Solution Manual for Prealgebra and Introductory Algebra, 5th Edition
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I NSTRUCTOR’S S OLUTIONS
M ANUAL
P REALGEBRA &
INTRODUCTORY ALGEBRA
FIFTH EDITION
Elayn Martin-Gay
University of New Orleans
Contents
Chapter 1 1
Chapter 2 42
Chapter 3 71
Chapter 4 101
Chapter 5 164
Chapter 6 209
Chapter 7 254
Chapter 8 285
Chapter 9 325
Chapter 10 368
Chapter 11 414
Chapter 12 454
Chapter 13 507
Chapter 14 567
Chapter 15 612
Chapter 16 647
Appendix 698
Practice Final Exam 704
Chapter 1 1
Chapter 2 42
Chapter 3 71
Chapter 4 101
Chapter 5 164
Chapter 6 209
Chapter 7 254
Chapter 8 285
Chapter 9 325
Chapter 10 368
Chapter 11 414
Chapter 12 454
Chapter 13 507
Chapter 14 567
Chapter 15 612
Chapter 16 647
Appendix 698
Practice Final Exam 704
1
Chapter 1
Section 1.2 Practice Exercises
1. The place value of the 8 in 38,760,005 is
millions.
2. The place value of the 8 in 67,890 is hundreds.
3. The place value of the 8 in 481,922 is ten-
thousands.
4. 54 is written as fifty-four.
5. 678 is written as six hundred seventy-eight.
6. 93,205 is written as ninety-three thousand, two
hundred five.
7. 679,430,105 is written as six hundred seventy-
nine million, four hundred thirty thousand, one
hundred five.
8. Thirty-seven in standard form is 37.
9. Two hundred twelve in standard form is 212.
10. Eight thousand, two hundred seventy-four in
standard form is 8,274 or 8274.
11. Five million, fifty-seven thousand, twenty-six in
standard form is 5,057,026.
12. 4,026,301
= 4,000,000 + 20,000 + 6000 + 300 + 1
13. a. Find Australia in the “Country” column.
Read from left to right until the “bronze”
column is reached. Australia won
10 bronze medals.
b. Find the countries for which the entry in the
“Total” column is greater than 60. The
United States, China, and Great Britain won
more than 60 medals.
Vocabulary, Readiness & Video Check 1.2
1. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, ... are called whole numbers.
2. The number 1286 is written in standard form.
3. The number “twenty-one” is written in words.
4. The number 900 + 60 + 5 is written in expanded
form.
5. In a whole number, each group of 3 digits is
called a period.
6. The place value of the digit 4 in the whole
number 264 is ones.
7. hundreds
8. To read (or write) a number, read from left to
right.
9. 80,000
10. Boxer
Exercise Set 1.2
2. The place value of the 5 in 905 is ones.
4. The place value of the 5 in 6527 is hundreds.
6. The place value of the 5 in 79,050,000 is ten-
thousands.
8. The place value of the 5 in 51,682,700 is ten-
millions.
10. 316 is written as three hundred sixteen.
12. 5445 is written as five thousand, four hundred
forty-five.
14. 42,009 is written as forty-two thousand, nine.
16. 3,204,000 is written as three million, two
hundred four thousand.
18. 47,033,107 is written as forty-seven million,
thirty-three thousand, one hundred seven.
20. 254 is written as two hundred fifty-four.
22. 119,926 is written as one hundred nineteen
thousand, nine hundred twenty-six.
24. 50,400,000,000 is written as fifty billion, four
hundred million.
26. 11,239 is written as eleven thousand, two
hundred thirty-nine.
28. 202,700 is written as two hundred two thousand,
seven hundred.
Chapter 1
Section 1.2 Practice Exercises
1. The place value of the 8 in 38,760,005 is
millions.
2. The place value of the 8 in 67,890 is hundreds.
3. The place value of the 8 in 481,922 is ten-
thousands.
4. 54 is written as fifty-four.
5. 678 is written as six hundred seventy-eight.
6. 93,205 is written as ninety-three thousand, two
hundred five.
7. 679,430,105 is written as six hundred seventy-
nine million, four hundred thirty thousand, one
hundred five.
8. Thirty-seven in standard form is 37.
9. Two hundred twelve in standard form is 212.
10. Eight thousand, two hundred seventy-four in
standard form is 8,274 or 8274.
11. Five million, fifty-seven thousand, twenty-six in
standard form is 5,057,026.
12. 4,026,301
= 4,000,000 + 20,000 + 6000 + 300 + 1
13. a. Find Australia in the “Country” column.
Read from left to right until the “bronze”
column is reached. Australia won
10 bronze medals.
b. Find the countries for which the entry in the
“Total” column is greater than 60. The
United States, China, and Great Britain won
more than 60 medals.
Vocabulary, Readiness & Video Check 1.2
1. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, ... are called whole numbers.
2. The number 1286 is written in standard form.
3. The number “twenty-one” is written in words.
4. The number 900 + 60 + 5 is written in expanded
form.
5. In a whole number, each group of 3 digits is
called a period.
6. The place value of the digit 4 in the whole
number 264 is ones.
7. hundreds
8. To read (or write) a number, read from left to
right.
9. 80,000
10. Boxer
Exercise Set 1.2
2. The place value of the 5 in 905 is ones.
4. The place value of the 5 in 6527 is hundreds.
6. The place value of the 5 in 79,050,000 is ten-
thousands.
8. The place value of the 5 in 51,682,700 is ten-
millions.
10. 316 is written as three hundred sixteen.
12. 5445 is written as five thousand, four hundred
forty-five.
14. 42,009 is written as forty-two thousand, nine.
16. 3,204,000 is written as three million, two
hundred four thousand.
18. 47,033,107 is written as forty-seven million,
thirty-three thousand, one hundred seven.
20. 254 is written as two hundred fifty-four.
22. 119,926 is written as one hundred nineteen
thousand, nine hundred twenty-six.
24. 50,400,000,000 is written as fifty billion, four
hundred million.
26. 11,239 is written as eleven thousand, two
hundred thirty-nine.
28. 202,700 is written as two hundred two thousand,
seven hundred.
Loading page 4...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
2
30. Four thousand, four hundred sixty-eight in
standard form is 4468.
32. Seventy-three thousand, two in standard form is
73,002.
34. Sixteen million, four hundred five thousand,
sixteen in standard form is 16,405,016.
36. Two million, twelve in standard form is
2,000,012.
38. Six hundred forty thousand, eight hundred
eighty-one in standard form is 640,881.
40. Two hundred thirty-four thousand in standard
form is 234,000.
42. One thousand, eight hundred fifteen in standard
form is 1815.
44. Two hundred eight million, eight hundred six
thousand, two hundred seventy in standard form
is 208,806,270.
46. Seven hundred nine in standard form is 709.
48. 789 = 700 + 80 + 9
50. 6040 = 6000 + 40
52. 20,215 = 20,000 + 200 + 10 + 5
54. 99,032 = 90,000 + 9000 + 30 + 2
56. 47,703,029 = 40,000,000 + 7,000,000 + 700,000
+ 3000 + 20 + 9
58. Mount Baker erupted in 1792, which is in
standard form.
60. Mount Shasta and Mount St. Helens have each
had two eruptions listed.
62. Mount St. Helens has an eruption listed in 1980.
All other eruptions listed in the table occurred
before this one.
64. More German shepherds are registered than
Golden retrievers.
66. German shepherds are second in popularity. 26
is written as twenty-six.
68. The maximum height of an average-size
standard poodle is 26 inches.
70. The largest number is 77,753.
72. Yes
74. answers may vary
76. A quadrillion in standard form is
1,000,000,000,000,000.
Section 1.3 Practice Exercises
1. 4135
252
4387
+
2.
1 1 1 1
47,364
135,898
183, 262
+
3. Notice 12 + 8 = 20 and 4 + 6 = 10.
12 + 4 + 8 + 6 + 5 = 20 + 10 + 5 = 35
4.
1 2 2
6432
789
54
28
7303
+
5. a. 14 − 6 = 8 because 8 + 6 = 14.
b. 20 − 8 = 12 because 12 + 8 = 20
c. 93 − 93 = 0 because 0 + 93 = 93.
d. 42 − 0 = 42 because 42 + 0 = 42.
6. a. 9143
122
9021
−
Check: 9021
122
9143
+
b. 978
851
127
−
Check: 127
851
978
+
7. a.
8 17
69 7
4 9
64 8
−
Check: 648
49
697
+
ISM: Prealgebra and Introductory Algebra
2
30. Four thousand, four hundred sixty-eight in
standard form is 4468.
32. Seventy-three thousand, two in standard form is
73,002.
34. Sixteen million, four hundred five thousand,
sixteen in standard form is 16,405,016.
36. Two million, twelve in standard form is
2,000,012.
38. Six hundred forty thousand, eight hundred
eighty-one in standard form is 640,881.
40. Two hundred thirty-four thousand in standard
form is 234,000.
42. One thousand, eight hundred fifteen in standard
form is 1815.
44. Two hundred eight million, eight hundred six
thousand, two hundred seventy in standard form
is 208,806,270.
46. Seven hundred nine in standard form is 709.
48. 789 = 700 + 80 + 9
50. 6040 = 6000 + 40
52. 20,215 = 20,000 + 200 + 10 + 5
54. 99,032 = 90,000 + 9000 + 30 + 2
56. 47,703,029 = 40,000,000 + 7,000,000 + 700,000
+ 3000 + 20 + 9
58. Mount Baker erupted in 1792, which is in
standard form.
60. Mount Shasta and Mount St. Helens have each
had two eruptions listed.
62. Mount St. Helens has an eruption listed in 1980.
All other eruptions listed in the table occurred
before this one.
64. More German shepherds are registered than
Golden retrievers.
66. German shepherds are second in popularity. 26
is written as twenty-six.
68. The maximum height of an average-size
standard poodle is 26 inches.
70. The largest number is 77,753.
72. Yes
74. answers may vary
76. A quadrillion in standard form is
1,000,000,000,000,000.
Section 1.3 Practice Exercises
1. 4135
252
4387
+
2.
1 1 1 1
47,364
135,898
183, 262
+
3. Notice 12 + 8 = 20 and 4 + 6 = 10.
12 + 4 + 8 + 6 + 5 = 20 + 10 + 5 = 35
4.
1 2 2
6432
789
54
28
7303
+
5. a. 14 − 6 = 8 because 8 + 6 = 14.
b. 20 − 8 = 12 because 12 + 8 = 20
c. 93 − 93 = 0 because 0 + 93 = 93.
d. 42 − 0 = 42 because 42 + 0 = 42.
6. a. 9143
122
9021
−
Check: 9021
122
9143
+
b. 978
851
127
−
Check: 127
851
978
+
7. a.
8 17
69 7
4 9
64 8
−
Check: 648
49
697
+
Loading page 5...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
3
b.
2 12
326
245
81
−
Check: 81
245
326
+
c. 1234
822
412
−
Check: 412
822
1234
+
8. a.
9
3 1010
4 0 0
1 6 4
2 3 6
−
Check: 236
164
400
+
b.
9
91010
10 0 0
7 6 2
2 3 8
−
Check: 238
762
1000
+
9. 2 cm + 8 cm + 15 cm + 5 cm = 30 cm
The perimeter is 30 centimeters.
10. 647 + 647 + 647 = 1941
The perimeter is 1941 feet.
11. 15, 759
458
15,301
−
The radius of Neptune is 15,301 miles.
12. a. The country with the fewest threatened
amphibians corresponds to the shortest bar,
which is Madagascar.
b. To find the total number of threatened
amphibians for Madagascar, Peru, and
Mexico, we add.
69
102
211
382
+
The total number of threatened amphibians
for Madagascar, Peru, and Mexico is 382.
Calculator Explorations
1. 89 + 45 = 134
2. 76 + 97 = 173
3. 285 + 55 = 340
4. 8773 + 652 = 9425
5. 985 + 1210 + 562 + 77 = 2834
6. 465 + 9888 + 620 + 1550 = 12,523
7. 865 − 95 = 770
8. 76 − 27 = 49
9. 147 − 38 = 109
10. 366 − 87 = 279
11. 9625 − 647 = 8978
12. 10,711 − 8925 = 1786
Vocabulary, Readiness & Video Check 1.3
1. The sum of 0 and any number is the same
number.
2. In 35 + 20 = 55, the number 55 is called the sum
and 35 and 20 are each called an addend.
3. The difference of any number and that same
number is 0.
4. The difference of any number and 0 is the same
number.
5. In 37 − 19 = 18, the number 37 is the minuend,
the 19 is the subtrahend, and the 18 is the
difference.
6. The distance around a polygon is called its
perimeter.
7. Since 7 + 10 = 10 + 7, we say that changing the
order in addition does not change the sum. This
property is called the commutative property of
addition.
8. Since (3 + 1) + 20 = 3 + (1 + 20), we say that
changing the grouping in addition does not
change the sum. This property is called the
associative property of addition.
9. To add whole numbers, we line up place values
and add from right to left.
10. We cannot take 7 from 2 in the ones place, so we
borrow one ten from the tens place and move it
over to the ones place to give us 10 + 2 or 12.
11. triangle; 3
Chapter 1: The Whole Numbers
3
b.
2 12
326
245
81
−
Check: 81
245
326
+
c. 1234
822
412
−
Check: 412
822
1234
+
8. a.
9
3 1010
4 0 0
1 6 4
2 3 6
−
Check: 236
164
400
+
b.
9
91010
10 0 0
7 6 2
2 3 8
−
Check: 238
762
1000
+
9. 2 cm + 8 cm + 15 cm + 5 cm = 30 cm
The perimeter is 30 centimeters.
10. 647 + 647 + 647 = 1941
The perimeter is 1941 feet.
11. 15, 759
458
15,301
−
The radius of Neptune is 15,301 miles.
12. a. The country with the fewest threatened
amphibians corresponds to the shortest bar,
which is Madagascar.
b. To find the total number of threatened
amphibians for Madagascar, Peru, and
Mexico, we add.
69
102
211
382
+
The total number of threatened amphibians
for Madagascar, Peru, and Mexico is 382.
Calculator Explorations
1. 89 + 45 = 134
2. 76 + 97 = 173
3. 285 + 55 = 340
4. 8773 + 652 = 9425
5. 985 + 1210 + 562 + 77 = 2834
6. 465 + 9888 + 620 + 1550 = 12,523
7. 865 − 95 = 770
8. 76 − 27 = 49
9. 147 − 38 = 109
10. 366 − 87 = 279
11. 9625 − 647 = 8978
12. 10,711 − 8925 = 1786
Vocabulary, Readiness & Video Check 1.3
1. The sum of 0 and any number is the same
number.
2. In 35 + 20 = 55, the number 55 is called the sum
and 35 and 20 are each called an addend.
3. The difference of any number and that same
number is 0.
4. The difference of any number and 0 is the same
number.
5. In 37 − 19 = 18, the number 37 is the minuend,
the 19 is the subtrahend, and the 18 is the
difference.
6. The distance around a polygon is called its
perimeter.
7. Since 7 + 10 = 10 + 7, we say that changing the
order in addition does not change the sum. This
property is called the commutative property of
addition.
8. Since (3 + 1) + 20 = 3 + (1 + 20), we say that
changing the grouping in addition does not
change the sum. This property is called the
associative property of addition.
9. To add whole numbers, we line up place values
and add from right to left.
10. We cannot take 7 from 2 in the ones place, so we
borrow one ten from the tens place and move it
over to the ones place to give us 10 + 2 or 12.
11. triangle; 3
Loading page 6...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
4
12. To find the sale price, subtract the discount from
the regular price.
Exercise Set 1.3
2. 27
31
58
+
4. 37
542
579
+
6. 23
45
30
98
+
8. 236
6243
6479
+
10.
1
17, 427
821, 059
838, 486
+
12. 3
5
8
5
7
28
+
14.
2 2
64
28
56
25
32
205
+
16.
1 1 2
16
1056
748
7770
9590
+
18.
1 1 1 1
6789
4321
5555
16, 665
+
20.
1 1 1
26
582
4 763
62,511
67,882
+
22.
1 1 1 2 1 2
504, 218
321,920
38,507
594, 687
1, 459,332
+
24. 957
257
700
−
Check: 700
257
957
+
26. 55
29
26
−
Check:
1
26
29
55
+
28. 674
299
375
−
Check:
1 1
375
299
674
+
30. 300
149
151
−
Check:
1 1
151
149
300
+
32. 5349
720
4629
−
Check:
1
4629
720
5349
+
34. 724
16
708
−
Check:
1
708
16
724
+
ISM: Prealgebra and Introductory Algebra
4
12. To find the sale price, subtract the discount from
the regular price.
Exercise Set 1.3
2. 27
31
58
+
4. 37
542
579
+
6. 23
45
30
98
+
8. 236
6243
6479
+
10.
1
17, 427
821, 059
838, 486
+
12. 3
5
8
5
7
28
+
14.
2 2
64
28
56
25
32
205
+
16.
1 1 2
16
1056
748
7770
9590
+
18.
1 1 1 1
6789
4321
5555
16, 665
+
20.
1 1 1
26
582
4 763
62,511
67,882
+
22.
1 1 1 2 1 2
504, 218
321,920
38,507
594, 687
1, 459,332
+
24. 957
257
700
−
Check: 700
257
957
+
26. 55
29
26
−
Check:
1
26
29
55
+
28. 674
299
375
−
Check:
1 1
375
299
674
+
30. 300
149
151
−
Check:
1 1
151
149
300
+
32. 5349
720
4629
−
Check:
1
4629
720
5349
+
34. 724
16
708
−
Check:
1
708
16
724
+
Loading page 7...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
5
36. 1983
1914
69
−
Check:
1
69
1914
1983
+
38. 40, 000
23,582
16, 418
−
Check:
1 1 1 1
16, 418
23,582
40, 000
+
40. 6050
1878
4172
−
Check:
1 1 1
4172
1878
6050
+
42. 62, 222
39,898
22,324
−
Check:
1 1 1 1
22,324
39,898
62, 222
+
44. 986
48
938
−
46.
2
80
93
17
9
2
201
+
48. 10, 000
1786
8214
−
50.
1 1 1
12, 468
3 211
1 988
17, 667
+
52. 3 + 4 + 5 = 12
The perimeter is 12 centimeters.
54. Opposite sides of a rectangle have the same
length.
9 + 3 + 9 + 3 = 12 + 12 = 24
The perimeter is 24 miles.
56. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37
The perimeter is 37 inches.
58. The unknown vertical side has length
3 + 5 = 8 feet. The unknown horizontal side has
length 8 + 4 = 12 feet.
8 + 3 + 4 + 5 + 12 + 8 = 40
The perimeter is 40 feet.
60. “Find the sum” indicates addition.
1
802
6487
7289
+
The sum of 802 and 6487 is 7289.
62. “Find the total” indicates addition.
1 2
89
45
2
19
341
496
+
The total of 89, 45, 2, 19, and 341 is 496.
64. “Find the difference” indicates subtraction.
16
5
11
−
The difference of 16 and 5 is 11.
66. “Increased by” indicates addition.
712
38
750
+
712 increased by 38 is 750.
68. “Less” indicates subtraction.
25
12
13
−
25 less 12 is 13.
70. “Subtracted from” indicates subtraction.
90
86
4
−
86 subtracted from 90 is 4.
72. Subtract 39,136 thousand from 44,126 thousand.
44 126
39 136
4 990
−
,
,
California’s projected population increase is
4990 thousand.
Chapter 1: The Whole Numbers
5
36. 1983
1914
69
−
Check:
1
69
1914
1983
+
38. 40, 000
23,582
16, 418
−
Check:
1 1 1 1
16, 418
23,582
40, 000
+
40. 6050
1878
4172
−
Check:
1 1 1
4172
1878
6050
+
42. 62, 222
39,898
22,324
−
Check:
1 1 1 1
22,324
39,898
62, 222
+
44. 986
48
938
−
46.
2
80
93
17
9
2
201
+
48. 10, 000
1786
8214
−
50.
1 1 1
12, 468
3 211
1 988
17, 667
+
52. 3 + 4 + 5 = 12
The perimeter is 12 centimeters.
54. Opposite sides of a rectangle have the same
length.
9 + 3 + 9 + 3 = 12 + 12 = 24
The perimeter is 24 miles.
56. 6 + 5 + 7 + 3 + 4 + 7 + 5 = 37
The perimeter is 37 inches.
58. The unknown vertical side has length
3 + 5 = 8 feet. The unknown horizontal side has
length 8 + 4 = 12 feet.
8 + 3 + 4 + 5 + 12 + 8 = 40
The perimeter is 40 feet.
60. “Find the sum” indicates addition.
1
802
6487
7289
+
The sum of 802 and 6487 is 7289.
62. “Find the total” indicates addition.
1 2
89
45
2
19
341
496
+
The total of 89, 45, 2, 19, and 341 is 496.
64. “Find the difference” indicates subtraction.
16
5
11
−
The difference of 16 and 5 is 11.
66. “Increased by” indicates addition.
712
38
750
+
712 increased by 38 is 750.
68. “Less” indicates subtraction.
25
12
13
−
25 less 12 is 13.
70. “Subtracted from” indicates subtraction.
90
86
4
−
86 subtracted from 90 is 4.
72. Subtract 39,136 thousand from 44,126 thousand.
44 126
39 136
4 990
−
,
,
California’s projected population increase is
4990 thousand.
Loading page 8...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
6
74. Subtract the discount from the regular price.
547
99
448
−
The sale price is $448.
76. 164, 000
40, 000
204, 000
+
The total U.S. land area drained by the Ohio and
Tennessee sub-basins is 204,000 square miles.
78. 189, 000
75, 000
114, 000
−
The Upper Mississippi sub-basin drains 114,000
square miles more than the Lower Mississippi
sub-basin.
80. Opposite sides of a rectangle have the same
length.
60 + 45 + 60 + 45 = 210
The perimeter is 210 feet.
82. 59,320
55, 492
3 828
−
They traveled 3828 miles on their trip.
84. 65 542
49 768
115 310
,
,
,
+
The total number of F-Series trucks and
Silverados sold that month was 115,310.
86. The shortest bar corresponds to the quietest
reading. Leaves rustling is the quietest.
88. 100
70
30
−
The difference in sound intensity between live
rock music and loud television is 30 dB.
90. 119
99
20
−
The difference in volume between the mid-size
and a sub-compact car is 20 cubic feet.
92. Opposite sides of a rectangle have the same
length.
18 + 12 + 18 + 12 = 60
The perimeter of the puzzle is 60 inches.
94. Indiana has the fewest CVS pharmacies.
96. 356 + 867 + 756 + 313 + 301 + 486 + 313 + 309
+ 408 + 659 = 4768
The total number of CVS pharmacies in the ten
states listed is 4768.
98. The total number of CVS pharmacies in the
states listed in the table is 4768.
4768
3048
7816
+
There are 7816 CVS pharmacies in the 50 states.
100.
1
5193
1222
6415
+
The total highway mileage in Rhode Island is
6415 miles.
102. The minuend is 2863 and the subtrahend is 1904.
104. The minuend is 86 and the subtrahend is 25.
106. answers may vary
108.
2 1
773
659
481
1913
+
The given sum is correct.
110.
1 2
19
214
49
651
933
+
The given sum is incorrect, the correct sum is
933.
112.
1 1
389
89
478
+
The given difference is correct.
ISM: Prealgebra and Introductory Algebra
6
74. Subtract the discount from the regular price.
547
99
448
−
The sale price is $448.
76. 164, 000
40, 000
204, 000
+
The total U.S. land area drained by the Ohio and
Tennessee sub-basins is 204,000 square miles.
78. 189, 000
75, 000
114, 000
−
The Upper Mississippi sub-basin drains 114,000
square miles more than the Lower Mississippi
sub-basin.
80. Opposite sides of a rectangle have the same
length.
60 + 45 + 60 + 45 = 210
The perimeter is 210 feet.
82. 59,320
55, 492
3 828
−
They traveled 3828 miles on their trip.
84. 65 542
49 768
115 310
,
,
,
+
The total number of F-Series trucks and
Silverados sold that month was 115,310.
86. The shortest bar corresponds to the quietest
reading. Leaves rustling is the quietest.
88. 100
70
30
−
The difference in sound intensity between live
rock music and loud television is 30 dB.
90. 119
99
20
−
The difference in volume between the mid-size
and a sub-compact car is 20 cubic feet.
92. Opposite sides of a rectangle have the same
length.
18 + 12 + 18 + 12 = 60
The perimeter of the puzzle is 60 inches.
94. Indiana has the fewest CVS pharmacies.
96. 356 + 867 + 756 + 313 + 301 + 486 + 313 + 309
+ 408 + 659 = 4768
The total number of CVS pharmacies in the ten
states listed is 4768.
98. The total number of CVS pharmacies in the
states listed in the table is 4768.
4768
3048
7816
+
There are 7816 CVS pharmacies in the 50 states.
100.
1
5193
1222
6415
+
The total highway mileage in Rhode Island is
6415 miles.
102. The minuend is 2863 and the subtrahend is 1904.
104. The minuend is 86 and the subtrahend is 25.
106. answers may vary
108.
2 1
773
659
481
1913
+
The given sum is correct.
110.
1 2
19
214
49
651
933
+
The given sum is incorrect, the correct sum is
933.
112.
1 1
389
89
478
+
The given difference is correct.
Loading page 9...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
7
114.
1 1
7168
547
7715
+
The given difference is incorrect.
7615
547
7068
−
116. 10, 244
8 534
1 710
−
118. answers may vary
Section 1.4 Practice Exercises
1. a. To round 57 to the nearest ten, observe that
the digit in the ones place is 7. Since the
digit is at least 5, we add 1 to the digit in the
tens place. The number 57 rounded to the
nearest ten is 60.
b. To round 641 to the nearest ten, observe that
the digit in the ones place is 1. Since the
digit is less than 5, we do not add 1 to the
digit in the tens place. The number 641
rounded to the nearest ten is 640.
c. To round 325 to the nearest ten observe that
the digit in the ones place is 5. Since the
digit is at least 5, we add 1 to the digit in the
tens place. The number 325 rounded to the
nearest ten is 330.
2. a. To round 72,304 to the nearest thousand,
observe that the digit in the hundreds place
is 3. Since the digit is less than 5, we do not
add 1 to the digit in the thousands place. The
number 72,304 rounded to the nearest
thousand is 72,000.
b. To round 9222 to the nearest thousand,
observe that the digit in the hundreds place
is 2. Since the digit is less than 5, we do not
add 1 to the digit in the thousands place. The
number 9222 rounded to the nearest
thousand is 9000.
c. To round 671,800 to the nearest thousand,
observe that the digit in the hundreds place
is 8. Since this digit is at least 5, we add 1 to
the digit in the thousands place. The number
671,800 rounded to the nearest thousand is
672,000.
3. a. To round 3474 to the nearest hundred,
observe that the digit in the tens place is 7.
Since this digit is at least 5, we add 1 to the
digit in the hundreds place. The number
3474 rounded to the nearest hundred is
3500.
b. To round 76,243 to the nearest hundred,
observe that the digit in the tens place is 4.
Since this digit is less than 5, we do not add
1 to the digit in the hundreds place. The
number 76,243 rounded to the nearest
hundred is 76,200.
c. To round 978,965 to the nearest hundred,
observe that the digit in the tens place is 6.
Since this digit is at least 5, we add 1 to the
digit in the hundreds place. The number
978,865 rounded to the nearest hundred is
979,000.
4. 49 rounds to 50
25 rounds to 30
32 rounds to 30
51 rounds to 50
98 rounds to + 100
260
5. 3785 rounds to 4000
2479 rounds to 2000
2000
− −
6. 11 rounds to 10
16 rounds to 20
19 rounds to 20
31 rounds to + 30
80
+
The total distance is approximately 80 miles.
7. 2930 rounds to 3000
18,166 rounds to 18,000
189 rounds to + 0
21,000
+
In 2015, there were approximately 21,000
reported cases of these diseases.
Vocabulary, Readiness & Video Check 1.4
1. To graph a number on a number line, darken the
point representing the location of the number.
2. Another word for approximating a whole
number is rounding.
Chapter 1: The Whole Numbers
7
114.
1 1
7168
547
7715
+
The given difference is incorrect.
7615
547
7068
−
116. 10, 244
8 534
1 710
−
118. answers may vary
Section 1.4 Practice Exercises
1. a. To round 57 to the nearest ten, observe that
the digit in the ones place is 7. Since the
digit is at least 5, we add 1 to the digit in the
tens place. The number 57 rounded to the
nearest ten is 60.
b. To round 641 to the nearest ten, observe that
the digit in the ones place is 1. Since the
digit is less than 5, we do not add 1 to the
digit in the tens place. The number 641
rounded to the nearest ten is 640.
c. To round 325 to the nearest ten observe that
the digit in the ones place is 5. Since the
digit is at least 5, we add 1 to the digit in the
tens place. The number 325 rounded to the
nearest ten is 330.
2. a. To round 72,304 to the nearest thousand,
observe that the digit in the hundreds place
is 3. Since the digit is less than 5, we do not
add 1 to the digit in the thousands place. The
number 72,304 rounded to the nearest
thousand is 72,000.
b. To round 9222 to the nearest thousand,
observe that the digit in the hundreds place
is 2. Since the digit is less than 5, we do not
add 1 to the digit in the thousands place. The
number 9222 rounded to the nearest
thousand is 9000.
c. To round 671,800 to the nearest thousand,
observe that the digit in the hundreds place
is 8. Since this digit is at least 5, we add 1 to
the digit in the thousands place. The number
671,800 rounded to the nearest thousand is
672,000.
3. a. To round 3474 to the nearest hundred,
observe that the digit in the tens place is 7.
Since this digit is at least 5, we add 1 to the
digit in the hundreds place. The number
3474 rounded to the nearest hundred is
3500.
b. To round 76,243 to the nearest hundred,
observe that the digit in the tens place is 4.
Since this digit is less than 5, we do not add
1 to the digit in the hundreds place. The
number 76,243 rounded to the nearest
hundred is 76,200.
c. To round 978,965 to the nearest hundred,
observe that the digit in the tens place is 6.
Since this digit is at least 5, we add 1 to the
digit in the hundreds place. The number
978,865 rounded to the nearest hundred is
979,000.
4. 49 rounds to 50
25 rounds to 30
32 rounds to 30
51 rounds to 50
98 rounds to + 100
260
5. 3785 rounds to 4000
2479 rounds to 2000
2000
− −
6. 11 rounds to 10
16 rounds to 20
19 rounds to 20
31 rounds to + 30
80
+
The total distance is approximately 80 miles.
7. 2930 rounds to 3000
18,166 rounds to 18,000
189 rounds to + 0
21,000
+
In 2015, there were approximately 21,000
reported cases of these diseases.
Vocabulary, Readiness & Video Check 1.4
1. To graph a number on a number line, darken the
point representing the location of the number.
2. Another word for approximating a whole
number is rounding.
Loading page 10...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
8
3. The number 65 rounded to the nearest ten is 70,
but the number 61 rounded to the nearest ten is
60.
4. An exact number of products is 1265, but an
estimate is 1000.
5. 3 is in the place we’re rounding to (tens), and the
digit to the right of this place is 5 or greater, so
we need to add 1 to the 3.
6. On a number line, 22 is closer to 20 than to 30.
Thus, 22 rounded to the nearest ten is 20.
7. Each circled digit is to the right of the place
value being rounded to and is used to determine
whether or not we add 1 to the digit in the place
value being rounded to.
Exercise Set 1.4
2. To round 273 to the nearest ten, observe that the
digit in the ones place is 3. Since this digit is less
than 5, we do not add 1 to the digit in the tens
place. The number 273 rounded to the nearest
ten is 270.
4. To round 846 to the nearest ten, observe that the
digit in the ones place is 6. Since this digit is at
least 5, we add 1 to the digit in the tens place.
The number 846 rounded to the nearest ten is
850.
6. To round 8494 to the nearest hundred, observe
that the digit in the tens place is 9. Since this
digit is at least 5, we add 1 to the digit in the
hundreds place. The number 8494 rounded to the
nearest hundred is 8500.
8. To round 898 to the nearest ten, observe that the
digit in the ones place is 8. Since this digit is at
least 5, we add 1 to the digit in the tens place.
The number 898 rounded to the nearest ten is
900.
10. To round 82,198 to the nearest thousand,
observe that the digit in the hundreds place is 1.
Since this digit is less than 5, we do not add 1 to
the digit in the thousands place. The number
82,198 rounded to the nearest thousand is
82,000.
12. To round 42,682 to the nearest ten-thousand,
observe that the digit in the thousands place is 2.
Since this digit is less than 5, we do not add 1 to
the digit in the ten-thousands place. The number
42,682 rounded to the nearest ten-thousand is
40,000.
14. To round 179,406 to the nearest hundred,
observe that the digit in the tens place is 0. Since
this digit is less than 5, we do not add 1 to the
digit in the hundreds place. The number 179,406
rounded to the nearest hundred is 179,400.
16. To round 96,501 to the nearest thousand,
observe that the digit in the hundreds place is 5.
Since this digit is at least 5, we add 1 to the digit
in the thousands place. The number 96,501
rounded to the nearest thousand is 97,000.
18. To round 99,995 to the nearest ten, observe that
the digit in the ones place is 5. Since this digit is
at least 5, we add 1 to the digit in the tens place.
The number 99,995 rounded to the nearest ten is
100,000.
20. To round 39,523,698 to the nearest million,
observe that the digit in the hundred-thousands
place is 5. Since this digit is at least 5, we add 1
to the digit in the millions place. The number
39,523,698 rounded to the nearest million is
40,000,000.
22. Estimate 7619 to a given place value by
rounding it to that place value. 7619 rounded to
the tens place is 7620, to the hundreds place is
7600, and to the thousands place is 8000.
24. Estimate 7777 to a given place value by
rounding it to that place value. 7777 rounded to
the tens place is 7780, to the hundreds place is
7800, and to the thousands place is 8000.
26. Estimate 85,049 to a given place value by
rounding it to that place value. 85,049 rounded
to the tens place is 85,050, to the hundreds place
is 85,000, and to the thousands place is 85,000.
28. To round 171,874 to the nearest thousand,
observe that the digit in the hundreds place is 8.
Since this digit is at least 5, we add 1 to the digit
in the thousands place. Therefore
171,874 miles rounded to the nearest thousand is
172,000 miles.
30. To round 38,387 to the nearest thousand,
observe that the digit in the hundreds place is 3.
Since this digit is less than 5, we do not add 1 to
the digit in the thousands place. Therefore,
38,387 points rounded to the nearest thousand is
38,000 points.
ISM: Prealgebra and Introductory Algebra
8
3. The number 65 rounded to the nearest ten is 70,
but the number 61 rounded to the nearest ten is
60.
4. An exact number of products is 1265, but an
estimate is 1000.
5. 3 is in the place we’re rounding to (tens), and the
digit to the right of this place is 5 or greater, so
we need to add 1 to the 3.
6. On a number line, 22 is closer to 20 than to 30.
Thus, 22 rounded to the nearest ten is 20.
7. Each circled digit is to the right of the place
value being rounded to and is used to determine
whether or not we add 1 to the digit in the place
value being rounded to.
Exercise Set 1.4
2. To round 273 to the nearest ten, observe that the
digit in the ones place is 3. Since this digit is less
than 5, we do not add 1 to the digit in the tens
place. The number 273 rounded to the nearest
ten is 270.
4. To round 846 to the nearest ten, observe that the
digit in the ones place is 6. Since this digit is at
least 5, we add 1 to the digit in the tens place.
The number 846 rounded to the nearest ten is
850.
6. To round 8494 to the nearest hundred, observe
that the digit in the tens place is 9. Since this
digit is at least 5, we add 1 to the digit in the
hundreds place. The number 8494 rounded to the
nearest hundred is 8500.
8. To round 898 to the nearest ten, observe that the
digit in the ones place is 8. Since this digit is at
least 5, we add 1 to the digit in the tens place.
The number 898 rounded to the nearest ten is
900.
10. To round 82,198 to the nearest thousand,
observe that the digit in the hundreds place is 1.
Since this digit is less than 5, we do not add 1 to
the digit in the thousands place. The number
82,198 rounded to the nearest thousand is
82,000.
12. To round 42,682 to the nearest ten-thousand,
observe that the digit in the thousands place is 2.
Since this digit is less than 5, we do not add 1 to
the digit in the ten-thousands place. The number
42,682 rounded to the nearest ten-thousand is
40,000.
14. To round 179,406 to the nearest hundred,
observe that the digit in the tens place is 0. Since
this digit is less than 5, we do not add 1 to the
digit in the hundreds place. The number 179,406
rounded to the nearest hundred is 179,400.
16. To round 96,501 to the nearest thousand,
observe that the digit in the hundreds place is 5.
Since this digit is at least 5, we add 1 to the digit
in the thousands place. The number 96,501
rounded to the nearest thousand is 97,000.
18. To round 99,995 to the nearest ten, observe that
the digit in the ones place is 5. Since this digit is
at least 5, we add 1 to the digit in the tens place.
The number 99,995 rounded to the nearest ten is
100,000.
20. To round 39,523,698 to the nearest million,
observe that the digit in the hundred-thousands
place is 5. Since this digit is at least 5, we add 1
to the digit in the millions place. The number
39,523,698 rounded to the nearest million is
40,000,000.
22. Estimate 7619 to a given place value by
rounding it to that place value. 7619 rounded to
the tens place is 7620, to the hundreds place is
7600, and to the thousands place is 8000.
24. Estimate 7777 to a given place value by
rounding it to that place value. 7777 rounded to
the tens place is 7780, to the hundreds place is
7800, and to the thousands place is 8000.
26. Estimate 85,049 to a given place value by
rounding it to that place value. 85,049 rounded
to the tens place is 85,050, to the hundreds place
is 85,000, and to the thousands place is 85,000.
28. To round 171,874 to the nearest thousand,
observe that the digit in the hundreds place is 8.
Since this digit is at least 5, we add 1 to the digit
in the thousands place. Therefore
171,874 miles rounded to the nearest thousand is
172,000 miles.
30. To round 38,387 to the nearest thousand,
observe that the digit in the hundreds place is 3.
Since this digit is less than 5, we do not add 1 to
the digit in the thousands place. Therefore,
38,387 points rounded to the nearest thousand is
38,000 points.
Loading page 11...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
9
32. To round 322,962,019 to the nearest million,
observe that the digit in the hundred-thousands
place is 9. Since this digit is at least 5, we add 1
to the digit in the millions place. Therefore,
322,962,019 rounded to the nearest million is
323,000,000.
34. To round 2,110,000 to the nearest million,
observe that the digit in the hundred-thousands
place is 1. Since this digit is less than 5, we do
not add 1 to the digit in the millions place.
Therefore, $2,110,000 rounded to the nearest
million is $2,000,000.
36. To round 15,226,000,000 to the nearest ten-
million, observe that the digit in the millions
place is 6. Since this digit is at least 5, we add 1
to the digit in the ten-millions place. Therefore,
15,226,000,000 bushels rounded to the nearest
ten-million is 15,230,000,000 bushels.
38. 52 rounds to 50
33 rounds to 30
15 rounds to 20
29 rounds to + 30
130
+
40. 555 rounds to 560
235 rounds to 240
320
− −
42. 4050 rounds to 4100
3133 rounds to 3100
1220 rounds to 1200
8400
+ +
44. 1989 rounds to 2000
1870 rounds to 1900
100
− −
46. 799 rounds to 800
1655 rounds to 1700
271 rounds to + 300
2800
+
48. 522 + 785 is approximately 520 + 790 = 1310.
The answer of 1307 is correct.
50. 542 + 789 + 198 is approximately
540 + 790 + 200 = 1530.
The answer of 2139 is incorrect.
52. 5233 + 4988 is approximately
5200 + 5000 = 10,200.
The answer of 9011 is incorrect.
54. 89 rounds to 90
97 rounds to 100
100 rounds to 100
79 rounds to 80
75 rounds to 80
82 rounds to + 80
530
+
The total score is approximately 530.
56. 588 rounds to 600
689 rounds to 700
277 rounds to 300
143 rounds to 100
59 rounds to 100
802 rounds to + 800
2600
+
The total distance is approximately 2600 miles.
58. 1895 rounds to 1900
1524 rounds to 1500
400
− −
The difference in price is approximately $400.
60. 64 rounds to 60
41 rounds to 40
133 rounds to + 130
230
+
The total distance is approximately 230 miles.
62. 51, 746 rounds to 52,000
49, 713 rounds to 50, 000
2 000
− −
The increase is approximately 2000 credit hours.
64. 769 hundred-thousands is 76,900,000 in standard
form. 76,900,000 rounded to the nearest million
is 77,000,000. 76,900,000 rounded to the nearest
ten-million is 80,000,000.
66. 568 hundred-thousands is 56,800,000 in standard
form. 56,800,000 rounded to the nearest million
is 57,000,000. 56,800,000 rounded to the nearest
ten-million is 60,000,000.
68. 5698, for example, rounded to the nearest ten is
5700.
Chapter 1: The Whole Numbers
9
32. To round 322,962,019 to the nearest million,
observe that the digit in the hundred-thousands
place is 9. Since this digit is at least 5, we add 1
to the digit in the millions place. Therefore,
322,962,019 rounded to the nearest million is
323,000,000.
34. To round 2,110,000 to the nearest million,
observe that the digit in the hundred-thousands
place is 1. Since this digit is less than 5, we do
not add 1 to the digit in the millions place.
Therefore, $2,110,000 rounded to the nearest
million is $2,000,000.
36. To round 15,226,000,000 to the nearest ten-
million, observe that the digit in the millions
place is 6. Since this digit is at least 5, we add 1
to the digit in the ten-millions place. Therefore,
15,226,000,000 bushels rounded to the nearest
ten-million is 15,230,000,000 bushels.
38. 52 rounds to 50
33 rounds to 30
15 rounds to 20
29 rounds to + 30
130
+
40. 555 rounds to 560
235 rounds to 240
320
− −
42. 4050 rounds to 4100
3133 rounds to 3100
1220 rounds to 1200
8400
+ +
44. 1989 rounds to 2000
1870 rounds to 1900
100
− −
46. 799 rounds to 800
1655 rounds to 1700
271 rounds to + 300
2800
+
48. 522 + 785 is approximately 520 + 790 = 1310.
The answer of 1307 is correct.
50. 542 + 789 + 198 is approximately
540 + 790 + 200 = 1530.
The answer of 2139 is incorrect.
52. 5233 + 4988 is approximately
5200 + 5000 = 10,200.
The answer of 9011 is incorrect.
54. 89 rounds to 90
97 rounds to 100
100 rounds to 100
79 rounds to 80
75 rounds to 80
82 rounds to + 80
530
+
The total score is approximately 530.
56. 588 rounds to 600
689 rounds to 700
277 rounds to 300
143 rounds to 100
59 rounds to 100
802 rounds to + 800
2600
+
The total distance is approximately 2600 miles.
58. 1895 rounds to 1900
1524 rounds to 1500
400
− −
The difference in price is approximately $400.
60. 64 rounds to 60
41 rounds to 40
133 rounds to + 130
230
+
The total distance is approximately 230 miles.
62. 51, 746 rounds to 52,000
49, 713 rounds to 50, 000
2 000
− −
The increase is approximately 2000 credit hours.
64. 769 hundred-thousands is 76,900,000 in standard
form. 76,900,000 rounded to the nearest million
is 77,000,000. 76,900,000 rounded to the nearest
ten-million is 80,000,000.
66. 568 hundred-thousands is 56,800,000 in standard
form. 56,800,000 rounded to the nearest million
is 57,000,000. 56,800,000 rounded to the nearest
ten-million is 60,000,000.
68. 5698, for example, rounded to the nearest ten is
5700.
Loading page 12...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
10
70. The largest possible number that rounds to
1,500,000 when rounded to the nearest hundred-
thousand is 1,549,999.
72. answers may vary
74. 5950 rounds to 6 000
7693 rounds to 7 700
8203 rounds to 8 200
21,900
+ +
The perimeter is approximately 21,900 miles.
Section 1.5 Practice Exercises
1. a. 6 × 0 = 0
b. (1)8 = 8
c. (50)(0) = 0
d. 75 ⋅ 1 = 75
2. a. 6(4 + 5) = 6 ⋅ 4 + 6 ⋅ 5
b. 30(2 + 3) = 30 ⋅ 2 + 30 ⋅ 3
c. 7(2 + 8) = 7 ⋅ 2 + 7 ⋅ 8
3. a. 5
29
6
174
×
b. 4 4
648
5
3240
×
4. 306
81
306
24 480
24, 786
×
5. 726
142
1 452
29 040
72 600
103, 092
×
6. Area length width
(360 miles)(280 miles)
100,800 square miles
= ⋅
=
=
The area of Wyoming is 100,800 square miles.
7. 16
45
80
640
720
×
The printer can print 720 pages in 45 minutes.
8. 8 11 88
5 9 45
× =
× =
1
88
45
133
+
The total cost is $133.
9. 163 rounds to 200
391 rounds to 400
80,000
× ×
There are approximately 80,000 words on 391
pages.
Calculator Explorations
1. 72 × 48 = 3456
2. 81 × 92 = 7452
3. 163 ⋅ 94 = 15,322
4. 285 ⋅ 144 = 41,040
5. 983(277) = 272,291
6. 1562(843) = 1,316,766
Vocabulary, Readiness & Video Check 1.5
1. The product of 0 and any number is 0.
2. The product of 1 and any number is the number.
3. In 8 ⋅ 12 = 96, the 96 is called the product and 8
and 12 are each called a factor.
4. Since 9 ⋅ 10 = 10 ⋅ 9, we say that changing the
order in multiplication does not change the
product. This property is called the commutative
property of multiplication.
ISM: Prealgebra and Introductory Algebra
10
70. The largest possible number that rounds to
1,500,000 when rounded to the nearest hundred-
thousand is 1,549,999.
72. answers may vary
74. 5950 rounds to 6 000
7693 rounds to 7 700
8203 rounds to 8 200
21,900
+ +
The perimeter is approximately 21,900 miles.
Section 1.5 Practice Exercises
1. a. 6 × 0 = 0
b. (1)8 = 8
c. (50)(0) = 0
d. 75 ⋅ 1 = 75
2. a. 6(4 + 5) = 6 ⋅ 4 + 6 ⋅ 5
b. 30(2 + 3) = 30 ⋅ 2 + 30 ⋅ 3
c. 7(2 + 8) = 7 ⋅ 2 + 7 ⋅ 8
3. a. 5
29
6
174
×
b. 4 4
648
5
3240
×
4. 306
81
306
24 480
24, 786
×
5. 726
142
1 452
29 040
72 600
103, 092
×
6. Area length width
(360 miles)(280 miles)
100,800 square miles
= ⋅
=
=
The area of Wyoming is 100,800 square miles.
7. 16
45
80
640
720
×
The printer can print 720 pages in 45 minutes.
8. 8 11 88
5 9 45
× =
× =
1
88
45
133
+
The total cost is $133.
9. 163 rounds to 200
391 rounds to 400
80,000
× ×
There are approximately 80,000 words on 391
pages.
Calculator Explorations
1. 72 × 48 = 3456
2. 81 × 92 = 7452
3. 163 ⋅ 94 = 15,322
4. 285 ⋅ 144 = 41,040
5. 983(277) = 272,291
6. 1562(843) = 1,316,766
Vocabulary, Readiness & Video Check 1.5
1. The product of 0 and any number is 0.
2. The product of 1 and any number is the number.
3. In 8 ⋅ 12 = 96, the 96 is called the product and 8
and 12 are each called a factor.
4. Since 9 ⋅ 10 = 10 ⋅ 9, we say that changing the
order in multiplication does not change the
product. This property is called the commutative
property of multiplication.
Loading page 13...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
11
5. Since (3 ⋅ 4) ⋅ 6 = 3 ⋅ (4 ⋅ 6), we say that
changing the grouping in multiplication does not
change the product. This property is called the
associative property of multiplication.
6. Area measures the amount of surface of a region.
7. Area of a rectangle = length ⋅ width.
8. We know 9(10 + 8) = 9 ⋅ 10 + 9 ⋅ 8 by the
distributive property.
9. distributive
10. To show that 8649 is actually multiplied by 70
and not by just 7.
11. Area is measured in square units, and here we
have meters by meters, or square meters; the
answer is 63 square meters, or the correct units
are square meters.
12. Multiplication is also an application of addition
since it is addition of the same addend.
Exercise Set 1.5
2. 55 ⋅ 1 = 55
4. 27 ⋅ 0 = 0
6. 7 ⋅ 6 ⋅ 0 = 0
8. 1 ⋅ 41 = 41
10. 5(8 + 2) = 5 ⋅ 8 + 5 ⋅ 2
12. 6(1 + 4) = 6 ⋅ 1 + 6 ⋅ 4
14. 12(12 + 3) = 12 ⋅ 12 + 12 ⋅ 3
16. 79
3
237
×
18. 638
5
3190
×
20. 882
2
1764
×
22. 9021
3
27, 063
×
24. 91
72
182
6370
6552
×
26. 526
23
1 578
10 520
12, 098
×
28. 708
21
708
14 160
14,868
×
30. 720
80
57, 600
×
32. (593)(47)(0) = 0
34. (240)(1)(20) = (240)(20) = 4800
36. 1357
79
12 213
94 990
107, 203
×
38. 807
127
5 649
16 140
80 700
102, 489
×
40. 1234
567
8 638
74 040
617 000
699, 678
×
Chapter 1: The Whole Numbers
11
5. Since (3 ⋅ 4) ⋅ 6 = 3 ⋅ (4 ⋅ 6), we say that
changing the grouping in multiplication does not
change the product. This property is called the
associative property of multiplication.
6. Area measures the amount of surface of a region.
7. Area of a rectangle = length ⋅ width.
8. We know 9(10 + 8) = 9 ⋅ 10 + 9 ⋅ 8 by the
distributive property.
9. distributive
10. To show that 8649 is actually multiplied by 70
and not by just 7.
11. Area is measured in square units, and here we
have meters by meters, or square meters; the
answer is 63 square meters, or the correct units
are square meters.
12. Multiplication is also an application of addition
since it is addition of the same addend.
Exercise Set 1.5
2. 55 ⋅ 1 = 55
4. 27 ⋅ 0 = 0
6. 7 ⋅ 6 ⋅ 0 = 0
8. 1 ⋅ 41 = 41
10. 5(8 + 2) = 5 ⋅ 8 + 5 ⋅ 2
12. 6(1 + 4) = 6 ⋅ 1 + 6 ⋅ 4
14. 12(12 + 3) = 12 ⋅ 12 + 12 ⋅ 3
16. 79
3
237
×
18. 638
5
3190
×
20. 882
2
1764
×
22. 9021
3
27, 063
×
24. 91
72
182
6370
6552
×
26. 526
23
1 578
10 520
12, 098
×
28. 708
21
708
14 160
14,868
×
30. 720
80
57, 600
×
32. (593)(47)(0) = 0
34. (240)(1)(20) = (240)(20) = 4800
36. 1357
79
12 213
94 990
107, 203
×
38. 807
127
5 649
16 140
80 700
102, 489
×
40. 1234
567
8 638
74 040
617 000
699, 678
×
Loading page 14...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
12
42. 426
110
4 260
42 600
46,860
×
44. 1876
1407
13 132
750 400
1 876 000
2, 639,532
×
46. Area (length)(width)
(13 inches)(3 inches)
39 square inches
=
=
=
Perimeter length width length width
13 3 13 3
32 inches
= + + +
= + + +
=
48. Area (length)(width)
(25 centimeters)(20 centimeters)
500 square centimeters
=
=
=
Perimeter length width length width
25 20 25 20
90 centimeters
= + + +
= + + +
=
50. 982 rounds to 1000
650 rounds to 700
700, 000
× ×
52. 111 rounds to 100
999 rounds to 1000
100, 000
× ×
54. 2872 × 12 is approximately 2872 × 10, which is
28,720.
The best estimate is b.
56. 706 × 409 is approximately 700 × 400, which is
280,000.
The best estimate is d.
58. 70 12 (7 10) 12
7 (10 12)
7 120
840
× = × ×
= × ×
= ×
=
60. 9 × 900 = 8100
62. 3310
3
9930
×
64. 14
8
112
×
There are 112 grams of fat in 8 ounces of hulled
sunflower seeds.
66. 34
14
136
340
476
×
There are 476 seats in the room.
68. a. 5 × 4 = 20
There are 20 apartments on one floor.
b. 20
3
60
×
There are 60 apartments in the building.
70. Area (length)(width)
(60 feet)(45 feet)
2700 square feet
=
=
=
The area is 2700 square feet.
72. Area (length)(width)
(776 meters)(639 meters)
495,864 square meters
=
=
=
The area is 495,864 square meters.
74. 700
17
4 900
7 000
11,900
×
The 17 discs hold 11,900 MB.
76. 365
3
1095
×
A cow eats 1095 pounds of grain each year.
ISM: Prealgebra and Introductory Algebra
12
42. 426
110
4 260
42 600
46,860
×
44. 1876
1407
13 132
750 400
1 876 000
2, 639,532
×
46. Area (length)(width)
(13 inches)(3 inches)
39 square inches
=
=
=
Perimeter length width length width
13 3 13 3
32 inches
= + + +
= + + +
=
48. Area (length)(width)
(25 centimeters)(20 centimeters)
500 square centimeters
=
=
=
Perimeter length width length width
25 20 25 20
90 centimeters
= + + +
= + + +
=
50. 982 rounds to 1000
650 rounds to 700
700, 000
× ×
52. 111 rounds to 100
999 rounds to 1000
100, 000
× ×
54. 2872 × 12 is approximately 2872 × 10, which is
28,720.
The best estimate is b.
56. 706 × 409 is approximately 700 × 400, which is
280,000.
The best estimate is d.
58. 70 12 (7 10) 12
7 (10 12)
7 120
840
× = × ×
= × ×
= ×
=
60. 9 × 900 = 8100
62. 3310
3
9930
×
64. 14
8
112
×
There are 112 grams of fat in 8 ounces of hulled
sunflower seeds.
66. 34
14
136
340
476
×
There are 476 seats in the room.
68. a. 5 × 4 = 20
There are 20 apartments on one floor.
b. 20
3
60
×
There are 60 apartments in the building.
70. Area (length)(width)
(60 feet)(45 feet)
2700 square feet
=
=
=
The area is 2700 square feet.
72. Area (length)(width)
(776 meters)(639 meters)
495,864 square meters
=
=
=
The area is 495,864 square meters.
74. 700
17
4 900
7 000
11,900
×
The 17 discs hold 11,900 MB.
76. 365
3
1095
×
A cow eats 1095 pounds of grain each year.
Loading page 15...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
13
78. 13
16
78
130
208
×
There are 208 grams of fat in 16 ounces.
80.
Person
Number
of
persons
Cost per
person Cost per
Category
Student 24 $5 $120
Nonstudent 4 $7 $28
Children
under 12 5 $2 $10
Total Cost $158
82. 3 × 18 = 54
There are projected to be 54 million “older”
Americans in 2020.
84. 126
8
118
−
86. 47 + 26 + 10 + 231 + 50 = 364
88. 19
4
76
×
The product of 19 and 4 is 76.
90. 14
9
23
+
The total of 14 and 9 is 23.
92. 11 + 11 + 11 + 11 + 11 + 11 = 6 ⋅ 11 or 11 ⋅ 6
94. a. 4 ⋅ 5 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4
b. answers may vary
96. 31
50
1550
×
98. 57 × 3 = 171
57 × 6 = 342
The problem is 57
63×
100. answers may vary
102. 3 × 87 = 261
2 × 650 = 1300
261 + 1300 + 359 = 1920
LeBron James scored 1920 points during the
2015−2016 regular season.
Section 1.6 Practice Exercises
1. a.
8
9 72 because 8 ⋅ 9 = 72.
b. 40 ÷ 5 = 8 because 8 ⋅ 5 = 40.
c. 24 4
6 = because 4 ⋅ 6 = 24.
2. a. 7 1
7 = because 1 ⋅ 7 = 7.
b. 5 ÷ 1 = 5 because 5 ⋅ 1 = 5.
c.
11
1 11 because 11 ⋅ 1 = 11.
d. 4 ÷ 1 = 4 because 4 ⋅ 1 = 4.
e. 10 10
1 = because 10 ⋅ 1 = 10.
f. 21 ÷ 21 = 1 because 1 ⋅ 21 = 21.
3. a. 0 0
7 = because 0 ⋅ 7 = 0.
b.
0
8 0 because 0 ⋅ 8 = 0.
c. 7 ÷ 0 is undefined because if 7 ÷ 0 is a
number, then the number times 0 would be
7.
d. 0 ÷ 14 = 0 because 0 ⋅ 14 = 0.
Chapter 1: The Whole Numbers
13
78. 13
16
78
130
208
×
There are 208 grams of fat in 16 ounces.
80.
Person
Number
of
persons
Cost per
person Cost per
Category
Student 24 $5 $120
Nonstudent 4 $7 $28
Children
under 12 5 $2 $10
Total Cost $158
82. 3 × 18 = 54
There are projected to be 54 million “older”
Americans in 2020.
84. 126
8
118
−
86. 47 + 26 + 10 + 231 + 50 = 364
88. 19
4
76
×
The product of 19 and 4 is 76.
90. 14
9
23
+
The total of 14 and 9 is 23.
92. 11 + 11 + 11 + 11 + 11 + 11 = 6 ⋅ 11 or 11 ⋅ 6
94. a. 4 ⋅ 5 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4
b. answers may vary
96. 31
50
1550
×
98. 57 × 3 = 171
57 × 6 = 342
The problem is 57
63×
100. answers may vary
102. 3 × 87 = 261
2 × 650 = 1300
261 + 1300 + 359 = 1920
LeBron James scored 1920 points during the
2015−2016 regular season.
Section 1.6 Practice Exercises
1. a.
8
9 72 because 8 ⋅ 9 = 72.
b. 40 ÷ 5 = 8 because 8 ⋅ 5 = 40.
c. 24 4
6 = because 4 ⋅ 6 = 24.
2. a. 7 1
7 = because 1 ⋅ 7 = 7.
b. 5 ÷ 1 = 5 because 5 ⋅ 1 = 5.
c.
11
1 11 because 11 ⋅ 1 = 11.
d. 4 ÷ 1 = 4 because 4 ⋅ 1 = 4.
e. 10 10
1 = because 10 ⋅ 1 = 10.
f. 21 ÷ 21 = 1 because 1 ⋅ 21 = 21.
3. a. 0 0
7 = because 0 ⋅ 7 = 0.
b.
0
8 0 because 0 ⋅ 8 = 0.
c. 7 ÷ 0 is undefined because if 7 ÷ 0 is a
number, then the number times 0 would be
7.
d. 0 ÷ 14 = 0 because 0 ⋅ 14 = 0.
Loading page 16...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
14
4. a.
818
6 4908
48
10
6
48
48
0
−
−
−
Check: 818
6
4908
×
b.
553
4 2212
20
21
20
12
12
0
−
−
−
Check: 553
4
2212
×
c.
251
3 753
6
15
15
03
3
0
−
−
−
Check: 251
3
753
×
5. a.
304
7 2128
21
02
0
28
28
0
−
−
−
Check: 304 × 7 = 2128
b.
5 100
9 45,900
45
0 9
9
000
−
−
Check: 5100 × 9 = 45,900
6. a.
234 R 3
4 939
8
13
12
19
16
3
−
−
−
Check: 234 ⋅ 4 + 3 = 939
b.
657 R 2
5 3287
30
28
25
37
35
2
−
−
−
Check: 657 ⋅ 5 + 2 = 3287
7. a.
9067 R 2
9 81, 605
81
0 6
0
60
54
65
63
2
−
−
−
−
Check: 9067 ⋅ 9 + 2 = 81,605
ISM: Prealgebra and Introductory Algebra
14
4. a.
818
6 4908
48
10
6
48
48
0
−
−
−
Check: 818
6
4908
×
b.
553
4 2212
20
21
20
12
12
0
−
−
−
Check: 553
4
2212
×
c.
251
3 753
6
15
15
03
3
0
−
−
−
Check: 251
3
753
×
5. a.
304
7 2128
21
02
0
28
28
0
−
−
−
Check: 304 × 7 = 2128
b.
5 100
9 45,900
45
0 9
9
000
−
−
Check: 5100 × 9 = 45,900
6. a.
234 R 3
4 939
8
13
12
19
16
3
−
−
−
Check: 234 ⋅ 4 + 3 = 939
b.
657 R 2
5 3287
30
28
25
37
35
2
−
−
−
Check: 657 ⋅ 5 + 2 = 3287
7. a.
9067 R 2
9 81, 605
81
0 6
0
60
54
65
63
2
−
−
−
−
Check: 9067 ⋅ 9 + 2 = 81,605
Loading page 17...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
15
b.
5827 R 2
4 23,310
20
3 3
3 2
11
8
30
28
2
−
−
−
−
Check: 5827 ⋅ 4 + 2 = 23,310
8.
524 R 12
17 8920
85
42
34
80
68
12
−
−
−
9.
49 R 60
678 33, 282
27 12
6 162
6 102
60
−
−
10.
57
3 171
15
21
21
0
−
−
Each student got 57 CDs.
11.
44
12 532
48
52
48
4
−
−
There will be 44 full boxes and 4 printers left
over.
12. Find the sum and divide by 7.
4
7
35
16
9
3
52
126
+
18
7 126
7
56
56
0
−
−
The average time is 18 minutes.
Calculator Explorations
1. 848 ÷ 16 = 53
2. 564 ÷ 12 = 47
3. 5890 ÷ 95 = 62
4. 1053 ÷ 27 = 39
5. 32,886 261
126 =
6. 143, 088 542
264 =
7. 0 ÷ 315 = 0
8. 315 ÷ 0 is an error.
Vocabulary, Readiness & Video Check 1.6
1. In 90 ÷ 2 = 45, the answer 45 is called the
quotient, 90 is called the dividend, and 2 is
called the divisor.
2. The quotient of any number and 1 is the same
number.
3. The quotient of any number (except 0) and the
same number is 1.
4. The quotient of 0 and any number (except 0) is
0.
5. The quotient of any number and 0 is undefined.
6. The average of a list of numbers is the sum of
the numbers divided by the number of numbers.
7. 0
Chapter 1: The Whole Numbers
15
b.
5827 R 2
4 23,310
20
3 3
3 2
11
8
30
28
2
−
−
−
−
Check: 5827 ⋅ 4 + 2 = 23,310
8.
524 R 12
17 8920
85
42
34
80
68
12
−
−
−
9.
49 R 60
678 33, 282
27 12
6 162
6 102
60
−
−
10.
57
3 171
15
21
21
0
−
−
Each student got 57 CDs.
11.
44
12 532
48
52
48
4
−
−
There will be 44 full boxes and 4 printers left
over.
12. Find the sum and divide by 7.
4
7
35
16
9
3
52
126
+
18
7 126
7
56
56
0
−
−
The average time is 18 minutes.
Calculator Explorations
1. 848 ÷ 16 = 53
2. 564 ÷ 12 = 47
3. 5890 ÷ 95 = 62
4. 1053 ÷ 27 = 39
5. 32,886 261
126 =
6. 143, 088 542
264 =
7. 0 ÷ 315 = 0
8. 315 ÷ 0 is an error.
Vocabulary, Readiness & Video Check 1.6
1. In 90 ÷ 2 = 45, the answer 45 is called the
quotient, 90 is called the dividend, and 2 is
called the divisor.
2. The quotient of any number and 1 is the same
number.
3. The quotient of any number (except 0) and the
same number is 1.
4. The quotient of 0 and any number (except 0) is
0.
5. The quotient of any number and 0 is undefined.
6. The average of a list of numbers is the sum of
the numbers divided by the number of numbers.
7. 0
Loading page 18...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
16
8. zero; this zero becomes a placeholder in the
quotient.
9. 202 ⋅ 102 + 15 = 20,619
10. This tells us we have a division problem since
division may be used to separate a quantity into
equal parts.
11. addition and division
Exercise Set 1.6
2. 72 ÷ 9 = 8
4. 24 ÷ 3 = 8
6. 0 ÷ 4 = 0
8. 38 ÷ 1 = 38
10. 49 1
49 =
12. 45 5
9 =
14. 12 is undefined
0
16. 6 ÷ 6 = 1
18. 7 ÷ 0 is undefined
20. 18 ÷ 3 = 6
22.
17
5 85
5
35
35
0
−
−
Check: 17 ⋅ 5 = 85
24.
80
8 640
64
00
−
Check: 80 ⋅ 8 = 640
26.
526
4 2104
20
10
8
24
24
0
−
−
−
Check: 526 ⋅ 4 = 2104
28. 0 0
30 =
Check: 0 ⋅ 30 = 0
30.
7
8 56
56
0
−
Check: 7 ⋅ 8 = 56
32.
11
11 121
11
11
11
0
−
−
Check: 11 ⋅ 11 = 121
34.
60 R 6
7 426
42
06
−
Check: 60 ⋅ 7 + 6 = 426
36.
413 R 1
3 1240
12
04
3
10
9
1
−
−
−
Check: 413 ⋅ 3 + 1 = 1240
ISM: Prealgebra and Introductory Algebra
16
8. zero; this zero becomes a placeholder in the
quotient.
9. 202 ⋅ 102 + 15 = 20,619
10. This tells us we have a division problem since
division may be used to separate a quantity into
equal parts.
11. addition and division
Exercise Set 1.6
2. 72 ÷ 9 = 8
4. 24 ÷ 3 = 8
6. 0 ÷ 4 = 0
8. 38 ÷ 1 = 38
10. 49 1
49 =
12. 45 5
9 =
14. 12 is undefined
0
16. 6 ÷ 6 = 1
18. 7 ÷ 0 is undefined
20. 18 ÷ 3 = 6
22.
17
5 85
5
35
35
0
−
−
Check: 17 ⋅ 5 = 85
24.
80
8 640
64
00
−
Check: 80 ⋅ 8 = 640
26.
526
4 2104
20
10
8
24
24
0
−
−
−
Check: 526 ⋅ 4 = 2104
28. 0 0
30 =
Check: 0 ⋅ 30 = 0
30.
7
8 56
56
0
−
Check: 7 ⋅ 8 = 56
32.
11
11 121
11
11
11
0
−
−
Check: 11 ⋅ 11 = 121
34.
60 R 6
7 426
42
06
−
Check: 60 ⋅ 7 + 6 = 426
36.
413 R 1
3 1240
12
04
3
10
9
1
−
−
−
Check: 413 ⋅ 3 + 1 = 1240
Loading page 19...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
17
38.
55 R 2
3 167
15
17
15
2
−
−
Check: 55 ⋅ 3 + 2 = 167
40.
833 R 1
4 3333
32
13
12
13
12
1
−
−
−
Check: 833 ⋅ 4 + 1 = 3333
42.
32
23 736
69
46
46
0
−
−
Check: 32 ⋅ 23 = 736
44.
48
42 2016
168
336
336
0
−
−
Check: 48 ⋅ 42 = 2016
46.
44 R 2
44 1938
176
178
176
2
−
−
Check: 44 ⋅ 44 + 2 = 1938
48.
612 R 10
12 7354
72
15
12
34
24
10
−
−
−
Check: 612 ⋅ 12 + 10 = 7354
50.
405
14 5670
56
07
0
70
70
0
−
−
−
Check: 405 ⋅ 14 = 5670
52.
39 R 9
64 2505
192
585
576
9
−
−
Check: 39 ⋅ 64 + 9 = 2505
54.
47
123 5781
492
861
861
0
−
−
Check: 47 ⋅ 123 = 5781
56.
96 R 52
240 23, 092
21 60
1 492
1 440
52
−
−
Check: 96 ⋅ 240 + 52 = 23,092
Chapter 1: The Whole Numbers
17
38.
55 R 2
3 167
15
17
15
2
−
−
Check: 55 ⋅ 3 + 2 = 167
40.
833 R 1
4 3333
32
13
12
13
12
1
−
−
−
Check: 833 ⋅ 4 + 1 = 3333
42.
32
23 736
69
46
46
0
−
−
Check: 32 ⋅ 23 = 736
44.
48
42 2016
168
336
336
0
−
−
Check: 48 ⋅ 42 = 2016
46.
44 R 2
44 1938
176
178
176
2
−
−
Check: 44 ⋅ 44 + 2 = 1938
48.
612 R 10
12 7354
72
15
12
34
24
10
−
−
−
Check: 612 ⋅ 12 + 10 = 7354
50.
405
14 5670
56
07
0
70
70
0
−
−
−
Check: 405 ⋅ 14 = 5670
52.
39 R 9
64 2505
192
585
576
9
−
−
Check: 39 ⋅ 64 + 9 = 2505
54.
47
123 5781
492
861
861
0
−
−
Check: 47 ⋅ 123 = 5781
56.
96 R 52
240 23, 092
21 60
1 492
1 440
52
−
−
Check: 96 ⋅ 240 + 52 = 23,092
Loading page 20...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
18
58.
201 R 50
203 40,853
40 6
25
0
253
203
50
−
−
−
Check: 201 ⋅ 203 + 50 = 40,853
60.
303 R 63
543 164,592
162 9
1 69
0
1 692
1 629
63
−
−
−
Check: 303 ⋅ 543 + 63 = 164,592
62.
13
8 104
8
24
24
0
−
−
64.
603 R 2
5 3017
30
01
0
17
15
2
−
−
−
66.
1714 R 47
50 85, 747
50
35 7
35 0
74
50
247
200
47
−
−
−
−
68.
3 040
214 650,560
642
8 5
0
8 56
8 56
00
0
0
−
−
−
−
70.
13 R 3
7 94
7
24
21
3
−
−
The quotient is 13 R 3.
72.
3 R 20
32 116
96
20
−
116 divided by 32 is 3 R 20.
74.
15 R 3
5 78
5
28
25
3
−
−
The quotient is 15 R 3.
76.
58
85 4930
425
680
680
0
−
−
There are 58 students in the group.
ISM: Prealgebra and Introductory Algebra
18
58.
201 R 50
203 40,853
40 6
25
0
253
203
50
−
−
−
Check: 201 ⋅ 203 + 50 = 40,853
60.
303 R 63
543 164,592
162 9
1 69
0
1 692
1 629
63
−
−
−
Check: 303 ⋅ 543 + 63 = 164,592
62.
13
8 104
8
24
24
0
−
−
64.
603 R 2
5 3017
30
01
0
17
15
2
−
−
−
66.
1714 R 47
50 85, 747
50
35 7
35 0
74
50
247
200
47
−
−
−
−
68.
3 040
214 650,560
642
8 5
0
8 56
8 56
00
0
0
−
−
−
−
70.
13 R 3
7 94
7
24
21
3
−
−
The quotient is 13 R 3.
72.
3 R 20
32 116
96
20
−
116 divided by 32 is 3 R 20.
74.
15 R 3
5 78
5
28
25
3
−
−
The quotient is 15 R 3.
76.
58
85 4930
425
680
680
0
−
−
There are 58 students in the group.
Loading page 21...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
19
78.
252000
21 5292000
42
109
105
42
42
0
−
−
−
Each person received $252,000.
80.
412
14 5768
56
16
14
28
28
0
−
−
−
The truck hauls 412 bushels on each trip.
82. Lane divider = 25 + 25 = 50
105
50 5280
50
28
0
280
250
30
−
−
−
There are 105 whole lane dividers.
84.
23 R 1
8 185
16
25
24
1
−
−
Yes, there is enough for a 22-student class.
There is one 8-foot length and 1 additional foot
of rope left over. That is, she has 9 feet of extra
rope.
86.
14
6 84
6
24
24
0
−
−
The players each scored 14 touchdowns.
88.
16
320 5280
320
2080
1920
160
−
−
There are 16 whole feet in 1 rod.
90.
3
37
26
15
29
51
22
180
+
30
6 180
18
00
−
180
Average 30
6
= =
92.
2 1
121
200
185
176
163
845
+
169
5 845
5
34
30
45
45
0
−
−
−
845
Average 169
5
= =
94.
2
92
96
90
85
92
79
534
+
89
6 534
48
54
54
0
−
−
534
Average 89
6
= =
96. 53
40
30
123
+
41
3 123
12
03
3
0
−
−
The average temperature is 41°.
Chapter 1: The Whole Numbers
19
78.
252000
21 5292000
42
109
105
42
42
0
−
−
−
Each person received $252,000.
80.
412
14 5768
56
16
14
28
28
0
−
−
−
The truck hauls 412 bushels on each trip.
82. Lane divider = 25 + 25 = 50
105
50 5280
50
28
0
280
250
30
−
−
−
There are 105 whole lane dividers.
84.
23 R 1
8 185
16
25
24
1
−
−
Yes, there is enough for a 22-student class.
There is one 8-foot length and 1 additional foot
of rope left over. That is, she has 9 feet of extra
rope.
86.
14
6 84
6
24
24
0
−
−
The players each scored 14 touchdowns.
88.
16
320 5280
320
2080
1920
160
−
−
There are 16 whole feet in 1 rod.
90.
3
37
26
15
29
51
22
180
+
30
6 180
18
00
−
180
Average 30
6
= =
92.
2 1
121
200
185
176
163
845
+
169
5 845
5
34
30
45
45
0
−
−
−
845
Average 169
5
= =
94.
2
92
96
90
85
92
79
534
+
89
6 534
48
54
54
0
−
−
534
Average 89
6
= =
96. 53
40
30
123
+
41
3 123
12
03
3
0
−
−
The average temperature is 41°.
Loading page 22...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
20
98.
1 1
23
407
92
7011
7533
+
100. 712
54
2 848
35 600
38, 448
×
102. 712
54
658
−
104. 0 0
23 = because 0 ⋅ 23 = 0
106.
9 R 25
31 304
279
25
−
108. The quotient of 200 and 20 is 200 ÷ 20, which is
choice b.
110. 40 divided by 8 is 40 ÷ 8, which is choice c.
112. 3,500, 000, 000
2, 680, 000, 000
2, 250, 000, 000
1,800, 000, 000
10, 230, 000, 000
+
2,557,500, 000
4 10, 230, 000, 000
8
2 2
2 0
23
20
30
28
2 0
2 0
000 000
−
−
−
−
−
The top four advertisers spent an average of
$2,557,500,000.
114. The average will decrease; answers may vary.
116. No; answers may vary
Possible answer: The average cannot be less than
each of the four numbers.
118. 84 ÷ 21 = 4
The width is 4 inches.
120. answers may vary
Possible answer: 2 and 2
122. 86
10
76
10
66
10
56
10
46
−
−
−
−
46
10
36
10
26
10
16
10
6
−
−
−
−
Therefore, 86 ÷ 10 = 8 R 6.
Integrated Review
1.
1
42
63
89
194
+
2. 7006
451
6555
−
3. 87
52
174
4350
4524
×
4.
562
8 4496
40
49
48
16
16
0
−
−
−
5. 1 ⋅ 67 = 67
6. 36
0 is undefined.
7. 16 ÷ 16 = 1
ISM: Prealgebra and Introductory Algebra
20
98.
1 1
23
407
92
7011
7533
+
100. 712
54
2 848
35 600
38, 448
×
102. 712
54
658
−
104. 0 0
23 = because 0 ⋅ 23 = 0
106.
9 R 25
31 304
279
25
−
108. The quotient of 200 and 20 is 200 ÷ 20, which is
choice b.
110. 40 divided by 8 is 40 ÷ 8, which is choice c.
112. 3,500, 000, 000
2, 680, 000, 000
2, 250, 000, 000
1,800, 000, 000
10, 230, 000, 000
+
2,557,500, 000
4 10, 230, 000, 000
8
2 2
2 0
23
20
30
28
2 0
2 0
000 000
−
−
−
−
−
The top four advertisers spent an average of
$2,557,500,000.
114. The average will decrease; answers may vary.
116. No; answers may vary
Possible answer: The average cannot be less than
each of the four numbers.
118. 84 ÷ 21 = 4
The width is 4 inches.
120. answers may vary
Possible answer: 2 and 2
122. 86
10
76
10
66
10
56
10
46
−
−
−
−
46
10
36
10
26
10
16
10
6
−
−
−
−
Therefore, 86 ÷ 10 = 8 R 6.
Integrated Review
1.
1
42
63
89
194
+
2. 7006
451
6555
−
3. 87
52
174
4350
4524
×
4.
562
8 4496
40
49
48
16
16
0
−
−
−
5. 1 ⋅ 67 = 67
6. 36
0 is undefined.
7. 16 ÷ 16 = 1
Loading page 23...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
21
8. 5 ÷ 1 = 5
9. 0 ⋅ 21 = 0
10. 7 ⋅ 0 ⋅ 8 = 0
11. 0 ÷ 7 = 0
12. 12 ÷ 4 = 3
13. 9 ⋅ 7 = 63
14. 45 ÷ 5 = 9
15. 207
69
138
−
16.
1
207
69
276
+
17. 3718
2549
1169
−
18.
1 1
1861
7965
9826
+
19.
182 R 4
7 1278
7
57
56
18
14
4
−
−
−
20. 1259
63
3 777
75 540
79,317
×
21.
1099 R 2
7 7695
7
06
0
69
63
65
63
2
−
−
−
−
22.
111 R 1
9 1000
9
10
9
10
9
1
−
−
−
23.
663 R 24
32 21, 240
19 2
2 04
1 92
120
96
24
−
−
−
24.
1 076 R 60
65 70, 000
65
5 0
0
5 00
4 55
450
390
60
−
−
−
−
25. 4000
2963
1037
−
26. 10, 000
101
9 899
−
Chapter 1: The Whole Numbers
21
8. 5 ÷ 1 = 5
9. 0 ⋅ 21 = 0
10. 7 ⋅ 0 ⋅ 8 = 0
11. 0 ÷ 7 = 0
12. 12 ÷ 4 = 3
13. 9 ⋅ 7 = 63
14. 45 ÷ 5 = 9
15. 207
69
138
−
16.
1
207
69
276
+
17. 3718
2549
1169
−
18.
1 1
1861
7965
9826
+
19.
182 R 4
7 1278
7
57
56
18
14
4
−
−
−
20. 1259
63
3 777
75 540
79,317
×
21.
1099 R 2
7 7695
7
06
0
69
63
65
63
2
−
−
−
−
22.
111 R 1
9 1000
9
10
9
10
9
1
−
−
−
23.
663 R 24
32 21, 240
19 2
2 04
1 92
120
96
24
−
−
−
24.
1 076 R 60
65 70, 000
65
5 0
0
5 00
4 55
450
390
60
−
−
−
−
25. 4000
2963
1037
−
26. 10, 000
101
9 899
−
Loading page 24...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
22
27. 303
101
303
30 300
30,603
×
28. (475)(100) = 47,500
29.
1
62
9
71
+
The total of 62 and 9 is 71.
30. 62
9
558
×
The product of 62 and 9 is 558.
31.
6 R 8
9 62
54
8
−
The quotient of 62 and 9 is 6 R 8.
32. 62
9
53
−
The difference of 62 and 9 is 53.
33. 200
17
183
−
17 subtracted from 200 is 183.
34. 432
201
231
−
The difference of 432 and 201 is 231.
35. 9735 rounded to the nearest ten is 9740.
9735 rounded to the nearest hundred is 9700.
9735 rounded to the nearest thousand is 10,000.
36. 1429 rounded to the nearest ten is 1430.
1429 rounded to the nearest hundred is 1400.
1429 rounded to the nearest thousand is 1000.
37. 20,801 rounded to the nearest ten is 20,800.
20,801 rounded to the nearest hundred is 20,800.
20,801 rounded to the nearest thousand is
21,000.
38. 432,198 rounded to the nearest ten is 432,200.
432,198 rounded to the nearest hundred is
432,200.
432,198 rounded to the nearest thousand is
432,000.
39. 6 + 6 + 6 + 6 = 24
6 × 6 = 36
The perimeter is 24 feet and the area is 36 square
feet.
40. 14 + 7 + 14 + 7 = 42
14
7
98
×
The perimeter is 42 inches and the area is
98 square inches.
41. 13
9
6
28
+
The perimeter is 28 miles.
42. The unknown vertical side has length
4 + 3 = 7 meters. The unknown horizontal side
has length 3 + 3 = 6 meters.
3
4
3
7
6
3
26
+
The perimeter is 26 meters.
43.
3
19
15
25
37
24
120
+
24
5 120
10
20
20
0
−
−
120
Average 24
5
= =
ISM: Prealgebra and Introductory Algebra
22
27. 303
101
303
30 300
30,603
×
28. (475)(100) = 47,500
29.
1
62
9
71
+
The total of 62 and 9 is 71.
30. 62
9
558
×
The product of 62 and 9 is 558.
31.
6 R 8
9 62
54
8
−
The quotient of 62 and 9 is 6 R 8.
32. 62
9
53
−
The difference of 62 and 9 is 53.
33. 200
17
183
−
17 subtracted from 200 is 183.
34. 432
201
231
−
The difference of 432 and 201 is 231.
35. 9735 rounded to the nearest ten is 9740.
9735 rounded to the nearest hundred is 9700.
9735 rounded to the nearest thousand is 10,000.
36. 1429 rounded to the nearest ten is 1430.
1429 rounded to the nearest hundred is 1400.
1429 rounded to the nearest thousand is 1000.
37. 20,801 rounded to the nearest ten is 20,800.
20,801 rounded to the nearest hundred is 20,800.
20,801 rounded to the nearest thousand is
21,000.
38. 432,198 rounded to the nearest ten is 432,200.
432,198 rounded to the nearest hundred is
432,200.
432,198 rounded to the nearest thousand is
432,000.
39. 6 + 6 + 6 + 6 = 24
6 × 6 = 36
The perimeter is 24 feet and the area is 36 square
feet.
40. 14 + 7 + 14 + 7 = 42
14
7
98
×
The perimeter is 42 inches and the area is
98 square inches.
41. 13
9
6
28
+
The perimeter is 28 miles.
42. The unknown vertical side has length
4 + 3 = 7 meters. The unknown horizontal side
has length 3 + 3 = 6 meters.
3
4
3
7
6
3
26
+
The perimeter is 26 meters.
43.
3
19
15
25
37
24
120
+
24
5 120
10
20
20
0
−
−
120
Average 24
5
= =
Loading page 25...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
23
44.
1 2
108
131
98
159
496
+
124
4 496
4
09
8
16
16
0
−
−
−
496
Average 124
4
= =
45. 28,547
26,372
2 175
−
The Lake Pontchartrain Bridge is longer by
2175 feet.
46. 309
18
2472
3090
5562
×
The amount spent on toys is $5562.
Section 1.7 Practice Exercises
1. 4
8 8 8 8 8⋅ ⋅ ⋅ =
2. 3
3 3 3 3⋅ ⋅ =
3. 5
10 10 10 10 10 10⋅ ⋅ ⋅ ⋅ =
4. 2 6
5 5 4 4 4 4 4 4 5 4⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅
5. 2
4 4 4 16= ⋅ =
6. 3
7 7 7 7 343= ⋅ ⋅ =
7. 1
11 11=
8. 2
2 3 2 3 3 18⋅ = ⋅ ⋅ =
9. 9 3 8 4 27 8 4 27 2 25⋅ − ÷ = − ÷ = − =
10. 2
48 3 2 48 3 4 16 4 64÷ ⋅ = ÷ ⋅ = ⋅ =
11. 4 2 4 2
(10 7) 2 3 3 2 3
81 2 9
81 18
99
− + ⋅ = + ⋅
= + ⋅
= +
=
12. 3 3
3
36 [20 (4 2)] 4 6 36 [20 8] 4 6
36 12 4 6
36 12 64 6
3 64 6
61
÷ − ⋅ + − = ÷ − + −
= ÷ + −
= ÷ + −
= + −
=
13.
3
25 8 2 3 25 8 2 27
2(3 2) 2(1)
25 16 27
2
14
2
7
+ ⋅ − + ⋅ −
=
−
+ −
=
=
=
14. 36 6 3 5 6 3 5 18 5 23÷ ⋅ + = ⋅ + = + =
15. 2
2
Area (side)
(12 centimeters)
144 square centimeters
=
=
=
The area of the square is 144 square centimeters.
Calculator Explorations
1. 6
4 4096=
2. 6
5 15, 625=
3. 5
5 3125=
4. 6
7 117, 649=
5. 11
2 2048=
6. 8
6 1, 679, 616=
7. 4 3
7 5 2526+ =
8. 4 4
12 8 16,640− =
9. 63 ⋅ 75 − 43 ⋅ 10 = 4295
10. 8 ⋅ 22 + 7 ⋅ 16 = 288
11. 4(15 ÷ 3 + 2) − 10 ⋅ 2 = 8
Chapter 1: The Whole Numbers
23
44.
1 2
108
131
98
159
496
+
124
4 496
4
09
8
16
16
0
−
−
−
496
Average 124
4
= =
45. 28,547
26,372
2 175
−
The Lake Pontchartrain Bridge is longer by
2175 feet.
46. 309
18
2472
3090
5562
×
The amount spent on toys is $5562.
Section 1.7 Practice Exercises
1. 4
8 8 8 8 8⋅ ⋅ ⋅ =
2. 3
3 3 3 3⋅ ⋅ =
3. 5
10 10 10 10 10 10⋅ ⋅ ⋅ ⋅ =
4. 2 6
5 5 4 4 4 4 4 4 5 4⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅
5. 2
4 4 4 16= ⋅ =
6. 3
7 7 7 7 343= ⋅ ⋅ =
7. 1
11 11=
8. 2
2 3 2 3 3 18⋅ = ⋅ ⋅ =
9. 9 3 8 4 27 8 4 27 2 25⋅ − ÷ = − ÷ = − =
10. 2
48 3 2 48 3 4 16 4 64÷ ⋅ = ÷ ⋅ = ⋅ =
11. 4 2 4 2
(10 7) 2 3 3 2 3
81 2 9
81 18
99
− + ⋅ = + ⋅
= + ⋅
= +
=
12. 3 3
3
36 [20 (4 2)] 4 6 36 [20 8] 4 6
36 12 4 6
36 12 64 6
3 64 6
61
÷ − ⋅ + − = ÷ − + −
= ÷ + −
= ÷ + −
= + −
=
13.
3
25 8 2 3 25 8 2 27
2(3 2) 2(1)
25 16 27
2
14
2
7
+ ⋅ − + ⋅ −
=
−
+ −
=
=
=
14. 36 6 3 5 6 3 5 18 5 23÷ ⋅ + = ⋅ + = + =
15. 2
2
Area (side)
(12 centimeters)
144 square centimeters
=
=
=
The area of the square is 144 square centimeters.
Calculator Explorations
1. 6
4 4096=
2. 6
5 15, 625=
3. 5
5 3125=
4. 6
7 117, 649=
5. 11
2 2048=
6. 8
6 1, 679, 616=
7. 4 3
7 5 2526+ =
8. 4 4
12 8 16,640− =
9. 63 ⋅ 75 − 43 ⋅ 10 = 4295
10. 8 ⋅ 22 + 7 ⋅ 16 = 288
11. 4(15 ÷ 3 + 2) − 10 ⋅ 2 = 8
Loading page 26...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
24
12. 155 − 2(17 + 3) + 185 = 300
Vocabulary, Readiness & Video Check 1.7
1. In 5
2 32,= the 2 is called the base and the 5 is
called the exponent.
2. To simplify 8 + 2 ⋅ 6, which operation should be
performed first? multiplication
3. To simplify (8 + 2) ⋅ 6, which operation should
be performed first? addition
4. To simplify 9(3 − 2) ÷ 3 + 6, which operation
should be performed first? subtraction
5. To simplify 8 ÷ 2 ⋅ 6, which operation should be
performed first? division
6. exponent; base
7. 1
8. division, multiplication, addition
9. The area of a rectangle is length ⋅ width. A
square is a special rectangle where
length = width. Thus, the area of a square is
side ⋅ side or 2
side)( .
Exercise Set 1.7
2. 4
5 5 5 5 5⋅ ⋅ ⋅ =
4. 7
6 6 6 6 6 6 6 6⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =
6. 3
10 10 10 10⋅ ⋅ =
8. 2 3
4 4 3 3 3 4 3⋅ ⋅ ⋅ ⋅ = ⋅
10. 3
7 4 4 4 7 4⋅ ⋅ ⋅ = ⋅
12. 4
4 6 6 6 6 4 6⋅ ⋅ ⋅ ⋅ = ⋅
14. 2 4
6 6 2 9 9 9 9 6 2 9⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅
16. 2
6 6 6 36= ⋅ =
18. 3
6 6 6 6 216= ⋅ ⋅ =
20. 5
3 3 3 3 3 3 243= ⋅ ⋅ ⋅ ⋅ =
22. 12
1 1 1 1 1 1 1 1 1 1 1 1 1 1= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =
24. 1
8 8=
26. 4
5 5 5 5 5 625= ⋅ ⋅ ⋅ =
28. 3
3 3 3 3 27= ⋅ ⋅ =
30. 3
4 4 4 4 64= ⋅ ⋅ =
32. 3
8 8 8 8 512= ⋅ ⋅ =
34. 2
11 11 11 121= ⋅ =
36. 3
10 10 10 10 1000= ⋅ ⋅ =
38. 1
14 14=
40. 5
4 4 4 4 4 4 1024= ⋅ ⋅ ⋅ ⋅ =
42. 2
5 3 5 3 3 45⋅ = ⋅ ⋅ =
44. 2
2 7 2 7 7 98⋅ = ⋅ ⋅ =
46. 24 + 6 ⋅ 3 = 24 + 18 = 42
48. 100 ÷ 10 ⋅ 5 + 4 = 10 ⋅ 5 + 4 = 50 + 4 = 54
50. 42 ÷ 7 − 6 = 6 − 6 = 0
52. 8
32 32 4 36
2
+ = + =
54. 3 ⋅ 4 + 9 ⋅ 1 = 12 + 9 = 21
56. 2
6 9 3 6 3 9 1
9 93
+ ÷ +
= = =
58. 2 2
6 (10 8) 6 2 36 2 72⋅ − = ⋅ = ⋅ =
60. 3 2 3 3 2 3
5 (10 15) 9 3 5 25 9 3
125 25 81 27
5 81 27
113
÷ + + + = ÷ + +
= ÷ + +
= + +
=
62. 2 2
40 8 48 48 3
25 9 165 3
+ = = =
−−
64. (9 − 7) ⋅ (12 + 18) = 2 ⋅ 30 = 60
ISM: Prealgebra and Introductory Algebra
24
12. 155 − 2(17 + 3) + 185 = 300
Vocabulary, Readiness & Video Check 1.7
1. In 5
2 32,= the 2 is called the base and the 5 is
called the exponent.
2. To simplify 8 + 2 ⋅ 6, which operation should be
performed first? multiplication
3. To simplify (8 + 2) ⋅ 6, which operation should
be performed first? addition
4. To simplify 9(3 − 2) ÷ 3 + 6, which operation
should be performed first? subtraction
5. To simplify 8 ÷ 2 ⋅ 6, which operation should be
performed first? division
6. exponent; base
7. 1
8. division, multiplication, addition
9. The area of a rectangle is length ⋅ width. A
square is a special rectangle where
length = width. Thus, the area of a square is
side ⋅ side or 2
side)( .
Exercise Set 1.7
2. 4
5 5 5 5 5⋅ ⋅ ⋅ =
4. 7
6 6 6 6 6 6 6 6⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =
6. 3
10 10 10 10⋅ ⋅ =
8. 2 3
4 4 3 3 3 4 3⋅ ⋅ ⋅ ⋅ = ⋅
10. 3
7 4 4 4 7 4⋅ ⋅ ⋅ = ⋅
12. 4
4 6 6 6 6 4 6⋅ ⋅ ⋅ ⋅ = ⋅
14. 2 4
6 6 2 9 9 9 9 6 2 9⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅
16. 2
6 6 6 36= ⋅ =
18. 3
6 6 6 6 216= ⋅ ⋅ =
20. 5
3 3 3 3 3 3 243= ⋅ ⋅ ⋅ ⋅ =
22. 12
1 1 1 1 1 1 1 1 1 1 1 1 1 1= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ =
24. 1
8 8=
26. 4
5 5 5 5 5 625= ⋅ ⋅ ⋅ =
28. 3
3 3 3 3 27= ⋅ ⋅ =
30. 3
4 4 4 4 64= ⋅ ⋅ =
32. 3
8 8 8 8 512= ⋅ ⋅ =
34. 2
11 11 11 121= ⋅ =
36. 3
10 10 10 10 1000= ⋅ ⋅ =
38. 1
14 14=
40. 5
4 4 4 4 4 4 1024= ⋅ ⋅ ⋅ ⋅ =
42. 2
5 3 5 3 3 45⋅ = ⋅ ⋅ =
44. 2
2 7 2 7 7 98⋅ = ⋅ ⋅ =
46. 24 + 6 ⋅ 3 = 24 + 18 = 42
48. 100 ÷ 10 ⋅ 5 + 4 = 10 ⋅ 5 + 4 = 50 + 4 = 54
50. 42 ÷ 7 − 6 = 6 − 6 = 0
52. 8
32 32 4 36
2
+ = + =
54. 3 ⋅ 4 + 9 ⋅ 1 = 12 + 9 = 21
56. 2
6 9 3 6 3 9 1
9 93
+ ÷ +
= = =
58. 2 2
6 (10 8) 6 2 36 2 72⋅ − = ⋅ = ⋅ =
60. 3 2 3 3 2 3
5 (10 15) 9 3 5 25 9 3
125 25 81 27
5 81 27
113
÷ + + + = ÷ + +
= ÷ + +
= + +
=
62. 2 2
40 8 48 48 3
25 9 165 3
+ = = =
−−
64. (9 − 7) ⋅ (12 + 18) = 2 ⋅ 30 = 60
Loading page 27...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
25
66. 2
5(12 7) 4 5(5) 4 25 4 21 3
25 18 25 18 75 18
− − − −
= = = =
− −−
68. 18 − 7 ÷ 0 = undefined
70. 3 3
2 3 (100 10) 2 3 10
8 3 10
24 10
14
⋅ − ÷ = ⋅ −
= ⋅ −
= −
=
72. 5 5
5
[40 (8 2)] 2 [40 6] 2
34 2
34 32
2
− − − = − −
= −
= −
=
74. (18 6) [(3 5) 2] (18 6) (8 2)
3 (8 2)
3 16
19
÷ + + ⋅ = ÷ + ⋅
= + ⋅
= +
=
76. 2 2
2 2
35 [3 (9 7) 2 ] 10 3
35 [3 2 2 ] 10 3
35 [9 2 4] 10 3
35 7 10 3
5 10 3
5 30
35
÷ + − − + ⋅
= ÷ + − + ⋅
= ÷ + − + ⋅
= ÷ + ⋅
= + ⋅
= +
=
78.
2 3 4
5 2 1 25 8 1 18 18 9
10 5 4 1 4 2 4 1 4 8 4 2
− + − +
= = = =
÷ ⋅ ⋅ ÷ ⋅ ⋅ ÷ ÷
80.
2
2 2
3 9 3 81
3(10 6) 2 1 3(4) 2 1
84
3(4) 4 1
84
12 4 1
84
8 1
84
7
12
+ +
=
− − − − −
= − −
= − −
= −
=
=
82. 3
10 2 3 2 20 10 2 27 2 20
5 27 2 20
5 54 20
39
÷ + ⋅ − = ÷ + ⋅ −
= + ⋅ −
= + −
=
84. 2 2 2 2
2
2
2
[15 (11 6) 2 ] (5 1) [15 5 2 ] 4
[15 5 4] 4
[3 4] 4
7 4
7 16
23
÷ − + + − = ÷ + +
= ÷ + +
= + +
= +
= +
=
86. 29 {5 3[8 (10 8)] 50}
29 {5 3[8 2] 50}
29 {5 3(16) 50}
29 {5 48 50}
29 3
26
− + ⋅ − −
= − + ⋅ −
= − + −
= − + −
= −
=
88. 2
2
Area of a square (side)
(9 centimeters)
81 square centimeters
=
=
=
Perimeter 4(side)
4(9 centimeters)
36 centimeters
=
=
=
90. 2
2
Area of a square (side)
(41 feet)
1681 square feet
=
=
=
Perimeter = 4(side) = 4(41 feet) = 164 feet
92. The statement is true.
94. 9
4 4 4 4 4 4 4 4 4 4= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
The statement is false.
96. (2 + 3) ⋅ (6 − 2) = (5) ⋅ (4) = 20
98. 24 (3 2 2) 5 24 (6 2) 5
24 8 5
3 5
15
÷ ⋅ + ⋅ = ÷ + ⋅
= ÷ ⋅
= ⋅
=
100. The total perimeter is 1260 feet.
4 × 1260 = 5040
The total charge is $5040.
102. 3 3
3
25 (45 7 5) 5 25 (45 35) 5
25 (10) 5
15, 625 10 5
156, 250 5
781, 250
⋅ − ⋅ ⋅ = ⋅ − ⋅
= ⋅ ⋅
= ⋅ ⋅
= ⋅
=
104. answers may vary
Chapter 1: The Whole Numbers
25
66. 2
5(12 7) 4 5(5) 4 25 4 21 3
25 18 25 18 75 18
− − − −
= = = =
− −−
68. 18 − 7 ÷ 0 = undefined
70. 3 3
2 3 (100 10) 2 3 10
8 3 10
24 10
14
⋅ − ÷ = ⋅ −
= ⋅ −
= −
=
72. 5 5
5
[40 (8 2)] 2 [40 6] 2
34 2
34 32
2
− − − = − −
= −
= −
=
74. (18 6) [(3 5) 2] (18 6) (8 2)
3 (8 2)
3 16
19
÷ + + ⋅ = ÷ + ⋅
= + ⋅
= +
=
76. 2 2
2 2
35 [3 (9 7) 2 ] 10 3
35 [3 2 2 ] 10 3
35 [9 2 4] 10 3
35 7 10 3
5 10 3
5 30
35
÷ + − − + ⋅
= ÷ + − + ⋅
= ÷ + − + ⋅
= ÷ + ⋅
= + ⋅
= +
=
78.
2 3 4
5 2 1 25 8 1 18 18 9
10 5 4 1 4 2 4 1 4 8 4 2
− + − +
= = = =
÷ ⋅ ⋅ ÷ ⋅ ⋅ ÷ ÷
80.
2
2 2
3 9 3 81
3(10 6) 2 1 3(4) 2 1
84
3(4) 4 1
84
12 4 1
84
8 1
84
7
12
+ +
=
− − − − −
= − −
= − −
= −
=
=
82. 3
10 2 3 2 20 10 2 27 2 20
5 27 2 20
5 54 20
39
÷ + ⋅ − = ÷ + ⋅ −
= + ⋅ −
= + −
=
84. 2 2 2 2
2
2
2
[15 (11 6) 2 ] (5 1) [15 5 2 ] 4
[15 5 4] 4
[3 4] 4
7 4
7 16
23
÷ − + + − = ÷ + +
= ÷ + +
= + +
= +
= +
=
86. 29 {5 3[8 (10 8)] 50}
29 {5 3[8 2] 50}
29 {5 3(16) 50}
29 {5 48 50}
29 3
26
− + ⋅ − −
= − + ⋅ −
= − + −
= − + −
= −
=
88. 2
2
Area of a square (side)
(9 centimeters)
81 square centimeters
=
=
=
Perimeter 4(side)
4(9 centimeters)
36 centimeters
=
=
=
90. 2
2
Area of a square (side)
(41 feet)
1681 square feet
=
=
=
Perimeter = 4(side) = 4(41 feet) = 164 feet
92. The statement is true.
94. 9
4 4 4 4 4 4 4 4 4 4= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
The statement is false.
96. (2 + 3) ⋅ (6 − 2) = (5) ⋅ (4) = 20
98. 24 (3 2 2) 5 24 (6 2) 5
24 8 5
3 5
15
÷ ⋅ + ⋅ = ÷ + ⋅
= ÷ ⋅
= ⋅
=
100. The total perimeter is 1260 feet.
4 × 1260 = 5040
The total charge is $5040.
102. 3 3
3
25 (45 7 5) 5 25 (45 35) 5
25 (10) 5
15, 625 10 5
156, 250 5
781, 250
⋅ − ⋅ ⋅ = ⋅ − ⋅
= ⋅ ⋅
= ⋅ ⋅
= ⋅
=
104. answers may vary
Loading page 28...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
26
Section 1.8 Practice Exercises
1. x − 2 = 7 − 2 = 5
2. y(x − 3) = 4(8 − 3) = 4(5) = 20
3. 6 18 6 24 4
6 6
y
x
+ +
= = =
4. 3 3
25 25 2 1 25 8 1 18z x− + = − + = − + =
5. 5( 32) 5(41 32) 5(9) 45 5
9 9 9 9
F − −
= = = =
6. 3( 6) 6
3(8 6) 6
3(2) 6
6 6 True
y − =
−
=
Yes, 8 is a solution.
7. 5n + 4 = 34
Let n be 10.
5(10) 4 34
50 4 34
54 34 False
+
+
=
No, 10 is not a solution.
Let n be 6.
5(6) 4 34
30 4 34
34 34 True
+
+
=
Yes, 6 is a solution.
Let n be 8.
5(8) 4 34
40 4 34
44 34 False
+
+
=
No, 8 is not a solution.
8. a. Twice a number is 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, Readiness & Video Check 1.8
1. A combination of operations on letters (variables) and numbers is an expression.
2. A letter that represents a number is a variable.
ISM: Prealgebra and Introductory Algebra
26
Section 1.8 Practice Exercises
1. x − 2 = 7 − 2 = 5
2. y(x − 3) = 4(8 − 3) = 4(5) = 20
3. 6 18 6 24 4
6 6
y
x
+ +
= = =
4. 3 3
25 25 2 1 25 8 1 18z x− + = − + = − + =
5. 5( 32) 5(41 32) 5(9) 45 5
9 9 9 9
F − −
= = = =
6. 3( 6) 6
3(8 6) 6
3(2) 6
6 6 True
y − =
−
=
Yes, 8 is a solution.
7. 5n + 4 = 34
Let n be 10.
5(10) 4 34
50 4 34
54 34 False
+
+
=
No, 10 is not a solution.
Let n be 6.
5(6) 4 34
30 4 34
34 34 True
+
+
=
Yes, 6 is a solution.
Let n be 8.
5(8) 4 34
40 4 34
44 34 False
+
+
=
No, 8 is not a solution.
8. a. Twice a number is 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, Readiness & Video Check 1.8
1. A combination of operations on letters (variables) and numbers is an expression.
2. A letter that represents a number is a variable.
Loading page 29...
ISM: Prealgebra and Introductory Algebra
Chapter 1: The Whole Numbers
27
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 the expression.
5. A statement of the form
“expression = expression” is called an equation.
6. A value for the variable that makes an equation a true statement is called a solution.
7. When a letter and a variable are next to each other, the operation is an understood multiplication.
8. When first replacing f with 8, we don’t know if the statement is true or false.
9. decreased by
Exercise Set 1.8
2. a b a + b a − b a ⋅ b a ÷ b
24 6 24 + 6 = 30 24 − 6 = 18 24 ⋅ 6 = 144 24 ÷ 6 = 4
4. a b a + b a − b a ⋅ b a ÷ b
298 0 298 + 0 = 298 298 − 0 = 298 298 ⋅ 0 = 0 298 ÷ 0 is undefined.
6. a b a + b a − b a ⋅ b a ÷ b
82 1 82 + 1 = 83 82 − 1 = 81 82 ⋅ 1 = 82 82 ÷ 1 = 82
8. 7 + 3z = 7 + 3(3) = 7 + 9 = 16
10. 4yz + 2x = 4(5)(3) + 2(2) = 60 + 4 = 64
12. x + 5y − z = 2 + 5(5) − 3 = 2 + 25 − 3 = 24
14. 2y + 5z = 2(5) + 5(3) = 10 + 15 = 25
16. 3 3
5 3 125 3 122y z− = − = − =
18. 2 2
3 1 3(5)(3) 1
3 5 9 1
135 1
136
yz + = +
= ⋅ ⋅ +
= +
=
20. 3 (2 4) 3 (2 5 4)
3 (10 4)
3 6
9
y+ − = + ⋅ −
= + −
= +
=
22. 4 4 4
( ) 2 (5 3) 2 2 16 2 14x y z− − = − − = − = − =
Chapter 1: The Whole Numbers
27
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 the expression.
5. A statement of the form
“expression = expression” is called an equation.
6. A value for the variable that makes an equation a true statement is called a solution.
7. When a letter and a variable are next to each other, the operation is an understood multiplication.
8. When first replacing f with 8, we don’t know if the statement is true or false.
9. decreased by
Exercise Set 1.8
2. a b a + b a − b a ⋅ b a ÷ b
24 6 24 + 6 = 30 24 − 6 = 18 24 ⋅ 6 = 144 24 ÷ 6 = 4
4. a b a + b a − b a ⋅ b a ÷ b
298 0 298 + 0 = 298 298 − 0 = 298 298 ⋅ 0 = 0 298 ÷ 0 is undefined.
6. a b a + b a − b a ⋅ b a ÷ b
82 1 82 + 1 = 83 82 − 1 = 81 82 ⋅ 1 = 82 82 ÷ 1 = 82
8. 7 + 3z = 7 + 3(3) = 7 + 9 = 16
10. 4yz + 2x = 4(5)(3) + 2(2) = 60 + 4 = 64
12. x + 5y − z = 2 + 5(5) − 3 = 2 + 25 − 3 = 24
14. 2y + 5z = 2(5) + 5(3) = 10 + 15 = 25
16. 3 3
5 3 125 3 122y z− = − = − =
18. 2 2
3 1 3(5)(3) 1
3 5 9 1
135 1
136
yz + = +
= ⋅ ⋅ +
= +
=
20. 3 (2 4) 3 (2 5 4)
3 (10 4)
3 6
9
y+ − = + ⋅ −
= + −
= +
=
22. 4 4 4
( ) 2 (5 3) 2 2 16 2 14x y z− − = − − = − = − =
Loading page 30...
Chapter 1: The Whole Numbers
ISM: Prealgebra and Introductory Algebra
28
24. 8 8 5 3 120 8
15 15 15
yz ⋅ ⋅
= = =
26. 6 3 6 3(2) 6 6 12 4
3 3 3
x
z
+ + +
= = = =
28. 2 6 2 3 6 6 6 12 4
3 3 3 3
z + ⋅ + +
= = = =
30. 70 15 70 15 70 15 7 5 2
2 2 5 3 10 3y z
− = − = − = − =
⋅
32. 2 2
3 2 5 3 2 2 2 5
3 4 2 2 5
12 4 5
11
x x+ − = ⋅ + ⋅ −
= ⋅ + ⋅ −
= + −
=
34. 2 2
2
2
(4 3 ) (4 5 3 3)
(20 9)
29
841
y z+ = ⋅ + ⋅
= +
=
=
36. 4 4 4 4
( 5) (2 3 5) (6 5) 1 1xz − = ⋅ − = − = =
38. 3 ( ) 3 2(5 3) 3 2(8) 6(8) 48x y z+ = ⋅ + = ⋅ = =
40. (2 ) 2 3(2 5 2 3)
2 3(10 2 3)
2 3(9)
6(9)
54
xz y x z+ − = ⋅ ⋅ + −
= ⋅ + −
= ⋅
=
=
42. 6 2 6 3 2 5
4 4
18 10
4
28
4
7
z y+ ⋅ + ⋅
=
+
=
=
=
44. F 50 59 68 77
5( 32)
9
F − 5(50 32) 5(18) 10
9 9
− = = 5(59 32) 5(27) 15
9 9
− = = 5(68 32) 5(36) 20
9 9
− = = 5(77 32) 5(45) 25
9 9
− = =
ISM: Prealgebra and Introductory Algebra
28
24. 8 8 5 3 120 8
15 15 15
yz ⋅ ⋅
= = =
26. 6 3 6 3(2) 6 6 12 4
3 3 3
x
z
+ + +
= = = =
28. 2 6 2 3 6 6 6 12 4
3 3 3 3
z + ⋅ + +
= = = =
30. 70 15 70 15 70 15 7 5 2
2 2 5 3 10 3y z
− = − = − = − =
⋅
32. 2 2
3 2 5 3 2 2 2 5
3 4 2 2 5
12 4 5
11
x x+ − = ⋅ + ⋅ −
= ⋅ + ⋅ −
= + −
=
34. 2 2
2
2
(4 3 ) (4 5 3 3)
(20 9)
29
841
y z+ = ⋅ + ⋅
= +
=
=
36. 4 4 4 4
( 5) (2 3 5) (6 5) 1 1xz − = ⋅ − = − = =
38. 3 ( ) 3 2(5 3) 3 2(8) 6(8) 48x y z+ = ⋅ + = ⋅ = =
40. (2 ) 2 3(2 5 2 3)
2 3(10 2 3)
2 3(9)
6(9)
54
xz y x z+ − = ⋅ ⋅ + −
= ⋅ + −
= ⋅
=
=
42. 6 2 6 3 2 5
4 4
18 10
4
28
4
7
z y+ ⋅ + ⋅
=
+
=
=
=
44. F 50 59 68 77
5( 32)
9
F − 5(50 32) 5(18) 10
9 9
− = = 5(59 32) 5(27) 15
9 9
− = = 5(68 32) 5(36) 20
9 9
− = = 5(77 32) 5(45) 25
9 9
− = =
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