CHAPTER 1 Introductory Information and Review University of Houston Department of Mathematics 36 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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CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 36
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:
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 37
A Method for Finding the GCD:
Least Common Multiple:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 38
A Method for Finding the LCM:
Example:
Solution:
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 39
The LCM is
Additional Example 1:
Solution:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 40
The LCM is 2 2 2 3 5 120 .
Additional Example 2:
Solution:
The LCM is 2 3 3 5 7 630 .
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 41
Additional Example 3:
Solution:
The LCM is 2 2 3 3 2 72 .
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 42
Additional Example 4:
Solution:
The LCM is 2 3 3 2 5 180 .
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 43
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:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 44
Addition and Subtraction of Fractions with Unlike
Denominators:
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 45
Example:
Solution:
Additional Example 1:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 46
Solution:
Additional Example 2:
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 47
Solution:
Additional Example 3:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 48
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.
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 49
Additional Example 4:
Solution:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 50
Multiplication and Division of Fractions
Multiplication of Fractions:
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 51
Example:
Solution:
Division of Fractions:
Example:
Solution:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 52
Additional Example 1:
Solution:
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 53
Additional Example 2:
Solution:
CHAPTER 1 Introductory Information and Review
University of Houston Department of Mathematics 54
Additional Example 3:
Solution:
SECTION 1.3 Fractions
MATH 1300 Fundamentals of Mathematics 55
Additional Example 4:
Solution:
Exercise Set 1.3: Fractions
University of Houston Department of Mathematics 56
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
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.
13. (a) 97
(b) 23
5 (c)
19
3
14. (a) 103
(b) 17
6 (c)
49
9
15. (a) 274
(b) 32
11 (c)
73
10
16. (a) 1513
(b) 43
8 (c)
57
7
Change each of the following mixed numbers to an
improper fraction.
17. (a) 16
5 (b) 49
7 (c) 23
8
18. (a) 12
3 (b) 78
10 (c) 35
6
19. (a) 57
2 (b) 23
5 (c) 14
12
20. (a) 19
4 (b) 45
11 (c) 37
9
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 17 7 (b)
8 4 3
11 11 11
22. (a) 3 1
5 5 (b)
4 5 2
9 9 9
23. (a) 4 15 5
8 2 (b) 7 23
3 3
24. (a) 3 21
5 5 (b) 6 2
11 117 5
25. (a) 3 14 4
5 2 (b) 3 45 5
6 7
26. (a) 5 37 7
9 2 (b) 511
4
27. (a) 23
7 (b) 3 910 10
7 3
28. (a) 7 1112 12
6 2 (b) 516 6
8 2
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)
4 3
11 7
33. (a) 1 1
35 10 (b)
3 5
4 6
Exercise Set 1.3: Fractions
MATH 1300 Fundamentals of Mathematics 57
34. (a) 1 1
6 24 (b)
8 7
15 12
35. (a) 3 17 6
4 5 (b) 7 110 2
7 5
36. (a) 5 17 4
10 3 (b) 3112 8
6 4
37. (a) 3 45 7
7 8 (b) 4 29 3
5 1
38. (a) 514 6
7 3 (b) 7 138 24
2 9
39. (a) 7215 12
5 2 (b) 7 516 6
9 2
40. (a) 9 510 8
7 6 (b) 5 314 4
11
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.)
41. (a) 2 3
9 4 (b)
4 8
15 9
42. (a) 7 9
16 10 (b)
11 17
14 35
43. (a) 13
5 (b) 23
7
44. (a) 25
9 (b) 27
6
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) 1
53 (b)
521
6 (c)
516
4
46. (a) 3
87 (b)
124
18 (c)
1125
10
47. (a) 1 25
7 11 (b)
10 9
21 8
(c)
3 16
20 15
48. (a) 36 1
25 8
(b) 8 7
19 3 (c)
1 42
14 5
49. (a) 1
520
(b) 8
43 (c)
75
10
50. (a) 3
611
(b) 8
205
(c)
422
9
51. (a) 12 18
35 7 (b)
35
59
(c)
15 5
16 24
52. (a)
14
516
(b) 36 9
5 50 (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.)
53. (a) 1045 77
8 (b) 7 98 10
1
54. (a) 329 4
2 (b) 7 416 5
3
55. (a) 1 1732 5 (b) 3 3
5 116 2
56. (a) 1 17 4
3 5 (b) 3 115 1225
57. (a) 5 18 4
5 2 (b) 1719 18
11 1
58. (a) 545 7
4 1 (b) 5 111 22
2 2
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