Algebra: A Combined Approach – 6th
ST
Edition
INSTRUCTOR’S
UV
SOLUTIONS
IA
_A
MANUAL
PP
Elayn Martin-Gay
RO
VE
Comprehensive Solutions Manual for Instructors
and Students
D?
© Elayn Martin-Gay
??
All rights reserved. Reproduction or distribution without permission is prohibited
©STUDYSTREAM
, Contents
ST
Chapter R 1
Chapter 1 23
UV
Chapter 2 55
Chapter 3 118
IA
Chapter 4 171
Chapter 5 215
_A
Chapter 6 259
Chapter 7 300
PP
Chapter 8 355
Chapter 9 388
RO
Chapter 10 429
Chapter 11 477
VE
Chapter 12 583
Chapter 13 642
D?
Appendices 699
Practice Final Exam 724
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, Chapter R
ST
Section R.1 Practice Exercises 3. A natural number that has exactly two different
factors, 1 and itself, is called a prime number.
1. 10 = 1 ⋅ 10, 10 = 2 ⋅ 5
The factors of 10 are 1, 2, 5, and 10. 4. The least common multiple of a list of numbers
is the smallest number that is a multiple of all the
UV
2. 18 = 1 ⋅ 18, 18 = 2 ⋅ 9, 18 = 3 ⋅ 6 numbers in the list.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
5. To factor means to write as a product.
3. 5 is a prime number. Its factors are 1 and 5 only.
16 is a composite number. Its factors are 1, 2, 4, 6. A multiple of a number is the product of that
8, and 16. number and any natural number.
23 is a prime number. Its factors are 1 and 23
IA
only. 7. No, the natural number 1 is neither prime nor
42 is a composite number. Its factors are 1, 2, 3, composite.
6, 7, 14, 21, and 42.
8. We may write factors in different order, but
4. 44 = 4 ⋅ 11 = 2 ⋅ 2 ⋅ 11 every natural number has only one prime
_A
The prime factorization of 44 is 2 ⋅ 2 ⋅ 11. factorization.
5. 60 = 4 ⋅ 15 = 2 ⋅ 2 ⋅ 3 ⋅ 5 9. The least common multiple, LCM, of a list of
numbers is the smallest number that is a multiple
The prime factorization of 60 is 2 ⋅ 2 ⋅ 3 ⋅ 5.
of each number in the list.
11
Exercise Set R.1
PP
6. 3 33
3 99 2. 8 = 1 ⋅ 8, 8 = 2 ⋅ 4
The factors of 8 are 1, 2, 4, and 8.
3 297
The prime factorization of 297 is 3 ⋅ 3 ⋅ 3 ⋅ 11. 4. 36 = 1 ⋅ 36, 36 = 2 ⋅ 18, 36 = 3 ⋅ 12, 36 = 4 ⋅ 9,
36 = 6 ⋅ 6
RO
7. 14 = 2 ⋅ 7 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and
35 = 5 ⋅ 7 36.
LCM = 2 ⋅ 5 ⋅ 7 = 70
6. 63 = 1 ⋅ 63, 63 = 3 ⋅ 21, 63 = 7 ⋅ 9
8. 5 = 5 The factors of 63 are 1, 3, 7, 9, 21, and 63.
9=3⋅3
8. 50 = 1 ⋅ 50, 50 = 2 ⋅ 25, 50 = 5 ⋅ 10
LCM = 3 ⋅ 3 ⋅ 5 = 45
VE
The factors of 50 are 1, 2, 5, 10, 25, and 50.
9. 4 = 2 ⋅ 2
10. 31 = 1 ⋅ 31
15 = 3 ⋅ 5 The factors of 31 are 1 and 31.
10 = 2 ⋅ 5
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 12. 21 is a composite number. Its factors are 1, 3, 7,
D?
and 21.
Vocabulary, Readiness & Video Check R.1
14. 53 is a prime number. Its factors are only 1 and
1. The number 40 equals 2 ⋅ 2 ⋅ 2 ⋅ 5. Since each 53.
factor is prime, we call 2 ⋅ 2 ⋅ 2 ⋅ 5 the prime
factorization of 40. 16. 51 is a composite number. Its factors are 1, 3, 17,
and 51.
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2. A natural number, other than 1, that is not prime
is called a composite number. 18. 307 is a prime number. Its factors are only 1 and
307.
Copyright © 2020 Pearson Education, Inc. 1
, Chapter R: Prealgebra Review ISM: Algebra A Combined Approach
20. 1798 is a composite number. Its factors are 1, 2, 44. 4 = 2 ⋅ 2
29, 31, 58, 62, 899, and 1798. 18 = 2 ⋅ 3 ⋅ 3
ST
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 3 = 36
22. 28 = 2 ⋅ 14 = 2 ⋅ 2 ⋅ 7
The prime factorization of 28 is 2 ⋅ 2 ⋅ 7. 46. 18 = 2 ⋅ 3 ⋅ 3
30 = 2 ⋅ 3 ⋅ 5
24. 30 = 2 ⋅ 15 = 2 ⋅ 3 ⋅ 5 LCM = 2 ⋅ 3 ⋅ 3 ⋅ 5 = 90
The prime factorization of 30 is 2 ⋅ 3 ⋅ 5.
UV
48. 50 = 2 ⋅ 5 ⋅ 5
26. 48 = 2 ⋅ 24 70 = 2 ⋅ 5 ⋅ 7
= 2 ⋅ 2 ⋅12 LCM = 2 ⋅ 5 ⋅ 5 ⋅ 7 = 350
= 2⋅2⋅2⋅6
= 2⋅ 2⋅ 2⋅ 2⋅3 50. 21 = 3 ⋅ 7
The prime factorization of 48 is 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3. 28 = 2 ⋅ 2 ⋅ 7
IA
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 7 = 84
28. 64 = 4 ⋅ 4 ⋅ 4 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2
The prime factorization of 64 is 52. 3 = 3
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2. 9=3⋅3
20 = 2 ⋅ 2 ⋅ 5
_A
5 LCM = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 5 = 180
30. 5 25
5 125 54. 3 = 3
5=5
2 250 7=7
LCM = 3 ⋅ 5 ⋅ 7 = 105
2 500
PP
The prime factorization of 500 is 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5. 56. 9 = 3 ⋅ 3
36 = 2 ⋅ 2 ⋅ 3 ⋅ 3
7 72 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3
32. 5 35 LCM = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 = 72
3 105
RO
58. 4 = 2 ⋅ 2
3 315 14 = 2 ⋅ 7
The prime factorization of 315 is 3 ⋅ 3 ⋅ 5 ⋅ 7. 35 = 5 ⋅ 7
LCM = 2 ⋅ 2 ⋅ 5 ⋅ 7 = 140
34. 63 = 3 ⋅ 21 = 3 ⋅ 3 ⋅ 7
The prime factorization of 63 is 3 ⋅ 3 ⋅ 7, which 60. answers may vary
VE
is choice c.
62. 35 = 5 ⋅ 7
36. 4 = 2 ⋅ 2 20 = 2 ⋅ 2 ⋅ 5
5=5 LCM = 2 ⋅ 2 ⋅ 5 ⋅ 7 = 140
LCM = 2 ⋅ 2 ⋅ 5 = 20 They are in New Orleans on the same day every
140 days.
38. 9 = 3 ⋅ 3
D?
64. 1000 = 25 ⋅ 40 = 25 ⋅ 5 ⋅ 8
15 = 3 ⋅ 5
1125 = 25 ⋅ 45 = 25 ⋅ 5 ⋅ 9
LCM = 3 ⋅ 3 ⋅ 5 = 45
LCM = 25 ⋅ 5 ⋅ 8 ⋅ 9 = 9000
40. 30 = 2 ⋅ 3 ⋅ 5
Section R.2 Practice Exercises
40 = 2 ⋅ 2 ⋅ 2 ⋅ 5
LCM = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5 = 120
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4
1. = 1 since 4 ÷ 4 = 1.
42. 2 = 2 4
11 = 11
LCM = 2 ⋅ 11 = 22
2 Copyright © 2020 Pearson Education, Inc.
ST
Edition
INSTRUCTOR’S
UV
SOLUTIONS
IA
_A
MANUAL
PP
Elayn Martin-Gay
RO
VE
Comprehensive Solutions Manual for Instructors
and Students
D?
© Elayn Martin-Gay
??
All rights reserved. Reproduction or distribution without permission is prohibited
©STUDYSTREAM
, Contents
ST
Chapter R 1
Chapter 1 23
UV
Chapter 2 55
Chapter 3 118
IA
Chapter 4 171
Chapter 5 215
_A
Chapter 6 259
Chapter 7 300
PP
Chapter 8 355
Chapter 9 388
RO
Chapter 10 429
Chapter 11 477
VE
Chapter 12 583
Chapter 13 642
D?
Appendices 699
Practice Final Exam 724
??
, Chapter R
ST
Section R.1 Practice Exercises 3. A natural number that has exactly two different
factors, 1 and itself, is called a prime number.
1. 10 = 1 ⋅ 10, 10 = 2 ⋅ 5
The factors of 10 are 1, 2, 5, and 10. 4. The least common multiple of a list of numbers
is the smallest number that is a multiple of all the
UV
2. 18 = 1 ⋅ 18, 18 = 2 ⋅ 9, 18 = 3 ⋅ 6 numbers in the list.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
5. To factor means to write as a product.
3. 5 is a prime number. Its factors are 1 and 5 only.
16 is a composite number. Its factors are 1, 2, 4, 6. A multiple of a number is the product of that
8, and 16. number and any natural number.
23 is a prime number. Its factors are 1 and 23
IA
only. 7. No, the natural number 1 is neither prime nor
42 is a composite number. Its factors are 1, 2, 3, composite.
6, 7, 14, 21, and 42.
8. We may write factors in different order, but
4. 44 = 4 ⋅ 11 = 2 ⋅ 2 ⋅ 11 every natural number has only one prime
_A
The prime factorization of 44 is 2 ⋅ 2 ⋅ 11. factorization.
5. 60 = 4 ⋅ 15 = 2 ⋅ 2 ⋅ 3 ⋅ 5 9. The least common multiple, LCM, of a list of
numbers is the smallest number that is a multiple
The prime factorization of 60 is 2 ⋅ 2 ⋅ 3 ⋅ 5.
of each number in the list.
11
Exercise Set R.1
PP
6. 3 33
3 99 2. 8 = 1 ⋅ 8, 8 = 2 ⋅ 4
The factors of 8 are 1, 2, 4, and 8.
3 297
The prime factorization of 297 is 3 ⋅ 3 ⋅ 3 ⋅ 11. 4. 36 = 1 ⋅ 36, 36 = 2 ⋅ 18, 36 = 3 ⋅ 12, 36 = 4 ⋅ 9,
36 = 6 ⋅ 6
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7. 14 = 2 ⋅ 7 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and
35 = 5 ⋅ 7 36.
LCM = 2 ⋅ 5 ⋅ 7 = 70
6. 63 = 1 ⋅ 63, 63 = 3 ⋅ 21, 63 = 7 ⋅ 9
8. 5 = 5 The factors of 63 are 1, 3, 7, 9, 21, and 63.
9=3⋅3
8. 50 = 1 ⋅ 50, 50 = 2 ⋅ 25, 50 = 5 ⋅ 10
LCM = 3 ⋅ 3 ⋅ 5 = 45
VE
The factors of 50 are 1, 2, 5, 10, 25, and 50.
9. 4 = 2 ⋅ 2
10. 31 = 1 ⋅ 31
15 = 3 ⋅ 5 The factors of 31 are 1 and 31.
10 = 2 ⋅ 5
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 12. 21 is a composite number. Its factors are 1, 3, 7,
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and 21.
Vocabulary, Readiness & Video Check R.1
14. 53 is a prime number. Its factors are only 1 and
1. The number 40 equals 2 ⋅ 2 ⋅ 2 ⋅ 5. Since each 53.
factor is prime, we call 2 ⋅ 2 ⋅ 2 ⋅ 5 the prime
factorization of 40. 16. 51 is a composite number. Its factors are 1, 3, 17,
and 51.
??
2. A natural number, other than 1, that is not prime
is called a composite number. 18. 307 is a prime number. Its factors are only 1 and
307.
Copyright © 2020 Pearson Education, Inc. 1
, Chapter R: Prealgebra Review ISM: Algebra A Combined Approach
20. 1798 is a composite number. Its factors are 1, 2, 44. 4 = 2 ⋅ 2
29, 31, 58, 62, 899, and 1798. 18 = 2 ⋅ 3 ⋅ 3
ST
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 3 = 36
22. 28 = 2 ⋅ 14 = 2 ⋅ 2 ⋅ 7
The prime factorization of 28 is 2 ⋅ 2 ⋅ 7. 46. 18 = 2 ⋅ 3 ⋅ 3
30 = 2 ⋅ 3 ⋅ 5
24. 30 = 2 ⋅ 15 = 2 ⋅ 3 ⋅ 5 LCM = 2 ⋅ 3 ⋅ 3 ⋅ 5 = 90
The prime factorization of 30 is 2 ⋅ 3 ⋅ 5.
UV
48. 50 = 2 ⋅ 5 ⋅ 5
26. 48 = 2 ⋅ 24 70 = 2 ⋅ 5 ⋅ 7
= 2 ⋅ 2 ⋅12 LCM = 2 ⋅ 5 ⋅ 5 ⋅ 7 = 350
= 2⋅2⋅2⋅6
= 2⋅ 2⋅ 2⋅ 2⋅3 50. 21 = 3 ⋅ 7
The prime factorization of 48 is 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3. 28 = 2 ⋅ 2 ⋅ 7
IA
LCM = 2 ⋅ 2 ⋅ 3 ⋅ 7 = 84
28. 64 = 4 ⋅ 4 ⋅ 4 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2
The prime factorization of 64 is 52. 3 = 3
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2. 9=3⋅3
20 = 2 ⋅ 2 ⋅ 5
_A
5 LCM = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 5 = 180
30. 5 25
5 125 54. 3 = 3
5=5
2 250 7=7
LCM = 3 ⋅ 5 ⋅ 7 = 105
2 500
PP
The prime factorization of 500 is 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5. 56. 9 = 3 ⋅ 3
36 = 2 ⋅ 2 ⋅ 3 ⋅ 3
7 72 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3
32. 5 35 LCM = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 = 72
3 105
RO
58. 4 = 2 ⋅ 2
3 315 14 = 2 ⋅ 7
The prime factorization of 315 is 3 ⋅ 3 ⋅ 5 ⋅ 7. 35 = 5 ⋅ 7
LCM = 2 ⋅ 2 ⋅ 5 ⋅ 7 = 140
34. 63 = 3 ⋅ 21 = 3 ⋅ 3 ⋅ 7
The prime factorization of 63 is 3 ⋅ 3 ⋅ 7, which 60. answers may vary
VE
is choice c.
62. 35 = 5 ⋅ 7
36. 4 = 2 ⋅ 2 20 = 2 ⋅ 2 ⋅ 5
5=5 LCM = 2 ⋅ 2 ⋅ 5 ⋅ 7 = 140
LCM = 2 ⋅ 2 ⋅ 5 = 20 They are in New Orleans on the same day every
140 days.
38. 9 = 3 ⋅ 3
D?
64. 1000 = 25 ⋅ 40 = 25 ⋅ 5 ⋅ 8
15 = 3 ⋅ 5
1125 = 25 ⋅ 45 = 25 ⋅ 5 ⋅ 9
LCM = 3 ⋅ 3 ⋅ 5 = 45
LCM = 25 ⋅ 5 ⋅ 8 ⋅ 9 = 9000
40. 30 = 2 ⋅ 3 ⋅ 5
Section R.2 Practice Exercises
40 = 2 ⋅ 2 ⋅ 2 ⋅ 5
LCM = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5 = 120
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4
1. = 1 since 4 ÷ 4 = 1.
42. 2 = 2 4
11 = 11
LCM = 2 ⋅ 11 = 22
2 Copyright © 2020 Pearson Education, Inc.
