet.
30. 11 + 20 + 35 = 66
The perimeter is 66 kilometers.
31.
32.
41. To round 3829 to the nearest hundred, observe
that the digit in the tens place is 2. Since this
digit is less than 5, we do not add 1 to the digit in
the hundreds place. The number 3829 rounded to
the nearest hundred is 3800.
1, 256,509
− 1,144, 646
111,863
The population increased by 111,863.
42. To round 57,534 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 57,534
rounded to the nearest thousand is 58,000.
1,517,550
− 1, 463, 281
54, 269
The population decreased by 54,269.
43. To round 39,583,819 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
39,583,819 rounded to the nearest million is
40,000,000.
33. Find the shortest bar. The balance was the least
in May.
34. Find the tallest bar. The balance was the greatest
in August.
35.
280
− 170
110
The balance decreased by $110 from February to
April.
36.
490
− 250
240
The balance increased by $240 from June to
August.
44. To round 768,542 to the nearest hundredthousand, observe that the digit in the tenthousands place is 6. Since this digit is at least 5,
we add 1 to the digit in the hundred-thousands
place. The number 768,542 rounded to the
nearest hundred-thousand is 800,000.
45.
3785
648
+ 2866
rounds to
rounds to
rounds to
49
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
2
3800
600
+ 2900
7300
Chapter 1: The Whole Numbers
46.
5925
− 1787
47.
630
192
271
56
703
454
+ 329
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
rounds to
ISM: Prealgebra
5900
− 1800
4100
600
200
300
100
700
500
+ 300
2700
They traveled approximately 2700 miles.
48.
1, 461,575
− 1, 213,825
rounds to
rounds to
57.
586
× 29
5 274
11 720
16,994
58.
242
× 37
1694
7260
8954
59.
642
177
4 494
44 940
64 200
113, 634
×
1,500,000
− 1,200,000
300,000
The population of Phoenix is approximately
300,000 larger than that of Dallas.
49.
276
× 8
2208
50.
349
× 4
1396
51.
57
× 40
2280
52.
69
× 42
138
2760
2898
60.
347
× 129
3 123
6 940
34 700
44, 763
61.
1026
401
1 026
410 400
411, 426
×
62.
2107
302
4 214
632 100
636,314
×
53. 20(7)(4) = 140(4) = 560
63. “Product” indicates multiplication.
250
× 6
1500
The product of 6 and 250 is 1500.
54. 25(9)(4) = 225(4) = 900
or
25(4)(9) = 100(9) = 900
55. 26 ⋅ 34 ⋅ 0 = 0
56. 62 ⋅ 88 ⋅ 0 = 0
64. “Product” indicates multiplication.
820
× 6
4920
The product of 6 and 820 is 4920.
50
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
65.
Chapter 1: The Whole Numbers
32
× 15
160
320
480
38
× 11
38
380
418
33 R 2
75. 5 167
−15
17
−15
2
480
+ 418
898
The total cost is $898.
66.
Check: 33 × 5 + 2 = 167
19 R 7
76. 8 159
−8
79
−72
7
4820
× 20
96, 400
The total cost is $96,400.
Check: 19 × 8 + 7 = 159
67. Area = (length)(width)
= (13 miles)(7 miles)
= 91 square miles
77. 26
68. Area = (length)(width)
= (25 centimeters)(20 centimeters)
= 500 square centimeters
69.
49
=7
7
Check:
7
×7
49
70.
36
=4
9
Check:
9
×4
36
24 R 2
626
−52
106
−104
2
Check: 24 × 26 + 2 = 626
78. 19
35 R 15
680
−57
110
−95
15
Check: 35 × 19 + 15 = 680
506 R 10
79. 47 23, 792
−23 5
29
−0
292
−282
10
5 R2
71. 5 27
−25
2
Check: 5 × 5 + 2 = 27
4 R2
72. 4 18
−16
2
Check: 506 × 47 + 10 = 23,792
Check: 4 × 4 + 2 = 18
73. 918 ÷ 0 is undefined.
74. 0 ÷ 668 = 0
Check: 0 ⋅ 668 = 0
51
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
80. 53
ISM: Prealgebra
907 R 40
48,111
−47 7
41
−0
411
−371
40
21 R 2
86
−8
06
−4
2
The quotient of 86 and 4 is 21 R 2.
84. 4
27
85. 24 648
−48
168
−168
0
27 boxes can be filled with cans of corn.
Check: 907 × 53 + 40 = 48,111
2793 R 140
81. 207 578, 291
−414
164 2
−144 9
19 39
−18 63
761
−621
140
13
22,880
−17 60
5 280
−5 280
0
There are 13 miles in 22,880 yards.
86. 1760
Check: 2793 × 207 + 140 = 578,291
2012 R 60
82. 306 615, 732
−612
37
−0
3 73
−3 06
672
−612
60
87. Divide the sum by 4.
76
49
32
+ 47
204
The average is 51.
4
51
204
−20
04
−4
0
88. Divide the sum by 4.
Check: 2012 × 306 + 60 = 615,732
23
85
62
+ 66
236
The average is 59.
18 R 2
83. 5 92
−5
42
−40
2
The quotient of 92 and 5 is 18 R 2.
4
89. 82 = 8 ⋅ 8 = 64
90. 53 = 5 ⋅ 5 ⋅ 5 = 125
91. 5 ⋅ 92 = 5 ⋅ 9 ⋅ 9 = 405
92. 4 ⋅102 = 4 ⋅10 ⋅10 = 400
52
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
59
236
−20
36
−36
0
ISM: Prealgebra
Chapter 1: The Whole Numbers
93. 18 ÷ 2 + 7 = 9 + 7 = 16
106. (7 − 5)3 ⋅ [92 ÷ (2 + 7)] = (7 − 5)3 ⋅ [92 ÷ 9]
= (7 − 5)3 ⋅ [81 ÷ 9]
94. 12 − 8 ÷ 4 = 12 − 2 = 10
2
95.
96.
5(6 − 3)
2
3 +2
7(16 − 8)
23
=
5(36 − 3) 5(33) 165
=
=
= 15
9+2
11
11
=
7(8) 56
=
=7
8
8
= 23 ⋅ 9
= 8⋅9
= 72
107.
97. 48 ÷ 8 ⋅ 2 = 6 ⋅ 2 = 12
108.
98. 27 ÷ 9 ⋅ 3 = 3 ⋅ 3 = 9
5⋅ 7 − 3⋅5
2
2(11 − 3 )
4 ⋅ 8 − 1 ⋅11
3
3(9 − 2 )
=
35 − 15
20
20
=
=
=5
2(11 − 9) 2(2) 4
=
32 − 11
21 21
=
=
=7
3(9 − 8) 3(1) 3
109. Area = (side)2 = (7 meters)2 = 49 square meters
99. 2 + 3[15 + (20 − 17) ⋅ 3] + 5 ⋅ 2
= 2 + 3[15 + 3 ⋅ 3] + 5 ⋅ 2
= 2 + 3[1 + 3 ⋅ 3] + 5 ⋅ 2
= 2 + 3[1 + 9] + 5 ⋅ 2
= 2 + 3 ⋅10 + 5 ⋅ 2
= 2 + 30 + 10
= 42
110. Area = (side) 2 = (3 inches) 2 = 9 square inches
111.
2 x 2 ⋅ 5 10
=
=
=5
2
2
z
112. 4x − 3 = 4 ⋅ 5 − 3 = 20 − 3 = 17
4
100. 21 − [2 − (7 − 5) − 10] + 8 ⋅ 2
= 21 − [24 − 2 − 10] + 8 ⋅ 2
= 21 − [16 − 2 − 10] + 8 ⋅ 2
= 21 − 4 + 8 ⋅ 2
= 21 − 4 + 16
= 33
113.
x +7 5+7
is undefined.
=
0
y
114.
y
0
0
=
=
=0
5 x 5 ⋅ 5 25
115. x3 − 2 z = 53 − 2 ⋅ 2 = 125 − 2 ⋅ 2 = 125 − 4 = 121
101. 19 − 2(32 − 22 ) = 19 − 2(9 − 4)
= 19 − 2(5)
= 19 − 10
=9
116.
7 + x 7 + 5 12
=
=
=2
3z
3⋅ 2
6
117. ( y + z )2 = (0 + 2)2 = 22 = 4
102. 16 − 2(42 − 32 ) = 16 − 2(16 − 9)
= 16 − 2(7)
= 16 − 14
=2
118.
100 y 100 0
+ =
+ = 20 + 0 = 20
x
3
5
3
103. 4 ⋅ 5 − 2 ⋅ 7 = 10 − 14 = 6
119. Five subtracted from a number is x − 5.
104. 8 ⋅ 7 − 3 ⋅ 9 = 56 − 27 = 29
120. Seven more than a number is x + 7.
105. (6 − 4)3 ⋅ [102 ÷ (3 + 17)] = (6 − 4)3 ⋅ [102 ÷ 20]
121. Ten divided by a number is 10 ÷ x or
3
= (6 − 4) ⋅ [100 ÷ 20]
= 23 ⋅ 5
= 8⋅5
= 40
122. The product of 5 and a number is 5x.
53
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
10
.
x
Chapter 1: The Whole Numbers
ISM: Prealgebra
123. Let n be 5.
n + 12 = 20 − 3
5 + 12 ⱨ 20 − 3
17 = 17 True
Yes, 5 is a solution.
129. 5(n + 4) = 90
Let n be 14.
5(14 + 4) ⱨ 90
5(18) ⱨ 90
90 = 90 True
Let n be 16.
5(16 + 4) ⱨ 90
5(20) ⱨ 90
100 = 90 False
Let n be 26.
5(26 + 4) ⱨ 90
5(30) ⱨ 90
150 = 90 False
14 is a solution.
124. Let n be 23.
n − 8 = 10 + 6
23 − 8 ⱨ 10 + 6
15 = 16 False
No, 23 is not a solution.
125. Let n = 14.
30 = 3(n − 3)
30 ⱨ 3(14 − 3)
30 ⱨ 3(11)
30 = 33 False
No, 14 is not a solution.
130. 3n − 8 = 28
Let n be 3.
3(3) − 8 ⱨ 28
9 − 8 ⱨ 28
1 = 28 False
Let n be 7.
3(7) − 8 ⱨ 28
21 − 8 ⱨ 28
13 = 28 False
Let n be 15.
3(15) − 8 ⱨ 28
45 − 8 ⱨ 28
37 = 28 False
None are solutions.
126. Let n be 20.
5(n − 7) = 65
5(20 − 7) ⱨ 65
5(13) ⱨ 65
65 = 65 True
Yes, 20 is a solution.
127. 7n = 77
Let n be 6.
7 ⋅ 6 ⱨ 77
42 = 77 False
Let n be 11.
7 ⋅11 ⱨ 77
77 = 77 True
Let n be 20.
7 ⋅ 20 ⱨ 77
140 = 77 False
11 is a solution.
128. n − 25 = 150
Let n be 125.
125 − 25 ⱨ 150
100 = 150 False
Let n be 145.
145 − 25 ⱨ 150
120 = 150 False
Let n be 175.
175 − 25 ⱨ 150
150 = 150 True
175 is a solution.
131.
485
− 68
417
132.
729
− 47
682
133.
732
× 3
2196
134.
629
× 4
2516
22
135.
374
29
+ 698
1101
54
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
144. To round 258,371 to the nearest hundredthousand, observe that the digit in the tenthousands place is 5. Since this digit is at least 5,
we add 1 to the digit in the hundred-thousands
place. The number 258,371 rounded to the
nearest hundred-thousand is 300,000.
21
136.
593
52
+ 766
1411
458 R 8
137. 13 5962
−52
76
−65
112
−104
8
145. 24 ÷ 4 ⋅ 2 = 6 ⋅ 2 = 12
146.
1968
× 36
11 808
59 040
70,848
140.
5324
× 18
42 592
53 240
95,832
141.
2000
− 356
1644
142.
9000
− 519
8481
3
2 +1
=
(18)(3) 54
=
=6
8 +1
9
147. Let n be 9.
5n − 6 = 40
5 ⋅ 9 − 6 ⱨ 40
45 − 6 ⱨ 40
39 = 40 False
No, 9 is not a solution.
237 R 1
138. 18 4267
−36
66
−54
127
−126
1
139.
(15 + 3) ⋅ (8 − 5)
148. Let n be 3.
2n − 6 = 5n − 15
2(3) − 6 ⱨ 5(3) − 15
6 − 6 ⱨ 15 − 15
0 = 0 True
Yes, 3 is a solution.
53
1714
−160
114
−96
18
There are 53 full boxes with 18 left over.
149. 32
150.
27
× 2
54
8
×4
32
54
+ 32
86
The total bill before taxes is $86.
Chapter 1 Test
1. 82,426 in words is eighty-two thousand, four
hundred twenty-six.
143. To round 842 to the nearest ten, observe that the
digit in the ones place is 2. Since this digit is less
than 5, we do not add 1 to the digit in the tens
place. The number 842 rounded to the nearest
ten is 840.
2. Four hundred two thousand, five hundred fifty in
standard form is 402,550.
55
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
Chapter 1: The Whole Numbers
ISM: Prealgebra
16. Divide the sum by 5.
1
3.
59
+ 82
141
4.
600
− 487
113
5.
496
× 30
14,880
6. 69
5
2
62
79
84
90
+ 95
410
The average is 82.
82
410
−40
10
−10
0
17. To round 52,369 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. The number
52,369 rounded to the nearest thousand is
52,000.
766 R 42
52,896
−48 3
4 59
−4 14
456
−414
42
7. 23 ⋅ 52 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 = 200
18.
6289
5403
+ 1957
rounds to
rounds to
rounds to
6 300
5 400
+ 2 000
13,700
19.
4267
− 2738
rounds to
rounds to
4300
− 2700
1600
20.
107
− 15
92
21.
15
+ 107
122
22.
107
× 15
535
1070
1605
8. 98 ÷ 1 = 98
9. 0 ÷ 49 = 0
10. 62 ÷ 0 is undefined.
11. (24 − 5) ⋅ 3 = (16 − 5) ⋅ 3 = 11 ⋅ 3 = 33
12. 16 + 9 ÷ 3 ⋅ 4 − 7 = 16 + 3 ⋅ 4 − 7
= 16 + 12 − 7
= 28 − 7
= 21
13. 61 ⋅ 23 = 6 ⋅ 2 ⋅ 2 ⋅ 2 = 48
14. 2[(6 − 4) 2 + (22 − 19)2 ] + 10 = 2[22 + 32 ] + 10
= 2[4 + 9] + 10
= 2[13] + 10
= 26 + 10
= 36
7 R2
23. 15 107
−105
2
15. 5698 ⋅ 1000 = 5,698,000
56
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall
ISM: Prealgebra
Chapter 1: The Whole Numbers
17
493
−29
203
−203
0
Each can cost $17.
29. Perimeter = (20 + 10 + 20 + 10) yards = 60 yards
Area = (length)(width)
= (20 yards)(10 yards)
= 200 square yards
25.
725
− 599
126
The higher-priced one is $126 more.
31. Let x be 7 and y be 8.
3x − 5 3(7) − 5 21 − 5 16
=
=
=
=1
2y
2 ⋅8
16
16
26.
45
× 8
360
There are 360 calories in 8 tablespoons of white
granulated sugar.
32. a.
430
× 16
2580
4300
6880
33. Let n be 6.
5n − 11 = 19
5(6) − 11 ⱨ 19
30 − 11 ⱨ 19
19 = 19 True
6 is a solution.
24. 29
27.
30. Let x be 2.
5( x3 − 2) = 5(23 − 2) = 5(8 − 2) = 5(6) = 30
The quotient of a number and 17 is x ÷ 17 or
x
.
17
b. Twice a number, decreased by 20 is 2x − 20.
205
× 5
1025
6880
+ 1025
7905
The total cost is $7905.
34. n + 20 = 4n − 10
Let n be 0.
0 + 20 ⱨ 4 ⋅ 0 − 10
20 ⱨ 0 − 10
20 = −10 False
Let n be 10.
10 + 20 ⱨ 4 ⋅10 − 10
30 ⱨ 40 − 10
30 = 30 True
Let n be 20.
20 + 20 ⱨ 4 ⋅ 20 − 10
40 ⱨ 80 − 10
40 = 70 False
10 is a solution.
28. Perimeter = (5 + 5 + 5 + 5) centimeters
= 20 centimeters
Area = (side) 2
= (5 centimeters)2
= 25 square centimeters
57
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