1. Fractions with the Same Denominator (Count, Compare, Add, Subtract)

2. Identify a fraction as part of a whole

3. Name the shaded fraction represented in each fraction bar:3 1 4 1 7 2 3 2 5 4 8 7

4. Compare fractions with either the same denominator or same numerator

5. Write < or >. 1 5 1 2 1 4 1 9 3 8 3 7 6 7 6 11
<
>
<
>

6. Order fractions with either the same denominator or same numerator

7. Order these fractions from smallest to largest:1 4 1 9 1 3 1 6 3 8 3 11 3 17 3 5 9 1 6 1 4 1 3 1
1 7 3
1 1 3 8 3 5 3
smallest
largest
smallest
largest

8. Add fractions with the same denominator within 1

9. 3 7 1 7 7 4 1 5 2 5 5 3 + = + = 3 10 2 10
1 0 5 2 9 5 9 9 7 + = + =

10. Subtract fractions with the same denominator within 1

11. 6 8 1 8 8 5 5 6 4 6 6 1 – = – = 6 7 2 7 7 4 4 9 1 9 9 3 – = – =

12. Solve missing number problems for addition and subtraction of fractions with the same denominator within 1

13. 1 6 6 4 5 6 1 3 3 1 2 3 + = + = 5 8 8 4 1 8 5 9 9 3 2 9 – = – =

14. Recognise pairs of fractions that add up to 1

15. 1 3 3 2 1 8 8 7 + = 1 + = 1 5 6 6 1 2 5 5 3 + = 1 + = 1

16. Count up in halves, thirds and quarters beyond 1

17. 1 2 1 2 2 1 3 1 2 1 2 3 4 1 2 2 3 2 4 2 5 2 6 2 7 2 8 2 1 3 2 3 1 3 2 3 1 1 3 2 2 3 1 3 2 3 1 2 3 4 1 3 2 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 1 4 2 4 3 4 1 4 2 4 1 3 4 1 1 4 2 2 4 3 4 2 1 4 3 2 4 3 3 4 1 2 3 4 1 4 2 4 3 4 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 4 13 4 14 4 15 4 16 4

18. Convert mixed numbers to improper fractions

19. Write these mixed numbers as improper fractions:1 3 2 3 5 4 3 4 13 19 = = = 3 5 4
1 x =
2 x =
4 x =
3 + 1 = 4 =
1 3 =
1 9

20. Convert improper fractions to mixed numbers

21. Write these improper fractions as mixed numbers:7 4 14 5 3 4 22 7 1 = = 2 = 1 3 5 4 7
7 ÷ 4 =
1 r 3
1 4 ÷ 5 =
2 r 4
2 2 ÷ 7 =
3 r 1

22. Add fractions with the same denominator beyond 1 whole, writing the answer as a mixed number

23. 5 6 2 6 6 7 1 6 4 5 4 5 5 8 3 1 5 + = = + = = 6 7 5 7 7
1 1 4 1 7 4 8 5 8 8 9 1 8 + = = + = =

24. Subtract a fraction from an improper fraction or mixed number with the same denominator and with 1 whole

25. 2 7 4 7 7 5 1 5 2 5 5 4 1 – = 1 – = 7 9 – 7 4 = 5 5 6 – 5 2 = 4 7 5 1 8 3 8 8 6 2 6 5 6 6 3 1 – = 1 – = 8 9 – 8 3 = 6 6 8 – 6 5 = 3 8 6

26. Solve missing number problems for addition and subtraction of fractions with the same denominator beyond 1

27. 1 3 3 2 2 3 4 1 3 4 2 4 9 7 4 9 2 9 1 – = – = + = 1 3 1 – 2 = + 4 3 = 2 5 9 2 1 – 4 = 4 3 4 – 3 2 = 2 9
1 1 – 9 4 = 7 3 9

28. Add a fraction to a whole number and subtract a fraction from a whole number

29. 2 3 3 2 5 1 5 5 4 5 7 7 2 5 + = 1 – = 1 – = 5 6 6 1 2 1 5 5 4 2 5 7 7 2 4 3 – = 3 – = 5 – =

30. Add a fraction to a mixed number with the same denominator, without regrouping

31. 5 12 1 6 12 11 2 4 1 4 3 1 7 2 4 7 5 + = 1 + = 2 + = 2 12 4 7

32. Add a fraction to a mixed number with the same denominator, regrouping to make 1 more whole

33. 2 5 3 5 3 4 2 2 4 1 3 6 1 5 6 2 + = 3 + = 3 + = 2 4 6 2 3 5 3 2 5 1 3 5 8 2 + =
= 1 + =
= 1 + =
= 1 5 5 5 4 4 4 4 6 6 6 6 1 1 2 2
2 + 1 = 3 = 3 = 2 4 4 6 6

34. Add a fraction to a mixed number with the same denominator by converting to an improper fraction

35. 2 5 3 5 3 4 2 2 4 1 3 6 1 5 6 2 + = 3 + = 3 + = 2 4 6
1 2 3
1 5
1 1 2
1 3 9 5
1 4 + = + = + = 5 5 5 4 4 4 6 6 6

36. 3 4 1 1 4 6 7 2 4 7 3 2 3 2 3 1 + = 2 + = 3 + = 3 7 3 7 1 8
2 0 4
2 4 8 2
1 0 + = + = + = 4 4 4 7 7 7 3 3 3

37. Add mixed numbers with the same denominator, without regrouping

38. 1 3 1 3 2 4 9 2 1 9 5 + 2 = 5 + 1 = 3 3 9

39. Add mixed numbers with the same denominator, regrouping to make 1 more whole

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

41. Add mixed numbers with the same denominator by converting to improper fractions

42. 3 4 2 2 4 4 1 4 5 2 3 5 5 2 + 1 = + 2 = 4
1 1 + 4 6 =
1 7 5
1 4 + 5
1 3 =
2 7 4 5

43. Subtract a fraction from a mixed number with the same denominator, without regrouping

44. 11 12 1 9 12 2 2 5 3 1 5 1 6 7 1 3 7 3 – = 1 – = 3 – = 1 12 5 7

45. Subtract a fraction from a mixed number with the same denominator, regrouping to make 1 fewer whole

46. 1 4 2 2 4 3 3 6 5 6 4 1 5 2 3 5 3 – = 1 – = 2 – = 1 4 6 5 5 2 3 9 5 4 6 3 3 1 – = 1 2 – = 2 1 – = 1 4 4 4 6 6 6 5 5 5

47. Subtract a fraction from a mixed number with the same denominator by converting to an improper fraction

48. 1 4 2 2 4 3 3 6 5 6 4 1 5 2 3 5 3 – = 1 – = 2 – = 1 4 6 5 9 2 7
2 1 5
1 6
1 1 3 8 – = – = – = 4 4 4 6 6 6 5 5 5

49. Subtract mixed numbers with the same denominator, without regrouping

50. 5 8 3 1 8 4 5 6 2 1 6 4 – 1 = 2 – 1 = 1 8 6

51. Subtract mixed numbers with the same denominator, regrouping to make 1 fewer whole

52. 1 8 2 7 8 2 2 5 3 4 5 3 – 1 = – 1 = 1 8 5 8 9 – 8 7 1 = 5 7 – 5 4 1 = 1 2

53. Subtract mixed numbers with the same denominator by converting to improper fractions

54. 1 8 2 7 8 2 2 5 3 4 5 3 – 1 = – 1 = 1 8 5 8
1 7 – 8
1 5 = 2 5
1 7 – 5 9 = 8 8 5

55. Fractions with Denominators which are Common Multiples (Count, Compare, Add, Subtract)

56. Identify equivalent fractions to a half

57. x2 x3 x4 x5 x6 1 2 1 3 1 4 1 5 1 6 = = = = = 2 4 2 6 2 8 2
1 0 2
1 2 x2 x3 x4 x5 x6

58. Use multiplication to find equivalent fractions

59. 2 7 6 2 9 8 2 6 12 1 4 8 2 5 15 2 3 18 = = = = = 21 36 x2 x3 x6 x3 x4 1 2 2 6 2
1 2 2 6 2 8 = = = = = 4 8 5
1 5 3
1 8 7
2 1 9
3 6 x2 x3 x6 x3 x4

60. Use division to find equivalent fractions

61. 10 15 2 9 27 1 3 1 4 6 8 4 4 20 5 16 28 7 = = = = = 3 3 ÷2 ÷4 ÷4 ÷5 ÷9 6 3 4 1
1 6 4
1 0 2 9 1 = = = = = 8 4
2 0 5
2 8 7
1 5 3
2 7 3 ÷2 ÷4 ÷4 ÷5 ÷9

62. Find equivalent improper fractions

63. 20 22 7 5 2 8 11 7 14 21 12 4 = = = x4 x2 ÷3 5
2 0
1 1
2 2
2 1 7 = = = 2 8 7
1 4
1 2 4 x4 x2 ÷3

64. Simplify fractions

65. Simplify these fractions to their lowest terms:4 3 8 16 2 1 12 16 20 25 5 4 6 15 5 2 = = = = ÷8 ÷4 ÷5 ÷3 8 1
1 2 3
2 0 4 6 2 = = = =
1 6 2
1 6 4
2 5 5
1 5 5 ÷8 ÷4 ÷5 ÷3

66. Compare fractions with denominators as common multiples

67. Write < or >. 1 3 2 9 13 21 5 7 5 8 17 24 > < < 1 3 5x3 x3 x3 1 3 5
1 5 5
1 5 = = = 3 9 7
2 1 8
2 4 x3 x3 x3

68. Compare improper fractions with denominators as common multiples

69. Write < or >. 7 4 20 12 29 15 5 3 > > 7 2 1 5 2 5 = = 4x3 x5 7
2 1 5
2 5 = = 4
1 2 3
1 5 x3 x5

70. Order fractions with denominators as common multiples

71. Order these fractions:x2 7
1 4 = 13 24 7 12 3 8 5 6
1 2
2 4 x2 8 3
2 4
1 3
1 2 7 6 5 x3 3 9 =
smallest
largest 8
2 4 x3 x4 5
2 0 = 6
2 4 x4

72. Add fractions with denominators as common multiples within 1

73. 2 3 1 9 9 7 3 5 7 25
2 5
2 2 8 27 1 9
2 7
1 1 + = + = + = x3 x5 x3 2 6 3
1 5 1 3 = = = 3 9 5
2 5 9
2 7 x3 x5 x3 9 6 + 9 1 = 7
2 5
1 5 +
2 5 7 =
2 2
2 7 8 +
2 7 3 =
1 1 9
2 5
2 7

74. Subtract fractions with denominators as common multiples within 1

75. 1 2 1 8 8 3 3 4 5 28
2 8
1 6 17 18 2 3
1 8 5 – = – = – = x4 x7 x6 1 4 3
2 1 2
1 2 = = = 2 8 4
2 8 3
1 8 x4 x7 x6 8 4 – 8 1 = 3
2 8
2 1 –
2 8 5 =
1 6
1 8
1 7 –
1 8
1 2 = 5 8
2 8
1 8

76. Solve missing number problems for addition and subtraction of fractions with denominators as common multiples within 1

77. 5 6
1 2 1 11 12 2 3 9 2 4 9 8 7 5 8 1 4 + = – = – =
1 2
1 1 – 6 5 = 3 2 – 9 4 = 4 1 + 8 5 =
1 2
1 1 –
1 2
1 0 = 1 9 6 – 9 4 = 2 8 2 + 8 5 = 7
1 2 9 8

78. Add fractions with denominators as common multiples beyond 1 whole, writing answers as mixed numbers

79. 4 5 4 15
1 5
1 6 1
1 5 9 21 6 7
2 1
2 7 1
2 1 6 + = = + = = x3 x3 4
1 2 6
1 8 = = 5
1 5 7
2 1 x3 x3
1 5
1 2 +
1 5 4 =
1 6
2 1 9 +
2 1
1 8 =
2 7
1 5
2 1

80. Subtract a fraction from an improper fraction or mixed number with denominators as common multiples and with 1 whole

81. 1 2 7 12
1 2
1 1 2 3 8 9 9 7 1 8 3 4 8 3 1 – = 1 – = 1 – = 1
1 2 6 – =
1 2 7 1 9 6 – 9 8 = 1 8 – 8 6 =
1 2
1 8 – =
1 2 7
1 1 9
1 5 – 9 8 = 7 8 9 – 8 6 = 3
1 2 9 8

82. Solve missing number problems for addition and subtraction of fractions with denominators as common multiples beyond 1

83. 1 8 8 7 1 4 9 2 1 2 3 5 9 4 3 3 4 1 2 1 – = – = + = 1 8 1 – 4 = 9 5 + 3 2 = 2 1 – 4 3 = 8 1 – 2 = 9 5 + 6 =
1 1 4 2 1 – 3 = 9 8 9 – 2 = 7 4 6 – 3 = 3 8 4

84. Add a fraction to a mixed number with denominators as common multiples, without regrouping

85. 1 3 7 15 12 1 2 1 6 4 2 9 1 1 3 5 + = 1 + = 2 + = 1 15 6 9 1
1 5 5 +
1 5 7 6 3 2 + 1 9 2 1 + 3

86. Add a fraction to a mixed number with denominators as common multiples, regrouping to make 1 more whole

87. 2 3 1 7 15 15 2 5 8 2 3 4 8 3 + = + = 1
1 5
1 0 +
1 5 7 8 5 2 + 6
1 7
1 1 1 + 2 +
1 5 8 1
1 5 2 1 8 3 1 + 2 +

88. Add a fraction to a mixed number with denominators as common multiples by converting to an improper fraction

89. 2 3 1 7 15 2 5 8 2 3 4 3 + = 2 + = 3
1 5 8 3 5
1 5 7 + = 8
2 1 4 3 + =
1 5
2 5
1 5 7 + =
3 2 8
2 1 8 6 + =
2 7
1 5 8

90. Add mixed numbers with denominators as common multiples, without regrouping

91. 1 9 2 2 3 9 7 1 2 1 6 6 4 + 1 = 3 + 2 = 4 9 1 2 + 9 6 1 = 6 3 2 + 6 1 2 =

92. Add mixed numbers with denominators as common multiples, regrouping to make 1 more whole

93. 5 6 2 7 18
1 8 4 11 12 2 2 3
1 2 7 + 2 = 5 + 1 = 4
1 8
1 5 2 +
1 8 7 2
1 2
1 1 2 +
1 2 8 1
1 8
2 2
1 2
1 9 4 + 3 + +
1 8 4 1 +
1 2 7 1 4 3

94. Add mixed numbers with denominators as common multiples by converting to improper fractions

95. 5 6 2 7 18 4 11 12 2 2 3 7 + 2 = 5 + 1 = 4
1 8
1 2 6
1 7 +
1 8
4 3 =
1 2
3 5 + 3 5 =
1 8
5 1 +
1 8
4 3 =
9 4
1 2
3 5 +
1 2
2 0 =
5 5
1 8
1 2

96. Subtract a fraction from a mixed number with denominators as common multiples, without regrouping

97. 3 4 1 5 12 4 2 3 4 15 6 7 8 1 1 4 5 – = 1 – = 2 – = 1 12 15 8 1
1 2 9 –
1 2 5
1 5
1 0 2 – 4 8 7 1 – 2

98. Subtract a fraction from a mixed number with denominators as common multiples, regrouping to make 1 fewer whole

99. 1 2 9 14
1 4
1 2 1 6 3 1 2 6 4 – = 1 – = 2 2
1 4 7 –
1 4 9 6 1 3 – 6 3
1 4
2 1 –
1 4 9 6 7 – 6 3 1 2

100. Subtract a fraction from a mixed number with denominators as common multiples by converting to improper fractions

101. 1 2 9 14
1 2 1 6 3 1 2 4 – = 1 – = 2
1 4 6 2 5
1 4 9 – = 6
1 9 2 1 – =
1 4
3 5
1 4 9 – =
2 6 6
1 9 6 3 – =
1 6
1 4 6

102. Subtract mixed numbers with denominators as common multiples, without regrouping

103. 5 9 2 1 3 9 2 1 2 3 1 4 4 1 – 1 = 1 – 1 = 2 9 5 2 – 9 3 1 = 4 2 3 – 4 1 =

104. Subtract mixed numbers with denominators as common multiples, regrouping to make 1 fewer whole

105. 1 3 2 7 12
1 2 9 1 10 4 1 5
1 0 9 – 1 = – 1 = 2
1 2 4 2 –
1 2 7 1
1 0 1 4 –
1 0 2 1
1 2
1 6 –
1 2 7 1
1 0
1 1 –
1 0 2 1 1 3

106. Subtract mixed numbers with denominators as common multiples by converting to improper fractions

107. 1 3 2 7 12
1 2 9 1 10 4 1 5 9 – 1 = – 1 = 2
1 0 3 7 –
1 2
1 9 =
1 0
4 1 – 5 6 =
1 2
2 8 –
1 2
1 9 = 9
1 0
4 1 –
1 0
1 2 =
2 9
1 2
1 0

108. Find a unit fraction of a number

109. 1 3 1 4 1 7
of 18 = 6
of 28 = 7
of 35 = 5
1 8 ÷ 3 =
2 8 ÷ 4 =
3 5 ÷ 7 =

110. Find a whole quantity given the quantity represented by a unit fraction

111. 1 6 1 8 1 9
of = 7 42
of = 5 40
of = 2 18
7 x 6 =
5 x 8 =
2 x 9 =

112. 1 3 1 6 1 2
of = 200
600
of = 60
360
of = 78
156
2 0 0 x 3 =
6 0 x 6 =
7 8 x 2 = 1
7 8 2 x
1 5 6

113. Find a quarter by halving twice, or an eighth by halving three times

114. ½ of 40 = 20
½ of 20 = 10
¼ of 40 = 10
½ of 10 = 5
⅛ of 40 = 5

115. ½ of 24 = 12
½ of 12 = 6
¼ of 24 = 6
½ of 6 = 3
⅛ of 24 = 3

116. Find a non-unit fraction of a number

117. 3 5 4 5 5 8
of 45 = 27
of 35 = 28
of 32 = 20
4 5 ÷ 5 = 9
3 5 ÷ 5 = 7
3 2 ÷ 8 = 4
9 x 3 = 2 7
7 x 4 = 2 8
4 x 5 = 2 0

118. Find a whole quantity, given the quantity represented by a non-unit fraction

119. 3 5 3 4 3 7
of = 15 25
of = 27 36
of = 21 49
1 5 ÷ 3 = 5
2 7 ÷ 3 = 9
2 1 ÷ 3 = 7
5 x 5 = 2 5
9 x 4 = 3 6
7 x 7 = 4 9

120. 3 5 3 4 3 7
of = 15 25
of = 27 36
of = 21 49
1 5 x 5 = 7 5
2 7 x 4 = 1 0 8
2 1 x 7 = 1 4 7
7 5 ÷ 3 = 2 5
1 0 8 ÷ 3 = 3 6
1 4 7 ÷ 3 = 4 9 2 2 5
2 7 4 x 3 6
2 1 7 x 4 9 3
7 5 1 3
1 0 8 1 3
1 4 7 2
1 0 8
1 4 7
Cut from recording

121. Express a remainder as a fraction

122. 1 3
13 ÷ 3 = 4
15 ÷ 4 = 3 3 4
1 3 ÷ 3 = 4 r1
1 5 ÷ 4 = 3 r3 2 2
802 ÷ 5 =
160
716 ÷ 7 =
102 5 7 1 6
0 r2 1
2 r2 5
8 0 2 3 7
7 1 6 1

123. Find a unit fraction of a number, writing the answer as a mixed number

124. 1 3 2 1 5 2 1 7 1
of 11 = 3
of 17 = 3
of 22 = 3 3 5 7
1 x 1 1 3 =
1 1 3
1 x 1 7 5 =
1 7 5
1 x 2 2 7 =
2 2 7

125. Find a non-unit fraction of a number, writing the answer as a mixed number

126. 7 8 5 3 4 1 3 5 1
of 11 = 9
of 23 = 17
of 17 = 10 8 4 5
7 x 1 1 8 =
7 7 8
3 x 2 3 4 =
6 9 4
3 x 1 7 5 =
5 1 5 2 1 7 1
1 7 3 x 4 4
6 9 2 5 1

127. Fractions with Denominators which are not Common Multiples

128. Compare fractions with denominators which are not common multiples

129. Write < or >. 1 3 2 7 5 6 7 8 3 5 7 11 > < < 1 3 2 1 =x7 x4
x11 1 3
2 1 = 7 5 6
2 4 =
2 0 3 5
5 5 =
3 3 x7 x4
x11 x3 x3 x5 2 6 7
2 1 7
3 5 = = = 7
2 1 8
2 4
1 1
5 5 x3 x3 x5

130. Compare improper fractions with denominators which are not common multiples

131. Write < or >. 4 3 7 5 7 5 3 2 < < 4 3 1 5 = 2 0 7 5 1 0 =x5 x2 4 3
1 5 =
2 0 7 5
1 0 =
1 4 x5 x2 x3 x5 7
2 1 3
1 5 = = 5
1 5 2
1 0 x3 x5

132. Order fractions with denominators which are not common multiples

133. Order these fractions:
x12 x3 1 2 5 8 7 12 2 3 1
1 2 5
1 5 = = 2
2 4 8
2 4
x12 x3 2 1
1 2 7 8 5 3 2 x2 x8
smallest
largest 7
1 4 2
1 6 = =
1 2
2 4 3
2 4 x2 x8

134. Order improper fractions with denominators which are not common multiples

135. Order these fractions:x5
x12 19 12 9 5 16 10 9 6
1 9
9 5 9
1 0 8 = =
1 2
6 0 5
6 0 x5
x12 6 9
1 2
1 9
1 0
1 6 5 9 x6
x10
smallest
largest
1 6
9 6 9
9 0 = =
1 0
6 0 6
6 0 x6
x10

136. Add fractions with denominators which are not common multiples within 1

137. 1 2 1 9
1 8
1 1 1 5 4 7
3 5
2 7 + = + = x9 x2 x7 x5 1 9 1 2 1 7 4
2 0 = = = = 2
1 8 9
1 8 5
3 5 7
3 5 x9 x2 x7 x5 9 2
1 1 7
2 0
2 7 + = + =
1 8
1 8
1 8
3 5
3 5
3 5

138. Subtract fractions with denominators which are not common multiples within 1

139. 5 6 1 4
1 2 7 3 5 2 7
3 5
1 1 – = – = x2 x3 x7 x5 5
1 0 1 3 3
2 1 2
1 0 = = = = 6
1 2 4
1 2 5
3 5 7
3 5 x2 x3 x7 x5
1 0 3 7
2 1
1 0
1 1 – = – =
1 2
1 2
1 2
3 5
3 5
3 5

140. Solve missing number problems for addition and subtraction of fractions with denominators which are not common multiples within 1

141. 2 5
3 0
1 3 5 6 1 3
2 4 5 1 8 + = – = 6 5 – 5 2 = 3 1 – 8 1 = x5 x6 x8 x3 5
2 5 2
1 2 1 8 1 3 = = = = 6
3 0 5
3 0 3
2 4 8
2 4 x5 x6 x8 x3
3 0
2 5 – =
3 0
1 2
1 3
2 4 8 – =
2 4 3 5
3 0
2 4

142. 5 6
2 3 2 7 1 8 – = 8 1 + 7 2 = x7 x8 1 7 2
1 6 = = 8
5 6 7
5 6 x7 x8
5 6 7 + =
5 6
1 6
2 3
5 6

143. Add fractions with denominators which are not common multiples beyond 1 whole, writing answers as mixed numbers

144. 4 5 2 3
1 5
2 2 1
1 5 7 7 8 1 6
2 4
2 5 1
2 4 + = = + = = x3 x5 x3 x4 4
1 2 2
1 0 7
2 1 1 4 = = = = 5
1 5 3
1 5 8
2 4 6
2 4 x3 x5 x3 x4
1 5
1 2 + =
1 5
1 0
2 2
2 4
2 1 + =
2 4 4
2 5
1 5
2 4

145. Subtract a fraction from an improper fraction or mixed number with a denominator which is not a multiple of the denominator in the fraction and with 1 whole

146. 1 3 1 2 6 5 1 4 3 5
2 0
1 3 1 – = 1 – = x2 x3 x5 x4 1 2 1 3 1 5 3
1 2 = = = = 3 6 2 6 4
2 0 5
2 0 x2 x3 x5 x4 1 6 2 – 6 3 = 1
2 0 5 –
2 0
1 2 6 8 – 6 3 = 5
2 0
2 5 – =
2 0
1 2
1 3 6
2 0

147. Solve missing number problems for addition and subtraction of fractions with denominators which are not common multiples beyond 1

148. 1 8
1 3 4 5 5 8
1 1 5 6 1 – = – = 1
4 0
2 4 8 9 – 5 4 = 6 5 + 8 = x5 x8 x4 x3 9
4 5 4
3 2 5
2 0 5
1 5 = = = = 8
4 0 5
4 0 6
2 4 8
2 4 x5 x8 x4 x3
4 0
4 5 – =
4 0
3 2
1 3
2 4
2 0 + =
2 4
1 5
3 5
4 0
2 4

149. 1 2 7 1 5 + = 1
1 0 5 6 – 2 1 = x2 x5 6
1 2 1 5 = = 5
1 0 2
1 0 x2 x5
1 0
1 2 – =
1 0 5 7
1 0

150. Add a fraction to a mixed number with a denominator which is not a multiple of the denominator in the fraction, without regrouping

151. 1 6 1
3 0
2 3 3 5 2
1 5
1 4 3 5 1 1 3 2 + = + = x6 x5 x5 x3 3
1 8 1 5 1 5 3 9 = = = = 5
3 0 6
3 0 3
1 5 5
1 5 x6 x5 x5 x3 1
3 0
1 8 +
3 0 5 = 1
3 0
2 3 2
1 5 5 +
1 5 9 = 2
1 5
1 4

152. Add a fraction to a mixed number with a denominator which is not a multiple of the denominator in the fraction, regrouping to make 1 more whole

153. 3 4 1 4 5 2
2 0
1 1 1 2 6 7 3
1 4 5 + = + = x5 x4 x7 x2 3
1 5 4
1 6 1 7 6
1 2 = = = = 4
2 0 5
2 0 2
1 4 7
1 4 x5 x4 x7 x2 1
2 0
1 5 +
2 0
1 6 = 2
1 4 7 +
1 4
1 2 =
3 1 1
2 0
1 1
1 9 1
1 4 5 1 + = 1 + 2 + = 2 +
2 0
1 4

154. Add a fraction to a mixed number with a denominator which is not a multiple of the denominator in the fraction by converting to an improper fraction

155. 3 4 1 4 5
1 1 1 2 6 7 5 + = 2 + = 3
2 0
1 4 4 7 5 4 + = 2 5 7 6 + = x5 x4 x7 x2 7
3 5 4
1 6 5
3 5 6
1 2 = = = = 4
2 0 5
2 0 2
1 4 7
1 4 x5 x4 x7 x2
2 0
3 5
2 0
1 6 + =
5 1
1 4
3 5
1 4
1 2 + =
4 7
2 0
1 4

156. Add mixed numbers with denominators which are not common multiples, without regrouping

157. 5 6 2 1 7
4 1 2 9 1 2
1 3 + 1 = 3 + 2 = 4
4 2
1 8 x7 x6 x2 x9 5
3 5 1 6 2 4 1 9 = = = = 6
4 2 7
4 2 9
1 8 2
1 8 x7 x6 x2 x9 2
4 2
3 5 +
4 2 6 = 1 2
1 8 4 +
1 8 9 = 2

158. Add mixed numbers with denominators which are not common multiples, regrouping to make 1 more whole

159. 1 2 3 5 1 4 5 2 3 4 4
2 0
1 1 + 2 = 5 + 1 =
1 0 x5 x2 x4 x5 1 5 3 6 4
1 6 3
1 5 = = = = 2
1 0 5
1 0 5
2 0 4
2 0 x5 x2 x4 x5 2
1 0 5 +
1 0 6 = 2 2
2 0
1 6 +
2 0
1 5 = 1
1 1 1
1 0
3 1 1
2 0
1 1 4 + = 4 + 3 + = 3 +
1 0
2 0

160. Add mixed numbers with denominators which are not common multiples by converting to improper fractions

161. 1 2 3 5 1 4 5 2 3 4
1 1 + 2 = 5 + 1 = 4
1 0
2 0 2 5 + 5
1 3 = 5
1 4 + 4 7 = x5 x2 x4 x5 5
2 5
1 3
2 6
1 4
5 6 7
3 5 = = = = 2
1 0 5
1 0 5
2 0 4
2 0 x5 x2 x4 x5
1 0
2 5 +
1 0
2 6 =
5 1
2 0
5 6 +
2 0
3 5 =
9 1
1 0
2 0

162. Subtract a fraction from a mixed number with a denominator which is not a multiple of the denominator in the fraction, without regrouping

163. 6 7 1 3 4
2 8 3 1 5 9 2 1 2 – = 1 – = 2
1 8 x4 x7 x2 x9 6
2 4 3
2 1 5
1 0 1 9 = = = = 7
2 8 4
2 8 9
1 8 2
1 8 x4 x7 x2 x9 1
2 8
2 4 –
2 8
2 1 = 2
1 8
1 0 –
1 8 9 =

164. Subtract a fraction from a mixed number with a denominator which is not a multiple of the denominator in the fraction, regrouping to make 1 fewer whole

165. 1 6 2 1 4
1 2
1 1 1 2 2 3 5 – = 1 – = 1 6 x2 x3 x3 x2 1 2 1 3 1 3 2 4 = = = = 6
1 2 4
1 2 2 6 3 6 x2 x3 x3 x2 2
1 2 –
1 2 3 = 2 6 3 – = 6 4 1
1 2
1 4 –
1 2 3 = 1 6 9 – = 6 4

166. Subtract a fraction from a mixed number with a denominator which is not a multiple of the denominator in the fraction by converting to an improper fraction

167. 1 6 2 1 4
1 1 1 2 2 3 5 – = 1 – = 1
1 2 6 6
1 3 4 1 – = 2 5 – 3 2 = x2 x3 x3 x2
1 3
2 6 1 3 5
1 5 2 4 = = = = 6
1 2 4
1 2 2 6 3 6 x2 x3 x3 x2
1 2
2 6 –
1 2 3 =
2 3 6
1 5 6 4 – =
1 1
1 2 6

168. Subtract mixed numbers with denominators which are not common multiples, without regrouping

169. 3 5 2 1 3
1 5 4 7 9 2 3 8
7 2
2 9 – 1 = 1 – 1 = 1 x3 x5 x8 x9 3 9 1 5 7
5 6 3
2 7 = = = = 5
1 5 3
1 5 9
7 2 8
7 2 x3 x5 x8 x9 2
1 5 9 –
1 5 5 = 1 2
7 2
5 6 –
7 2
2 7 = 1

170. Subtract mixed numbers with denominators which are not common multiples, regrouping to make 1 fewer whole

171. 1 4 3 1 3
1 2
1 1 2 5 4 1 2
1 0 9 – 1 = 1 – 1 = 2 x3 x4 x2 x5 1 3 1 4 2 4 1 5 = = = = 4
1 2 3
1 2 5
1 0 2
1 0 x3 x4 x2 x5
1 2 3 –
1 2 4 1
1 0 4 –
1 0 5 1
1 2
1 5 –
1 2 4 1
1 0
1 4 –
1 0 5 1 2 3

172. Subtract mixed numbers with denominators which are not common multiples by converting to improper fractions

173. 1 4 3 1 3
1 1 2 5 4 1 2 9 – 1 = 1 – 1 = 2
1 2
1 0 4
1 3 – 3 4 = 5
2 2 – 2 3 = x3 x4 x2 x5
1 3
3 9 4
1 6
2 2
4 4 3
1 5 = = = = 4
1 2 3
1 2 5
1 0 2
1 0 x3 x4 x2 x5
1 2
3 9 –
1 2
1 6 =
2 3
1 0
4 4 –
1 0
1 5 =
2 9
1 2
1 0

174. Find the fraction that lies halfway between two fractions

175. Which fraction lies halfway between and ? 4 7 2 3
1 3
2 1 x3 4
1 2 = 7
2 1 x3 x7 2
1 4 = 3
2 1 x7

176. Which fraction lies halfway between and ? 2 7 1 3
4 2 x3 x2 2 6
1 2 = = 7
2 1
4 2 x3 x2 x7 x2 1 7
1 4 = = 3
2 1
4 2 x7 x2

177. Multiply by a unit fraction

178. 1 4 1 4 1
1 6 3 4 1 5 3
2 0 5 12 1 2 5
2 4 x = x = x =
1 x 1
4 x 4 = 1
3 x 1
4 x 5 = 3
5 x 1
1 2 x 2 = 5
1 6
2 0
2 4

179. Multiply non-unit fractions

180. 1 6
2 5 4 5 4 5 2 5 3 4 6
2 0 x = x =
4 x 4
5 x 5 =
1 6
2 x 3
5 x 4 = 6
2 5
2 0

181. Multiply non-unit fractions, simplifying at the end

182. 4 5 5 6 3 2 8 10 4 10 8
2 5 x = x =
4 x 5
5 x 6 =
2 0
8 x 4
1 0 x 1 0 =
3 2
3 0
1 0 0
÷10 ÷4
2 0 2
3 2 8 = =
3 0 3
1 0 0
2 5
÷10 ÷4

183. Multiply non-unit fractions, cross-simplifying

184. 6 15 5 12 1 6 5 18 9 11 5
2 2 x = x = 1 1 1 6 5 1 5 9 5 x = x =
1 5
1 2 6
1 8
1 1
2 2 3 2 2

185. Divide a fraction by a whole number

186. 1 4 8 1 3 4 3
2 0 3 10 3
5 0 ÷ 2 = ÷ 5 = ÷ 5 = 1 3
1 0 3 4
x 2 4
x 5
x 5

187. Multiply a fraction by a whole number

188. 5 6 1 3 4 1 x 5 = 4 x 7 = 5 6 4
5 x 5 6 =
2 5
3 x 7 4 =
2 1 6 4

189. Multiply a mixed number by a whole number by partitioning

190. 4 5 1 5 2 3 2 3 3 x 4 = 15 2 x 7 = 18
3 x 4 = 1 2
2 x 7 = 1 4 4 5
x 4 = 5
1 6 = 3 1 2 3
x 7 = 3
1 4 = 4 2 5 3
1 2 + = 3 1 5
1 5 1
1 4 + = 4 2 3
1 8 2 5 3

191. 1 4 1 2 1 2 1 x 40 = 50 25 x 1 = 37
1 x 4 0 = 4 0
1 x 2 5 = 2 5 1 4
x 4 0 = 4
4 0
= 1 0 1 2
x 2 5 = 2
2 5 =
1 2 1 2
= 5 0
2 5 +
1 2 1 2 3 7 1 2

192. Multiply a mixed number by a whole number by converting to an improper fraction

193. 4 5 1 2 3 2 3 x 4 = 15 2 x 7 = 18 5 3
1 9 x 4 =
7 6 8 x 7 =
5 6 5 5 3 3 2 1 5 1 1 8 5 3 5
7 6 3
5 6 2 2

194. 5
x 4 0 =
2 0 0 1 4 1 x 40 = 50 4 4
2 0 0 ÷ 4 =
5 0 1 2 1 2 3
x 2 5 =
7 5 = 3 7 1 25 x 1 = 37 2 2 2 3 7 1 2 2
7 5 1