1. Equivalent Fractions Today we will be
finding fractions with the same value
cancelling fractions
comparing fractions
ordering fractions

2. finding fractions with the same value

3. 1 2

4. 1 2 2 4

5. 1 2 3 6

7. 1 2 4 8

10. 1 3

11. 1 3 2 6

12. 1 3 3 9

13. 1 3 4 12

16. 2 3

17. 2 3 4 6

18. 2 3 6 9

19. 2 3 8 12

21. Here is an example of a fraction chain1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90
100

22. And another 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90
100

23. And another 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90
100

24. Use the table to create a fraction chain for1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90
100

25. We use these columns to get1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90
100

26. 1 4 2 8 3 12 4 16 5 20
etcetera

27. Make some chains for these fractions:

28. Make some chains for these fractions:

29. Filling in the gaps 3 4 ? 20 =

30. 3 4 15 20 =
How did we do that?

31. × 5 3 4 15 20 =
× 5

32. What about this one? 2 3 ? 18 =

33. What is the multiplier? 2 3 ? 18 =
× 6

34. 2 3 12 18 What we do to the denominator × 6 = × 6
we must do to the numerator

35. And what we do to the numerator3 8 12 ? =

36. And what we do to the numerator
× 4 3 8 12 ? =

37. 3 8 12 32 And what we do to the numerator = × 4
we do to the denominator

38. Try these: 2 7 ? 21 = 1 6 ? 24 = 4 9 12 ? = 3 8 18 ? =

39. And the answers are: 2 7 6 21 = 1 6 4 24 = 4 9 12 27 = 3 8 18 48 =

40. cancelling fractions

41. 24 36 Consider the fraction:
There are any number of fractions equivalent to this…

42. ÷ 2
÷ 2
÷ 3 24 36 12 18 6 9 2 3
When we get to ⅔ we stop because there is nothing else we can divide by.

43. 24 36 2 3 Dividing in this way is called cancelling, or simplifying.
We could have got from the first fraction to last one by dividing by different numbers, for example: 24 36 2 3
÷ 12

44. Look for common factors – numbers that will divide into both numerator and denominator.21 28 ?
÷ ?

45. The common factor is 7 – the only number that will divide 21 and 283 4
÷ 7

46. What are the common factors of 6 and 12?
÷ ?

47. We could divide by 2, 3, or 6 6 12 ?
÷ ?

48. Whatever we do, it doesn’t matter, as long as we keep dividing until we can’t divide any more.6 12 3 6 1 2
÷ 2
÷ 3
÷ 2
÷ 3

49. Try cancelling these: 12 15 ? = 8 20 ? = 15 25 ? = 18 30 ? =

50. Try cancelling these: 12 15 4 5 = 8 20 2 5 = 15 25 3 5 = 18 30 3 5 =

51. comparing fractions

52. Now that we can we can find equivalent fractions, we can look at comparing fractions

53. For example, is it possible to say which is biggest out of these pairs?3 7 2 5
& 3 4 5 6
& 3 8 2
& 5 6 7 9
&

54. The only one we can say for certain is this one:3 8 2
&
Because they have the same denominator.

55. For example, this pair could be converted thus, and we can say:
For the others, we need to create equivalent fractions with the same denominator. 3 4 5 6
&
For example, this pair could be converted thus, and we can say: 9 12 10
<

56. And these will give us: & These: >5 6 7 9
& 15 18 14
>
These:
We use 18 because it is the lowest common denominator – we could have used any other suitable denominator.

57. And finally these will give us: &3 7 2 5
&
These: 15 35 14
>
Again, 35 is the lowest common denominator.

58. Replace the ? with <, >, or =
Try these: 3 5 7 10 ? 5 8 3 4 ? 3 4 2 ? 2 3 10 15 ?
Replace the ? with <, >, or =

59. And the answers are: < < > = 7 10 5 8 6 6 10 9 12 8 12 10 15

60. Finally, make fractions using a set of numbered cards, and order them yourself.