A graphical representation of arithmetic operations on fractions. Students usually struggle with addition and subtraction of unlike fractions. This should help them understand the how and why of working with unlike fractions

1. Addition / Subtraction of Fractions

2. Fractions
Like Fractions
denominator is same
size of parts is same
1 / 4 , 3 / 4 , 7 / 4
Unlike Fractions
denominator is diff
size of parts is diff
1 / 5 , 3 / 2 , 7 / 10

3. Adding Like Fractions
denominator is same
size of parts is same
1 / 4 , 3 / 4 , 7 / 4

4. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
2 halves make 1

5. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
2 halves make 1

6. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
2 halves make 1

7. 1
1 / 3 1 / 3
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
2 halves make 1
1/2 + 1/2 = 1
1 / 21 / 2

8. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
3 one­thirds make 1

9. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
3 one­thirds make 1

10. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
3 one­thirds make 1

11. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
3 one­thirds make 1

12. 1
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 4
1 / 5
1 / 6
3 one­thirds make 1
1/3 + 1/3 + 1/3 = 1
1 / 3 1 / 31 / 3

13. Adding Unlike Fractions
denominator is different
size of parts is NOT same
1 / 5 , 3 / 2 , 7 / 40

14. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3

15. 1
1 / 3 1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3

16. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3

17. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3
THE PROBLEM IS

18. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3
THE PROBLEM IS
How do we name this fraction?

19. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3
THE PROBLEM IS
How do we name this fraction?
How many equal parts of whole have we made?

20. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3
THE PROBLEM IS
How do we name this fraction?
How many equal parts of whole have we made?
How many equal parts are there in the addition of these 2 fractions?

21. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3

22. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3

23. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 2
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/3
1 / 3
1 / 3
5/6

24. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/3 + 1/4
1 / 3
1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
1 / 2

25. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/3 + 1/4
1 / 3
1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
1 / 2

26. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/3 + 1/4
1 / 3
1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
1 / 2
1 / 3

27. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/3 + 1/4
1 / 3
1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
1 / 2
1 / 3

28. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/3 + 1/4
1 / 3
1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
1 / 2
1 / 3

29. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/3 + 1/4
1 / 3
7/12
1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12
1 / 2
1 / 3

30. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/5
1 / 3
1 / 2

31. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/5
1 / 3
1 / 2

32. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/5
1 / 3
1 / 2 1 / 5

33. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/5
1 / 3
1 / 2 1 / 5
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10

34. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/5
1 / 3
1 / 2 1 / 5
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10

35. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 1/5
1 / 3
1 / 2 1 / 5
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10
7/10

36. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2

37. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2

38. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2 1 / 31 / 3

39. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2
1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1 / 3
1 / 2

40. 1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2
1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1 / 3
1 / 2

41. 1
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2
1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 4
1 / 5
1 / 6
1 / 3
1 / 21 / 3
1 / 31 / 3
1 / 3

42. 1
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2
1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 4
1 / 5
1 / 6
1 / 3
1 / 21 / 3
1 / 31 / 3
1 / 3

43. 1
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2
1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 4
1 / 5
1 / 6
1 / 3
1 / 21 / 3
1 / 31 / 3
1 / 3

44. 1
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 3
1 / 4
1 / 5
1 / 6
1/2 + 2/3
1 / 3
1 / 2
1
1 / 3
1 / 2
1 / 4 1 / 4 1 / 4
1 / 5 1 / 5 1 / 5 1 / 5
1 / 6 1 / 6 1 / 6 1 / 6 1 / 6
1 / 4
1 / 5
1 / 6
1 / 3
1 / 21 / 3
1 / 31 / 3
1 / 3
7/6

45. 1/2 + 1/3 =
1/3 + 1/4 =
1/2 + 1/5 =
1/2 + 2/3 =
2/3 + 4/5 =

46. 1/2 + 1/3 =
1/3 + 1/4 =
1/2 + 1/5 =
1/2 + 2/3 =
2/3 + 4/5 =
5/6
7/12
7/10
7/6
22/15

47. Addition of Unlike Fractions
How to Calculate?

48. +
1
2
1
3

49. +
we have to make the denominators equal
1
2
1
3

50. +
we have to make the denominators equal
THINK
what could the new
denominator be?
1
2
1
3

51. +
we have to make the denominators equal
THINK
what could the new
denominator be?
?
1
2
1
3

52. +
we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 3
3
6
9
12
.
.
.
1
2
1
3

53. +
we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3

54. +
we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3

55. +
we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3

56. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
new
denominator

57. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
=

58. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
?
6
=

59. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
=

60. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=

61. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
6 6
=

62. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
6 6
=
x 3

63. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
6 6
=
x 3
x 3

64. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
3
6 6
=
x 3
x 3

65. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
3
6 6
=
x 3
x 3
x 2

66. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
3
6 6
=
x 3
x 3
x 2
x 2

67. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
3
6
2
6
=
x 3
x 3
x 2
x 2

68. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
3
6
2
6
=
x 3
x 3
x 2
x 2
6
=

69. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
3
6
2
6
=
x 3
x 3
x 2
x 2
5
6
=

70. +
we have to make the denominators equal
THINK
what could the new
denominator be?
6
table of 3table of 2
3
6
9
12
.
.
.
2
4
6
8
.
.
.
1
2
1
3
+
?
6
?
6
=
+
3
6
2
6
=
x 3
x 3
x 2
x 2
5
6
=

71. Subtraction of Unlike Fractions
How to Calculate?

72. 3
4
7
12
–

73. we have to make the denominators equal
3
4
7
12
–

74. we have to make the denominators equal
THINK
what could the new
denominator be?
3
4
7
12
–

75. we have to make the denominators equal
THINK
what could the new
denominator be?
?
3
4
7
12
–

76. we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 12
12
24
36
48
.
.
.
3
4
7
12
–

77. we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–

78. we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–

79. we have to make the denominators equal
THINK
what could the new
denominator be?
?
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–

80. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
new
denominator

81. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
=
–

82. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
?
12
=
–

83. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
–

84. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
–
?
12

85. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
12 12
=
–
?
12
–

86. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
12 12
=
x 3
–
?
12
–

87. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
12 12
=
x 3
x 3
–
?
12
–

88. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12 12
=
x 3
x 3
–
?
12
–

89. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12 12
=
x 3
x 3
x 1
–
?
12
–

90. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12 12
=
x 3
x 3
x 1
x 1
–
?
12
–

91. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12
7
12
=
x 3
x 3
x 1
x 1
–
?
12
–

92. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12
7
12
=
x 3
x 3
x 1
x 1
12
=
–
?
12
–

93. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12
7
12
=
x 3
x 3
x 1
x 1
2
12
=
–
?
12
–

94. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12
7
12
=
x 3
x 3
x 1
x 1
2
12
=
–
?
12
–
1
6
=

95. we have to make the denominators equal
THINK
what could the new
denominator be?
12
table of 12table of 4
12
24
36
48
.
.
.
4
8
12
16
.
.
.
3
4
7
12
–
?
12
=
9
12
7
12
=
x 3
x 3
x 1
x 1
2
12
=
–
?
12
–
1
6
=