El documento describe la adición y sustracción de fracciones, diferenciando entre fracciones semejantes (con el mismo denominador) y fracciones no semejantes (con denominadores diferentes). Se presentan ejemplos que demuestran cómo sumar fracciones de diferentes tipos y cómo se representan visualmente las fracciones. También se abordamos la nomenclatura y la interpretación de fracciones resultantes en problemas de suma.

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
=