Elementary & Intermediate Algebra (4th Edition) – Michael Sullivan – Complete Solutions Manual (Chapters 1–13)

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, Contents
Chapter 1 1
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Chapter 2 50
Chapter 3 124
Chapter 4 202
Chapter 5 267
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Chapter 6 315
Getting Ready for Intermediate Algebra:
A Review of Chapters 1−6 362
Chapter 7 365
Getting Ready for Intermediate Algebra:
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A Review of Chapters 1−7 443
Chapter 8 448
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Chapter 9 530
Chapter 10 606
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Chapter 11 747
Chapter 12 812
Chapter 13 894
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Appendix A 938
Appendix B 941
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Appendix C 949
Appendix E 994

, Chapter 1
Section 1.2 10. 14 = 2 · 7
9= 3·3
1.2 Quick Checks
2·7·3·3
1. A natural number is prime if its only factors are
1 and itself. The LCM is 2 ⋅ 7 ⋅ 3 ⋅ 3 = 126.

2. In the statement 6 ⋅ 8 = 48, 6 and 8 are called 11. 12 = 2 · 2 · 3
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18 = 2 · 3·3
factors and 48 is called the product.
30 = 2 · 3· 5
3. 12
2·2·3·3·5
2 6
The LCM is 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 5 = 180.
2 ·2·3
The prime factorization of 12 is 2 ⋅ 2 ⋅ 3. 7
12. In the fraction , 7 is called the numerator and
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12
4. 120
12 is called the denominator.
4 30
13. Fractions which represent the same portion of a
2 2 2 15
whole are called equivalent fractions.
2·2·2·3 ·5
The prime factorization of 120 is 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5. 1
14. Multiply the numerator and denominator of
2
5. 31 is a prime number. by 5.
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1 1⋅ 5 5
6. 117 = =
/ \ 2 2 ⋅ 5 10
9 13
/\ \ 5
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15. Multiply the numerator and denominator of
3 ⋅ 3 ⋅ 13 8
The prime factorization of 117 is 3 ⋅ 3 ⋅ 13. by 6.
5 5 ⋅ 6 30
7. The least common multiple of two or more = =
8 8 ⋅ 6 48
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natural numbers is the smallest number that is a
multiple of each of the numbers.
16. The least common denominator is the least
8. 6 = 2 · 3 common multiple of the denominators of a group
8=2· ·2·2 of fractions.
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17. The denominators are 4 and 6.
2·3·2·2 4=2·2
The LCM is 2 ⋅ 3 ⋅ 2 ⋅ 2 = 24. 6=2· 3
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9. 45 = 3 · 3 · 5 LCD = 2 · 2 · 3 = 12
72 = 3 · 3 · 2·2·2
1 1⋅ 3 3
= =
3·3·5·2·2·2 4 4 ⋅ 3 12
The LCM is 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 5 = 360. 5 5 ⋅ 2 10
= =
6 6 ⋅ 2 12




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, Chapter 1: Operations on Real Numbers and Algebraic Expressions ISM: Elementary & Intermediate Algebra


18. The denominators are 20 and 16. 0 .4
20 = 2 · 2 · 5 32. 5 2.0
16 = 2 · 2 · 2·2 20
0
LCD = 2 · 2 · 5 · 2 · 2 = 80
2
9 9 ⋅ 4 36 = 0 .4
= = 5
20 20 ⋅ 4 80
11 11 ⋅ 5 55 0.833
= =
16 16 ⋅ 5 80 33. 6 5.000
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48
19. A fraction is written in lowest terms if the
20
numerator and denominator share no common
factor other than 1. 18
20
45 3⋅3⋅5 3⋅3⋅ 5 9 18
20. = = =
80 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 16 2
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5
4 2⋅2 4 = 0.83
21. = = 6
9 3⋅ 3 9
1.375
16 2 ⋅ 2 ⋅ 2 ⋅ 2 2 ⋅ 2 ⋅ 2 ⋅ 2 2 34. 8 11.000
22. = = =
56 2 ⋅ 2 ⋅ 2 ⋅ 7 2 ⋅ 2 ⋅ 2 ⋅ 7 7 8
30
23. The 1 is two places to the right of the decimal; 24
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this is the hundredths place.
60
24. The 2 is one place to the right of the decimal; 56
this the tenths place. 40
40
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25. The 8 is four places to the left of the decimal;
0
this is the thousands place.
11
= 1.375
26. The 9 is three places to the right of the decimal; 8
this is the thousandths place.
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0.428571
27. The number 1 is in the tenths place. The number 35. 7 3.000000
to its right is 7. Since 7 is greater than 5, we
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round to 0.2.
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28. The number 3 is in the hundredths place. The 14
number to its right is 2. Since 2 is less than 5, we 60
round to 0.93.
56
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29. The number 9 is in the hundredths place. The 40
number to its right is 6. Since 6 is greater than 5, 35
we round to 1.40. 50
49
30. The number 0 is in the hundredths place. The
number to its right is 4. Since 4 is less than 5, we 10
round to 690.00. 7
3
31. The number 9 is in the tenths place. The number
3
to its right is 8. Since 8 is greater than 5, we = 0.428571
round to 60.0. 7

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