CHAPTER 1 Introductory Information and Review
Section 1.3:
Fractions
 Greatest Common Divisor and Least Common Multiple
 Addition and Subtraction of Fractions
 Multiplication and Division of Fractions
Greatest Common Divisor and Least Common Multiple
Greatest Common Divisor:
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
A Method for Finding the GCD:
Least Common Multiple:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
A Method for Finding the LCM:
Example:
Solution:
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
The LCM is
Additional Example 1:
Solution:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
The LCM is 2  2  2  3  5  120 .
Additional Example 2:
Solution:
The LCM is 2  3  3  5  7  630 .
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Additional Example 3:
Solution:
The LCM is 2  2  3  3  2  72 .
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
Additional Example 4:
Solution:
The LCM is 2  3  3  2  5  180 .
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions with Like Denominators:
a b a b
 
c c
c
and
a b a b
 
c c
c
Example:
Solution:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
Addition and Subtraction of Fractions with Unlike
Denominators:
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Example:
Solution:
Additional Example 1:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
Solution:
Additional Example 2:
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Solution:
Additional Example 3:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
Solution:
(b) We must rewrite the given fractions so that they have a common denominator.
Find the LCM of the denominators 14 and 21 to find the least common denominator.
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Additional Example 4:
Solution:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
Multiplication and Division of Fractions
Multiplication of Fractions:
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Example:
Solution:
Division of Fractions:
Example:
Solution:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
Additional Example 1:
Solution:
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Additional Example 2:
Solution:
MATH 1300 Fundamentals of Mathematics
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CHAPTER 1 Introductory Information and Review
Additional Example 3:
Solution:
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University of Houston Department of Mathematics
SECTION 1.3 Fractions
Additional Example 4:
Solution:
MATH 1300 Fundamentals of Mathematics
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Exercise Set 1.3: Fractions
For each of the following groups of numbers,
(a) Find their GCD (greatest common divisor).
(b) Find their LCM (least common multiple).
1.
6 and 8
2.
4 and 5
3.
7 and 10
4.
12 and 15
5.
14 and 28
6.
6 and 22
7.
8 and 20
8.
9 and 18
9.
18 and 30
19. (a)
2 75
(b)
5 23
(c)
12 14
20. (a)
4 19
(b)
11 54
(c)
9 73
Evaluate the following. Write all answers in simplest
form. (If the answer is a mixed number/improper
fraction, then write the answer as a mixed number.)
21. (a) 2  1
7 7
(b)
8 4 3
 
11 11 11
22. (a)
3 1

5 5
(b)
4 5 2
 
9 9 9
23. (a)
8 54  2 15
(b)
7 23

3 3
24. (a)
3 21

5 5
(b)
7 116  5 112
25. (a)
5 34  2 14
(b)
6 53  7 54
26. (a)
9 75  2 73
(b)
4  115
27. (a)
7  23
(b)
7 103  3 109
28. (a)
11
6 127  2 12
(b)
8 16  2 56
10. 60 and 210
11. 16, 20, and 24
12. 15, 21, and 27
Change each of the following improper fractions to a
mixed number.
23
5
19
3
13. (a) 9
7
(b)
14. (a) 10
3
17
(b)
6
15. (a)  27
4
(b) 
32
11
(c) 
73
10
16. (a)  15
13
(b) 
43
8
(c) 
57
7
(c)
49
(c)
9
Change each of the following mixed numbers to an
improper fraction.
56
17. (a)
5 16
(b)
7 94
(c)
8 23
18. (a)
3 12
(b)
10 78
(c)
6 53
Evaluate the following. Write all answers in simplest
form. (If the answer is a mixed number/improper
fraction, then write the answer as a mixed number.)
29. (a)
1 1

4 2
(b)
1 1

3 7
30. (a)
1 1

8 10
(b)
1 1

6 5
31. (a)
1 1 1
 
4 5 6
(b)
2 3

7 5
32. (a)
1 1 1
 
2 7 5
(b) 
33. (a)
1 1

35 10
(b)
4 3

11 7
3 5

4 6
University of Houston Department of Mathematics
Exercise Set 1.3: Fractions
8 7

15 12
1 1

6 24
(b)
35. (a)
4 73  5 16
(b)
7 107  5 12
36. (a)
10 75  3 14
(b)
6 121  4 83
34. (a)
37. (a)
7 53  8 74
(b)
49. (a) 5 
7 14  3 65
(b)
2 78  9 13
24
39. (a)
5 152  2 127
(b)
9 167  2 56
40. (a)
7 109  6 85
(b)
11 145  43
(b)
8
4
3
10
(c)
7
5
50. (a)
3
6
11
4
 8
(b) 20     (c) 22 
9
 5
51. (a)
12 18

35 7
(b)
52. (a)
1
4
5
16
(b) 
5 94  1 23
38. (a)
1
20
 53
 95
36 9

5 50
(c)
15 5

16 24
(c)
49 35

24 32
Evaluate the following. Write all answers in simplest
form. (If the answer is a mixed number/improper
fraction, then write the answer as a mixed number.)
Evaluate the following. Write all answers in simplest
form. (If the answer is a mixed number/improper
fraction, then write the answer as an improper
fraction.)
53. (a)
8 54    1077 
(b)
1 78    109 
54. (a)
 2 92    43 
(b)
 3 167    54 
41. (a)
2 3

9 4
(b)
4 8

15 9
55. (a)
 2 13   5 71 
(b)
 6 53    2 113 
42. (a)
7 9

16 10
(b)
11 17

14 35
56. (a)
 3 17    5 14 
(b)
5 53    2 1211 
43. (a)
5  13
(b)
7  23
57. (a) 5 85  2 14
   
(b)
 11 19   1 1718 
44. (a)
9  52
(b)
6  72
58. (a)
 4 54   1 75 
(b)
 2 115    2 221 
Evaluate the following. Write all answers in simplest
form. (If the answer is a mixed number/improper
fraction, then write the answer as an improper
fraction.)
45. (a) 5 
1
3
(b) 21 
5
6
(c) 16 
5
4
46. (a) 8 
3
7
(b) 24 
1
18
(c) 25 
11
10
47. (a)
1 25

7 11
(b) 
48. (a)
36  1 
  
25  8 
(b)
3 16
10  9 

    (c)
20 15
21  8 
8 7

19 3
(c)
1 42

14 5
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