1. © T Madas

2. Imagine two identical cakes We slice each of them into equal portions The slices in the first cake are bigger Some of the cake is taken away What portion has been taken away from each cake? 1 3 3 9

3. Imagine two identical cakes These fractions are called Equivalent Fractions They are in fact the same fraction 1 3 3 9 1 3 3 9 =

4. © T Madas Let’s Find Some Equivalent Fractions

5. © T Madas The fraction of has been shaded on several diagrams below: 1 2 1 2 2 4 3 6 4 8 5 10 6 12 15 30 50 100

6. © T Madas The fraction of has been shaded on several diagrams below: 1 3 1 3 2 6 3 9 5 15 8 24 10 30 20 60 4 12

7. © T Madas The fraction of has been shaded on several diagrams below: 2 5 2 5 4 10 6 15 8 20 10 25 16 40 20 50 40 100

8. © T Madas How do we find equivalent fractions without diagrams? x 2 8 2 x 3 12 3 x 4 16 4

9. © T Madas How do we find equivalent fractions without diagrams? x 2 6 4 x 5 15 10 x 7 21 14

10. © T Madas x 6 12 What is the missing numerator so that the two fractions are equivalent? x 4 16

11. © T Madas x 5 15 What is the missing numerator so that the two fractions are equivalent? x 6 24

12. © T Madas x 3 6 What is the missing numerator so that the two fractions are equivalent? x 9 9

13. © T Madas Now we start with a fraction with “big” numerator and denominator. We will try to find an equivalent fraction with smaller numerator and denominator. This is called cancelling down

14. What is in its simplest form?

15. © T Madas What is in its simplest form?

16. © T Madas Cancel down these fractions, to their simplest form: ÷ 6 2 1 ÷ 4 3 1 ÷ 3 5 1

17. © T Madas Cancel down these fractions, to their simplest form: ÷ 4 3 2 5 2 ÷ 3 5 4

18. © T Madas Cancel down these fractions, to their simplest form: ÷ 3 4 3 ÷ 6 5 2 ÷ 5 6 5

19. © T Madas We can cancel down in stages. [usually with bigger numbers] ÷ 2 15 24 ÷ 3 5 8 ÷ 6

20. © T Madas ÷ 2 12 60 ÷ 2 6 30 We can cancel down in stages. [usually with bigger numbers] ÷ 2 3 15 ÷ 3 1 5 ÷ 24

21. © T Madas Fraction Wall

22. © T Madas

24. 1 whole 1/21/2 1/31/3 1/41/4 1/51/5 1/61/6 1/71/7 1/81/8 1/91/9 1 / 10 1 / 11 1 / 12 1 / 13 1 / 14 1 / 15 1 / 16

25. © T Madas 1 whole

26. © T Madas 1 whole 1/21/2 2/42/4 3/63/6 4/84/8 5 / 10 6 / 12 7 / 14 8 / 16

27. © T Madas 1 whole 1/21/2 1/31/3 1/41/4 1/51/5 1/61/6 1/71/7 1/81/8 1/91/9 1 / 10 1 / 11 1 / 12 1 / 13 1 / 14 1 / 15 1 / 16

28. © T Madas 1 whole 1/31/3 2/62/6 3/93/9 4 / 12 5 / 15

29. © T Madas 1 whole 1/21/2 1/31/3 1/41/4 1/51/5 1/61/6 1/71/7 1/81/8 1/91/9 1 / 10 1 / 11 1 / 12 1 / 13 1 / 14 1 / 15 1 / 16

30. © T Madas 1 whole 1/41/4 2/82/8 3 / 12 4 / 16

31. © T Madas

32. 12 What is the missing numerator so that the two fractions are equivalent? 124 8 x3x3 x3x3 x4x4 x4x4 x2x2 x2x2 x2x2 x2x2

33. © T Madas 15 What is the missing numerator so that the two fractions are equivalent? 1012 10 x3x3 x3x3 x5x5 x5x5 x4x4 x4x4 x5x5 x5x5

34. © T Madas 30 What is the missing numerator so that the two fractions are equivalent? 2827 16 x6x6 x6x6 x7x7 x7x7 x9x9 x9x9 x8x8 x8x8

35. © T Madas 16 What is the missing numerator so that the two fractions are equivalent? 918 20 x4x4 x4x4 x3x3 x3x3 x9x9 x9x9 x5x5 x5x5

36. © T Madas 30 What is the missing numerator so that the two fractions are equivalent? 89 12 x6x6 x6x6 x4x4 x4x4 x3x3 x3x3 x6x6 x6x6

37. © T Madas 30 What is the missing numerator so that the two fractions are equivalent? 2827 16 x6x6 x6x6 x7x7 x7x7 x9x9 x9x9 x8x8 x8x8

38. © T Madas 10 What is the missing numerator so that the two fractions are equivalent? 615 12 x2x2 x2x2 x3x3 x3x3 x5x5 x5x5 x4x4 x4x4

39. © T Madas 14 What is the missing numerator so that the two fractions are equivalent? 3010 28 x7x7 x7x7 x 10 x5x5 x5x5 x7x7 x7x7

40. © T Madas 30 What is the missing numerator so that the two fractions are equivalent? 4821 18 x6x6 x6x6 x 12 x7x7 x7x7 x9x9 x9x9

41. © T Madas 12 What is the missing numerator so that the two fractions are equivalent? 1810 16 x3x3 x3x3 x6x6 x6x6 x5x5 x5x5 x4x4 x4x4

42. © T Madas 35 What is the missing numerator so that the two fractions are equivalent? 627 16 x7x7 x7x7 x3x3 x3x3 x9x9 x9x9 x8x8 x8x8

43. © T Madas 14 What is the missing numerator so that the two fractions are equivalent? 2426 33 x 14 x 12 x 13 x 11

44. © T Madas

45. 4 Cancel down each of the following fractions to their simplest form 7 3 5 2 9 4 7 ÷3÷3 ÷3÷3 ÷4÷4 ÷4÷4 ÷2÷2 ÷2÷2 ÷2÷2 ÷2÷2

46. © T Madas 5 Cancel down each of the following fractions to their simplest form 6 2 5 3 8 2 7 ÷3÷3 ÷3÷3 ÷5÷5 ÷5÷5 ÷4÷4 ÷4÷4 ÷5÷5 ÷5÷5

47. © T Madas 5 Cancel down each of the following fractions to their simplest form 6 4 5 3 8 2 7 ÷6÷6 ÷6÷6 ÷7÷7 ÷7÷7 ÷9÷9 ÷9÷9 ÷8÷8 ÷8÷8

48. © T Madas 4 Cancel down each of the following fractions to their simplest form 7 3 5 2 9 4 7 ÷4÷4 ÷4÷4 ÷3÷3 ÷3÷3 ÷9÷9 ÷9÷9 ÷5÷5 ÷5÷5

49. © T Madas 5 Cancel down each of the following fractions to their simplest form 6 2 5 3 8 2 7 ÷6÷6 ÷6÷6 ÷4÷4 ÷4÷4 ÷3÷3 ÷3÷3 ÷6÷6 ÷6÷6

50. © T Madas 5 Cancel down each of the following fractions to their simplest form 7 4 9 3 4 2 3 ÷6÷6 ÷6÷6 ÷7÷7 ÷7÷7 ÷9÷9 ÷9÷9 ÷8÷8 ÷8÷8

51. © T Madas 5 Cancel down each of the following fractions to their simplest form 6 2 5 3 8 3 10 ÷2÷2 ÷2÷2 ÷3÷3 ÷3÷3 ÷5÷5 ÷5÷5 ÷4÷4 ÷4÷4

52. © T Madas 2 Cancel down each of the following fractions to their simplest form 3 3 5 2 9 4 7 ÷7÷7 ÷7÷7 ÷ 10 ÷5÷5 ÷5÷5 ÷7÷7 ÷7÷7

53. © T Madas 8 Cancel down each of the following fractions to their simplest form 9 4 5 3 8 2 7 ÷4÷4 ÷4÷4 ÷ 12 ÷7÷7 ÷7÷7 ÷9÷9 ÷9÷9

54. © T Madas 4 Cancel down each of the following fractions to their simplest form 7 3 5 2 9 4 7 ÷3÷3 ÷3÷3 ÷6÷6 ÷6÷6 ÷5÷5 ÷5÷5 ÷4÷4 ÷4÷4

55. © T Madas 5 Cancel down each of the following fractions to their simplest form 6 2 5 3 8 2 7 ÷7÷7 ÷7÷7 ÷3÷3 ÷3÷3 ÷9÷9 ÷9÷9 ÷8÷8 ÷8÷8

56. © T Madas 1 Cancel down each of the following fractions to their simplest form 2 2 3 2 3 3 4 ÷ 14 ÷ 12 ÷ 13 ÷ 11

57. © T Madas

58. 12 What is the missing numerator so that the two fractions are equivalent? 124 8 x3x3 x3x3 x4x4 x4x4 x2x2 x2x2 x2x2 x2x2 151012 10 x3x3 x3x3 x5x5 x5x5 x4x4 x4x4 x5x5 x5x5

59. © T Madas 121810 16 x3x3 x3x3 x6x6 x6x6 x5x5 x5x5 x4x4 x4x4 30 What is the missing numerator so that the two fractions are equivalent? 2827 16 x6x6 x6x6 x7x7 x7x7 x9x9 x9x9 x8x8 x8x8

60. © T Madas 3089 12 x6x6 x6x6 x4x4 x4x4 x3x3 x3x3 x6x6 x6x6 16 What is the missing numerator so that the two fractions are equivalent? 918 20 x4x4 x4x4 x3x3 x3x3 x9x9 x9x9 x5x5 x5x5

61. © T Madas 10615 12 x2x2 x2x2 x3x3 x3x3 x5x5 x5x5 x4x4 x4x4 30 What is the missing numerator so that the two fractions are equivalent? 2827 16 x6x6 x6x6 x7x7 x7x7 x9x9 x9x9 x8x8 x8x8

62. © T Madas 304821 18 x6x6 x6x6 x 12 x7x7 x7x7 x9x9 x9x9 14 What is the missing numerator so that the two fractions are equivalent? 3010 28 x7x7 x7x7 x 10 x5x5 x5x5 x7x7 x7x7

63. © T Madas 35627 16 x7x7 x7x7 x3x3 x3x3 x9x9 x9x9 x8x8 x8x8 142426 33 x 14 x 12 x 13 x 11 What is the missing numerator so that the two fractions are equivalent?

64. © T Madas

65. 5 6 2 5 3 8 2 7 ÷3÷3 ÷3÷3 ÷5÷5 ÷5÷5 ÷4÷4 ÷4÷4 ÷5÷5 ÷5÷5 4 Cancel down each of the following fractions to their simplest form 7 3 5 2 9 4 7 ÷3÷3 ÷3÷3 ÷4÷4 ÷4÷4 ÷2÷2 ÷2÷2 ÷2÷2 ÷2÷2

66. © T Madas 4 7 3 5 2 9 4 7 ÷4÷4 ÷4÷4 ÷3÷3 ÷3÷3 ÷9÷9 ÷9÷9 ÷5÷5 ÷5÷5 5 Cancel down each of the following fractions to their simplest form 6 4 5 3 8 2 7 ÷6÷6 ÷6÷6 ÷7÷7 ÷7÷7 ÷9÷9 ÷9÷9 ÷8÷8 ÷8÷8

67. © T Madas 5 7 4 9 3 4 2 3 ÷6÷6 ÷6÷6 ÷7÷7 ÷7÷7 ÷9÷9 ÷9÷9 ÷8÷8 ÷8÷8 5 Cancel down each of the following fractions to their simplest form 6 2 5 3 8 2 7 ÷6÷6 ÷6÷6 ÷4÷4 ÷4÷4 ÷3÷3 ÷3÷3 ÷6÷6 ÷6÷6

68. © T Madas 2 3 3 5 2 9 4 7 ÷7÷7 ÷7÷7 ÷ 10 ÷5÷5 ÷5÷5 ÷7÷7 ÷7÷7 5 Cancel down each of the following fractions to their simplest form 6 2 5 3 8 3 10 ÷2÷2 ÷2÷2 ÷3÷3 ÷3÷3 ÷5÷5 ÷5÷5 ÷4÷4 ÷4÷4

69. © T Madas 4 7 3 5 2 9 4 7 ÷3÷3 ÷3÷3 ÷6÷6 ÷6÷6 ÷5÷5 ÷5÷5 ÷4÷4 ÷4÷4 8 Cancel down each of the following fractions to their simplest form 9 4 5 3 8 2 7 ÷4÷4 ÷4÷4 ÷ 12 ÷7÷7 ÷7÷7 ÷9÷9 ÷9÷9

70. © T Madas 1 2 2 3 2 3 3 4 ÷ 14 ÷ 12 ÷ 13 ÷ 11 5 Cancel down each of the following fractions to their simplest form 6 2 5 3 8 2 7 ÷7÷7 ÷7÷7 ÷3÷3 ÷3÷3 ÷9÷9 ÷9÷9 ÷8÷8 ÷8÷8

71. © T Madas