1. Fractions Year 6

3. ÷2 ÷3 6 3 1 = = 18 9 3 ÷2 ÷3

4. ÷6 6 1 = 18 3 ÷6

5. 6 18 1 3

6. ÷2 ÷2 8 4 2 = = 12 6 3 ÷2 ÷2

7. ÷4 8 2 = 12 3 ÷4

8. 8
eight twelfths 12 2 3
two thirds

9. ÷2 ÷2 12 6 3 = = 20 10 5 ÷2 ÷2

10. ÷4 12 3 = 20 5 ÷4

11. 12
twelve twentieths 20 3
three fifths 5

12. ÷7 ÷7 ÷5 14 2 7 1 25 5 = = = 35 5 28 4 30 6 ÷7 ÷7 ÷5

14. = = 10 ? 12 ? 2 3 4 5 15 15 Which fraction is larger: or ? x5 x3 x5 x3
When one denominator is not a multiple of another, you need to convert both fractions. x5 x3 10 ? 12 ? 2 3 4 5 = = 15 15
15 is a multiple of both 3 and 5, so we can find two equivalent fractions with a denominator of 15. x5 x3

15. Which fraction is larger: or ?2 3 4 5
Which fraction is larger: or ?

16. = = 9 ? 10 ? 3 4 5 6 12 12 Which fraction is larger: or ? x3 x2 x3 x2
12 is a multiple of both 4 and 6, so we can find two equivalent fractions with a denominator of 12. 9 ? 10 ? 3 4 5 6 = = 12 12 x3 x2

17. Which fraction is larger: or ?3 4 5 6
Which fraction is larger: or ?

18. = = 15 ? 14 ? 5 6 7 9 18 18 Which fraction is larger: or ? x3 x2 x3 x2
18 is a multiple of both 6 and 9, so we can find two equivalent fractions with a denominator of 18. 15 ? 14 ? 5 6 7 9 = = 18 18 x3 x2

19. Which fraction is larger: or ?5 6 7 9
Which fraction is larger: or ?

21. Order these fractions from smallest to largest.3 5 11 20 1 2 7 10 3 4 12 11 14 15 20 20 10 20 20 20 1 2 11 20 3 5 7 10 3 4

22. 1/2
10/20
11/20
11/20
3/5
12/20
7/10
14/20
3/4
15/20

23. Order these fractions from smallest to largest.3 4 2 3 1 2 1 3 5 6 9 10 8 4 12 12 6 12 12 12 1 3 1 2 2 3 3 4 5 6

24. 1/3
4/12
1/2
6/12
2/3
8/12
3/4
9/12
5/6
10/12

26. 2 3 1 4 8 12 3 12 11 12 + = + = x4 x3 ? 8 3 ? 2 3 1 4 = = 12 12 x4 x3

27. 2 3 1 4 8 12 3 12 11 12 + = + =

28. 1 2 2 5 5 10 4 10 1 10 - = - = x5 x2 ? 5 4 ? 1 2 2 5 = = 10 10 x5 x2

29. 1 2 2 5 5 10 4 10 1 10 - = - =

30. 3 4 1 5 15 20 4 20 19 20 + = + = x5 x4 15 ? 4 ? 3 4 1 5 = = 20 20 x5 x4

31. 3 4 1 5 15 20 4 20 19 20 + = + =

33. 3 5 3 4 12 20 15 20 27 20 7 20 + = + = = 1 x4 x5
27 ÷ 20 = 12 ? 15 ? 3 5 3 4 = = 7 20
1 r 7 = 1 20 20 x4 x5

34. 3 5 3 4 12 20 15 20 27 20 7 20 + = + = = 1

36. 1 3 5 12 4 12 5 12 9 12 3 + 2 = 3 + 2 = 5 x3 4 ? 1 3 = 12 x3

37. 1 3 1 5 5 15 3 15 8 15 3 + 3 = 3 + 3 = 6 x5 x3 5 ? 3 ? 1 3 1 5 = = 15 15 x5 x3

39. 5 8 1 8 6 8 3 4 3 + 2 = 5 = 5

40. 5 6 5 6 10 6 4 6 4 6 2 3 4 + 2 = 6 + = 6 + 1 = 7 = 7

41. 3 7 5 7 8 7 1 7 1 7 3 + 1 = 4 + = 4 + 1 = 5

42. 2 5 3 5 5 4 + 3 = 7 + = 7 + 1 = 8

44. 1 2 7 10 5 10 7 10 12 10 4 + 2 = 4 + 2 = 6 + = x5 2 10 2 10 6 + 1 = 7 5 ? 1 2 = 10 x5

45. 2 3 3 5 10 15 9 15 19 15 4 + 3 = 4 + 3 = 7 + = x5 x3 4 15 4 15 7 + 1 = 8 10 ? ? 9 2 3 3 5 = = 15 15 x5 x3

47. 3 2 7 10 15 10 7 10 8 10 - = - = x5 15 ? 3 2 = 10 x5

48. 3 2 7 10 15 10 7 10 8 10 - = - =

49. 7 5 3 4 28 20 15 20 13 20 - = - = x4 x5 28 ? 15 ? 7 5 3 4 = = 20 20 x4 x5

50. 7 5 3 4 13 20 - =

51. 7 5 3 4 28 20 15 20 13 20 - = - =

53. 3 4 7 8 14 8 7 8 7 8 1 - = - = x2 3 4 7 4 1 = 14 ? 7 4 =
(1 x 4) + 3 = 7 8 x2

54. 3 4 7 8 14 8 7 8 7 8 1 - = - =

55. 1 3 1 2 8 6 3 6 5 6 1 - = - = x2 x3 1 3 4 3 1 = 8 ? 3 ? 4 3 1 2 = =
(1 x 3) + 1 = 4 6 6 x2 x3

56. 1 3 1 2 5 6 1 - =

57. 1 3 1 2 8 6 3 6 5 6 1 - = - =

59. 5 8 3 8 2 8 3 - 1 = 2

60. 1 2 3 8 4 8 3 8 1 8 4 - 2 = 4 - 2 = 2 x4 4 ? 1 2 = 8 x4

61. 2 3 1 4 8 12 3 12 5 12 5 - 3 = 5 - 3 = 2 x4 x3 8 ? 3 ? 2 3 1 4 = = 12 12 x4 x3

63. 5 8 3 8 2 8 1 4 4 - 2 = 2 = 2

64. 1 6 5 6 7 6 5 6 2 6 1 3 4 - 2 = 3 - 2 = = 1 1

65. 2 7 5 7 9 7 5 7 4 7 3 - 1 = 2 - 1 = 1

66. 2 5 3 5 7 5 3 5 4 5 4 - 3 = 3 - 3 =

68. 1 5 2 5 6 5 2 5 4 5 5 - 2 = 4 - 2 = 2 1 5 6 5 1 =

69. 1 5 1 3 3 15 5 15 18 15 5 15 13 15 4 - 3 = 4 - 3 = 3 - 3 = x3 x5 3 15 18 15 1 = 3 ? 5 ? 1 5 1 3 = = 15 15 x3 x5

70. 3 4 4 5 15 20 16 20 35 20 16 20 19 20 6 - 3 = 6 - 3 = 5 - 3 = 2 x5 x4 15 20 35 20 1 = 15 ? 16 ? 3 4 4 5 = = 20 20 x5 x4

71. 2 7 2 5 10 35 14 35 45 35 14 35 31 35 4 - 2 = 4 - 2 = 3 - 2 = 1 x5 x7 10 35 45 35 1 = 10 ? 14 ? 2 7 2 5 = = 35 35 x5 x7

73. 2 5
Count from 0 in steps of . 2 5 4 5 1 1 5 1 3 5 2 2 2 5 2 4 5 3 1 5 3 3 5

74. 2 9
Count from 0 in steps of . 2 9 4 9 6 9 8 9 1 1 9 1 3 9 1 5 9 1 7 9 2

75. 3 4
Count from 0 in steps of . 3 4 1 1 2 2 1 4 3 3 3 4 4 1 2 5 1 4 6 6 3 4

77. 3 4 1 2
Count back from in steps of . 5 5 3 4 5 1 4 4 3 4 4 1 4 3 3 4 3 1 4 2 3 4 2 1 4 1 3 4 1 1 4

78. 2 5 4
Count back from in steps of . 4 3 3 5 3 1 5 2 4 5 2 2 5 2 1 3 5 1 1 5 4 5 2 5

79. 8 9 3 9
Count back from in steps of . 7 7 8 9 7 5 9 7 2 9 6 8 9 6 5 9 6 2 9 5 8 9 5 5 9 5 2 9 4 8 9

81. 1 of 24 = 8 3

82. 1 of 30 = 6 5

83. 1 of 24 = 4 6

84. 1 of
400 =
100
100 x 4 = 400 4 1 of
210 = 70
70 x 3 = 210 3 1 1 of
215 = 43
4 3
x 5 5
2 1 5

86. 3 x 21 63 3 4 3 4
of 21 = = = 15 4 4

87. 2 x 23 46 1 5 2 5
of 23 = = = 9 5 5

88. 2 x 17 34 1 3 2 3
of 17 = = = 11 3 3
3 x 14 42 2 5 3 5
of 14 = = = 8 5 5
5 x 9 45 3 6 5 6
of 9 = = = 7 6 6

90. 3
3 x 5 4 15 4 3
x 5 = = = 3 4 4

91. 2
2 x 6 3 12 3
x 6 = = = 4 3

93. 3 4 9 4 1 1 2
x 3 = 6 + = 6 + 2 = 8 4 4

94. 1 4 6 4 2 1 2
x 6 = 12 + = 12 + 1 = 12 + 1 4 2 1 = 13 2

95. 1 3 7 3 1 1 2
x 7 = 14 + = 14 + 2 = 16 3 3 7 10 14 10 4 2 4
x 2 = 8 + = 8 + 1 = 9 10 5 1 6 9 6 3 1 5
x 9 = 45 + = 45 + 1 = 46 6 2

97. 3 4 11 4 3 1 33 4 1 2
x 3 = x = = 8 4

98. 1 4 9 4 6 1 54 4 2 4 1 2 2
x 6 = x = = 13 = 13 1 3 2 4 4
5 4 1

99. 1 3 7 3 7 1 49 3 1 3 2
x 7 = x = = 16 1 6 1 3 3
4 9 1

100. 7 10 47 10 2 1 94 10 4 2 5 4
x 2 = x = = 9 = 9 10 1
4 7
x 2 9 4

101. 1 6 31 6 9 1
279 6 3 6 1 2 5
x 9 = x = = 46 = 46
3 1
x 9 4 6 3 6
2 7 9 6
2 7 9 2 3

103. To multiply a mixed number by a whole number, change the mixed number to an improper fraction and put the whole number over 1, then multiply, then change your answer to a mixed number. 3 4 11 4 3 1 33 4 1 4 2
x 3 = x = = 8

104. When multiplying by a mixed number, you can simplify by ‘cancelling’ a numerator and a denominator, which means finding a factor of both numbers and dividing by that factor. 1 4 9 4 6 1 3 27 2 1 2 2
x 6 = x = = 13 2

105. 1 6 31 6 9 1 3 93 2 1 2 5
x 9 = x = = 46 2 1 3 7 3 7 1 49 3 1 3 2
x 7 = x = = 16 7 10 47 10 2 1 1 47 5 2 5 4
x 2 = x = = 9 5