fractions - section 1.3 - math 1300, fundamentals of mathematics

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:



A Method for Finding the LCM:

Example:

Solution:



The LCM is

Additional Example 1:

Solution:



The LCM is 2 2 2 3 5 120 .


Solution:

The LCM is 2 3 3 5 7 630 .




Solution:

The LCM is 2 2 3 3 2 72 .




Solution:

The LCM is 2 3 3 2 5 180 .



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:



Addition and Subtraction of Fractions with Unlike

Denominators:



Example:

Solution:




Solution:




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.




Solution:



Multiplication and Division of Fractions

Multiplication of Fractions:



Example:

Solution:

Division of Fractions:

Example:

Solution:




Solution:

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

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




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


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



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



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




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

fractions - section 1.3 - math 1300, fundamentals of mathematics

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