Solution Manual – Algebra: A Combined Approach
(6th Edition) Elayn Martin-Gay
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All Chapters Included | Verified Solutions | Graded A+
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,
INSTRUCTOR’S
SOLUTIONS MANUAL
ALGEBRA:
A COMBINED APPROACH
Unistudydocs Unistudydocs
SIXTH EDITION
Elayn Martin-Gay
University of New Orleans
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, Contents
Chapter R 1
Chapter 1 23
Chapter 2 55
Chapter 3 118
Chapter 4 171
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Chapter 5 215
Chapter 6 259
Chapter 7 300
Chapter 8 355
Chapter 9 388
Chapter 10 429
Chapter 11 477
Chapter 12 583
Chapter 13 642
Appendices 699
Practice Final Exam 724
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, Chapter R
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
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
only. 7. No, the natural number 1 is neither prime nor
42 is a composite number. Its factors are 1, 2, 3, composite.
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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
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
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
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
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,
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
Unistudydocs
(6th Edition) Elayn Martin-Gay
Unistudydocs
Unistudydocs
All Chapters Included | Verified Solutions | Graded A+
Unistudydocs
,
INSTRUCTOR’S
SOLUTIONS MANUAL
ALGEBRA:
A COMBINED APPROACH
Unistudydocs Unistudydocs
SIXTH EDITION
Elayn Martin-Gay
University of New Orleans
Unistudydocs
, Contents
Chapter R 1
Chapter 1 23
Chapter 2 55
Chapter 3 118
Chapter 4 171
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Chapter 5 215
Chapter 6 259
Chapter 7 300
Chapter 8 355
Chapter 9 388
Chapter 10 429
Chapter 11 477
Chapter 12 583
Chapter 13 642
Appendices 699
Practice Final Exam 724
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, Chapter R
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
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
only. 7. No, the natural number 1 is neither prime nor
42 is a composite number. Its factors are 1, 2, 3, composite.
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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
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
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
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
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,
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.
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