SOLUTIONS for
Elementary & Intermediate Algebra,
TU
4th edition
Author (s): Michael Sullivan, Katherine R. Struve, Janet Mazzarella
VI
A
AP
PR
O
VE
D
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, Chapter 1
ST
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.
U
2. In the statement 6 ⋅ 8 = 48, 6 and 8 are called 11. 12 = 2 · 2 · 3
18 = 2 · 3·3
factors and 48 is called the product.
30 = 2 · 3· 5
VI
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
A
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
AP
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.
1 1⋅ 5 5
6. 117 = =
/ \ 2 2 ⋅ 5 10
9 13
PR
/\ \ 5
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
natural numbers is the smallest number that is a
multiple of each of the numbers.
16. The least common denominator is the least
O
8. 6 = 2 · 3 common multiple of the denominators of a group
8=2· ·2·2 of fractions.
17. The denominators are 4 and 6.
2·3·2·2 4=2·2
VE
The LCM is 2 ⋅ 3 ⋅ 2 ⋅ 2 = 24. 6=2· 3
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
= =
D
6 6 ⋅ 2 12
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Copyright © 2018 Pearson Education, Inc. 1
, Chapter 1: Operations on Real Numbers and Algebraic Expressions ISM: Elementary Algebra
18. The denominators are 20 and 16. 0 .4
ST
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
U
= = 0.833
16 16 ⋅ 5 80 33. 6 5.000
48
19. A fraction is written in lowest terms if the
20
VI
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
A
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. = = =
AP
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
this is the hundredths place.
60
24. The 2 is one place to the right of the decimal; 56
this the tenths place. 40
PR
40
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.
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
O
28
round to 0.2.
20
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
VE
round to 0.93.
56
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
D
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
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round to 60.0. 7
2 Copyright © 2018 Pearson Education, Inc.
, ISM: Elementary Algebra Chapter 1: Operations on Real Numbers and Algebraic Expressions
6 2 ⋅3 3 52. 100
36. 0.6 = = =
ST
10 2 ⋅ 5 5 4 25
2·2·5·5
17 The prime factorization of 100 is 2 ⋅ 2 ⋅ 5 ⋅ 5.
37. 0.17 =
100
54. 35
625 5 ⋅ 125 5 5·7
38. 0.625 = = =
U
1000 8 ⋅ 125 8 The prime factorization of 35 is 5 ⋅ 7.
39. The word percent means parts per hundred, so 56. 54
35 6 9
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35% means 35 parts out of 100 parts or .
100 2·3·3·3
The prime factorization of 54 is 2 ⋅ 3 ⋅ 3 ⋅ 3.
1 23
40. 23% = 23% ⋅ = = 0.23
100% 100 58. 70
A
2 35
1 1
41. 1% = 1% ⋅ = = 0.01 2 ·5·7
100% 100
The prime factorization of 70 is 2 ⋅ 5 ⋅ 7.
1 72.4
42. 72.4% = 72.4% ⋅ = = 0.724 60. 79 is a prime number.
AP
100% 100
62. 315
1 127
43. 127% = 127% ⋅ = = 1.27 9 35
100% 100
3·3·5·7
44. To convert a decimal to a percent, multiply the The prime factorization of 315 is 3 ⋅ 3 ⋅ 5 ⋅ 7.
100%
decimal by . 64. 10 = 2 · 5
PR
1 14 = 2 · 7
100% 2·5·7
45. 0.15 = 0.15 ⋅ = 15%
1 The LCM is 2 ⋅ 5 ⋅ 7 = 70.
46. 0.8 = 0.8 ⋅
100%
= 80% 66. 42 = 2 · 3·7
1 18 = 2 · 3 · 3
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100% 2·3·3·7
47. 1.372 = 1.372 ⋅ = 137.2%
1 The LCM of 42 and 18 is 2 ⋅ 3 ⋅ 3 ⋅ 7 = 126.
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100% 68. 55 = 5 · 11
48. 0.004 = 0.004 ⋅ = 0.4% 6=2·3
1
1.2 Exercises 2 · 3 · 5 · 11
The LCM of 55 and 6 is 2 ⋅ 3 ⋅ 5 ⋅ 11 = 330.
50. 9
70. 8=2·2·2
3·3
60 = 2·2·3·5
D
The prime factorization of 9 is 3 ⋅ 3.
2·2·2·3·5
The LCM of 8 and 60 is 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5 = 120.
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Copyright © 2018 Pearson Education, Inc. 3
Elementary & Intermediate Algebra,
TU
4th edition
Author (s): Michael Sullivan, Katherine R. Struve, Janet Mazzarella
VI
A
AP
PR
O
VE
D
?
, Chapter 1
ST
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.
U
2. In the statement 6 ⋅ 8 = 48, 6 and 8 are called 11. 12 = 2 · 2 · 3
18 = 2 · 3·3
factors and 48 is called the product.
30 = 2 · 3· 5
VI
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
A
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
AP
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.
1 1⋅ 5 5
6. 117 = =
/ \ 2 2 ⋅ 5 10
9 13
PR
/\ \ 5
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
natural numbers is the smallest number that is a
multiple of each of the numbers.
16. The least common denominator is the least
O
8. 6 = 2 · 3 common multiple of the denominators of a group
8=2· ·2·2 of fractions.
17. The denominators are 4 and 6.
2·3·2·2 4=2·2
VE
The LCM is 2 ⋅ 3 ⋅ 2 ⋅ 2 = 24. 6=2· 3
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
= =
D
6 6 ⋅ 2 12
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Copyright © 2018 Pearson Education, Inc. 1
, Chapter 1: Operations on Real Numbers and Algebraic Expressions ISM: Elementary Algebra
18. The denominators are 20 and 16. 0 .4
ST
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
U
= = 0.833
16 16 ⋅ 5 80 33. 6 5.000
48
19. A fraction is written in lowest terms if the
20
VI
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
A
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. = = =
AP
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
this is the hundredths place.
60
24. The 2 is one place to the right of the decimal; 56
this the tenths place. 40
PR
40
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.
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
O
28
round to 0.2.
20
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
VE
round to 0.93.
56
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
D
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
2 Copyright © 2018 Pearson Education, Inc.
, ISM: Elementary Algebra Chapter 1: Operations on Real Numbers and Algebraic Expressions
6 2 ⋅3 3 52. 100
36. 0.6 = = =
ST
10 2 ⋅ 5 5 4 25
2·2·5·5
17 The prime factorization of 100 is 2 ⋅ 2 ⋅ 5 ⋅ 5.
37. 0.17 =
100
54. 35
625 5 ⋅ 125 5 5·7
38. 0.625 = = =
U
1000 8 ⋅ 125 8 The prime factorization of 35 is 5 ⋅ 7.
39. The word percent means parts per hundred, so 56. 54
35 6 9
VI
35% means 35 parts out of 100 parts or .
100 2·3·3·3
The prime factorization of 54 is 2 ⋅ 3 ⋅ 3 ⋅ 3.
1 23
40. 23% = 23% ⋅ = = 0.23
100% 100 58. 70
A
2 35
1 1
41. 1% = 1% ⋅ = = 0.01 2 ·5·7
100% 100
The prime factorization of 70 is 2 ⋅ 5 ⋅ 7.
1 72.4
42. 72.4% = 72.4% ⋅ = = 0.724 60. 79 is a prime number.
AP
100% 100
62. 315
1 127
43. 127% = 127% ⋅ = = 1.27 9 35
100% 100
3·3·5·7
44. To convert a decimal to a percent, multiply the The prime factorization of 315 is 3 ⋅ 3 ⋅ 5 ⋅ 7.
100%
decimal by . 64. 10 = 2 · 5
PR
1 14 = 2 · 7
100% 2·5·7
45. 0.15 = 0.15 ⋅ = 15%
1 The LCM is 2 ⋅ 5 ⋅ 7 = 70.
46. 0.8 = 0.8 ⋅
100%
= 80% 66. 42 = 2 · 3·7
1 18 = 2 · 3 · 3
O
100% 2·3·3·7
47. 1.372 = 1.372 ⋅ = 137.2%
1 The LCM of 42 and 18 is 2 ⋅ 3 ⋅ 3 ⋅ 7 = 126.
VE
100% 68. 55 = 5 · 11
48. 0.004 = 0.004 ⋅ = 0.4% 6=2·3
1
1.2 Exercises 2 · 3 · 5 · 11
The LCM of 55 and 6 is 2 ⋅ 3 ⋅ 5 ⋅ 11 = 330.
50. 9
70. 8=2·2·2
3·3
60 = 2·2·3·5
D
The prime factorization of 9 is 3 ⋅ 3.
2·2·2·3·5
The LCM of 8 and 60 is 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5 = 120.
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Copyright © 2018 Pearson Education, Inc. 3
