GRADE 6 TERM 4 MATHEMATICS WORKSHEET 5 (Q& A) • Teacha! - Free Printable

Let's solve each section of the worksheet step by step.

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Section 1: Convert.

Convert mixed numbers to improper fractions.

> To convert a mixed number $ a \frac{b}{c} $ to an improper fraction:
> $$
> \frac{a \times c + b}{c}
> $$

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54. $ 7 \frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{21 + 2}{3} = \frac{23}{3} $

55. $ 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} $

56. $ 8 \frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{32 + 1}{4} = \frac{33}{4} $

57. $ 5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3} $

58. $ 8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{40 + 2}{5} = \frac{42}{5} $

59. $ 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6} $

60. $ 7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3} $

61. $ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} $

62. $ 1 \frac{3}{6} = \frac{1 \times 6 + 3}{6} = \frac{6 + 3}{6} = \frac{9}{6} = \frac{3}{2} $ (simplified)

63. $ 4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5} $

64. $ 8 \frac{2}{3} = \frac{8 \times 3 + 2}{3} = \frac{24 + 2}{3} = \frac{26}{3} $

65. $ 8 \frac{1}{8} = \frac{8 \times 8 + 1}{8} = \frac{64 + 1}{8} = \frac{65}{8} $

66. $ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} $

67. $ 5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{25 + 3}{5} = \frac{28}{5} $

68. $ 8 \frac{2}{6} = \frac{8 \times 6 + 2}{6} = \frac{48 + 2}{6} = \frac{50}{6} = \frac{25}{3} $ (simplified)

69. $ 7 \frac{5}{6} = \frac{7 \times 6 + 5}{6} = \frac{42 + 5}{6} = \frac{47}{6} $

70. $ 9 \frac{1}{4} = \frac{9 \times 4 + 1}{4} = \frac{36 + 1}{4} = \frac{37}{4} $

71. $ 1 \frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{6 + 4}{6} = \frac{10}{6} = \frac{5}{3} $ (simplified)

72. $ 4 \frac{7}{8} = \frac{4 \times 8 + 7}{8} = \frac{32 + 7}{8} = \frac{39}{8} $

73. $ 9 \frac{1}{3} = \frac{9 \times 3 + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3} $

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Section 2: Calculate

We'll perform addition and subtraction of mixed numbers.

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74. $ 9 \frac{2}{5} - 8 \frac{4}{5} $

Convert both to improper fractions:

- $ 9 \frac{2}{5} = \frac{47}{5} $
- $ 8 \frac{4}{5} = \frac{44}{5} $

$$
\frac{47}{5} - \frac{44}{5} = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $

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75. $ 5 \frac{1}{10} + 5 \frac{5}{10} $

Add whole parts and fractions:

- Whole: $ 5 + 5 = 10 $
- Fraction: $ \frac{1}{10} + \frac{5}{10} = \frac{6}{10} = \frac{3}{5} $

So, $ 10 \frac{3}{5} $

✔ Answer: $ 10 \frac{3}{5} $

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76. $ 7 \frac{9}{18} + 4 \frac{1}{18} $

Simplify $ \frac{9}{18} = \frac{1}{2} $, but keep denominator as 18 for now.

- Whole: $ 7 + 4 = 11 $
- Fraction: $ \frac{9}{18} + \frac{1}{18} = \frac{10}{18} = \frac{5}{9} $

✔ Answer: $ 11 \frac{5}{9} $

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77. $ 7 \frac{1}{9} - 1 \frac{5}{9} $

- Whole: $ 7 - 1 = 6 $
- Fraction: $ \frac{1}{9} - \frac{5}{9} = -\frac{4}{9} $

Borrow 1 from 6 → $ 5 + \frac{9}{9} = 5 \frac{9}{9} $, then subtract:

$ 5 \frac{9}{9} - \frac{5}{9} = 5 \frac{4}{9} $

Wait — we're doing $ 7 \frac{1}{9} - 1 \frac{5}{9} $

Better: convert both to improper:

- $ 7 \frac{1}{9} = \frac{64}{9} $
- $ 1 \frac{5}{9} = \frac{14}{9} $
- $ \frac{64}{9} - \frac{14}{9} = \frac{50}{9} = 5 \frac{5}{9} $

✔ Answer: $ 5 \frac{5}{9} $

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78. $ 6 \frac{2}{21} + 8 \frac{14}{21} $

- Whole: $ 6 + 8 = 14 $
- Fraction: $ \frac{2}{21} + \frac{14}{21} = \frac{16}{21} $

✔ Answer: $ 14 \frac{16}{21} $

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79. $ 2 \frac{3}{4} + 1 \frac{3}{4} $

- Whole: $ 2 + 1 = 3 $
- Fraction: $ \frac{3}{4} + \frac{3}{4} = \frac{6}{4} = 1 \frac{2}{4} = 1 \frac{1}{2} $

Add to whole: $ 3 + 1 = 4 $, so $ 4 \frac{1}{2} $

✔ Answer: $ 4 \frac{1}{2} $

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80. $ 4 \frac{3}{10} + 5 \frac{8}{10} $

- Whole: $ 4 + 5 = 9 $
- Fraction: $ \frac{3}{10} + \frac{8}{10} = \frac{11}{10} = 1 \frac{1}{10} $

Add to whole: $ 9 + 1 = 10 $, so $ 10 \frac{1}{10} $

✔ Answer: $ 10 \frac{1}{10} $

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81. $ 7 \frac{5}{7} + 7 \frac{6}{7} $

- Whole: $ 7 + 7 = 14 $
- Fraction: $ \frac{5}{7} + \frac{6}{7} = \frac{11}{7} = 1 \frac{4}{7} $

Total: $ 14 + 1 = 15 $, so $ 15 \frac{4}{7} $

✔ Answer: $ 15 \frac{4}{7} $

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82. $ 7 \frac{12}{23} - 3 \frac{14}{23} $

Since $ \frac{12}{23} < \frac{14}{23} $, borrow 1 from 7:

- $ 7 \frac{12}{23} = 6 + \frac{23}{23} + \frac{12}{23} = 6 \frac{35}{23} $
- Now subtract: $ 6 \frac{35}{23} - 3 \frac{14}{23} = (6 - 3) + \left( \frac{35 - 14}{23} \right) = 3 \frac{21}{23} $

✔ Answer: $ 3 \frac{21}{23} $

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83. $ 3 \frac{8}{11} + 8 \frac{4}{11} $

- Whole: $ 3 + 8 = 11 $
- Fraction: $ \frac{8}{11} + \frac{4}{11} = \frac{12}{11} = 1 \frac{1}{11} $
- Total: $ 11 + 1 = 12 $, so $ 12 \frac{1}{11} $

✔ Answer: $ 12 \frac{1}{11} $

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Section 3: Compare the fractions. Use < or >

Compare using cross-multiplication or common denominators.

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84. $ \frac{1}{4} \quad \text{vs} \quad \frac{1}{3} $

Cross multiply: $ 1 \times 3 = 3 $, $ 1 \times 4 = 4 $ → $ 3 < 4 $, so $ \frac{1}{4} < \frac{1}{3} $

✔ Answer: $ < $

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85. $ \frac{1}{4} \quad \text{vs} \quad \frac{1}{6} $

$ \frac{1}{4} = 0.25 $, $ \frac{1}{6} \approx 0.166 $ → $ \frac{1}{4} > \frac{1}{6} $

✔ Answer: $ > $

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86. $ \frac{3}{8} \quad \text{vs} \quad \frac{3}{5} $

Same numerator: larger denominator → smaller fraction → $ \frac{3}{8} < \frac{3}{5} $

✔ Answer: $ < $

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87. $ \frac{1}{3} \quad \text{vs} \quad \frac{1}{4} $

$ \frac{1}{3} \approx 0.333 $, $ \frac{1}{4} = 0.25 $ → $ \frac{1}{3} > \frac{1}{4} $

✔ Answer: $ > $

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88. $ \frac{5}{6} \quad \text{vs} \quad \frac{1}{5} $

$ \frac{5}{6} \approx 0.833 $, $ \frac{1}{5} = 0.2 $ → $ \frac{5}{6} > \frac{1}{5} $

✔ Answer: $ > $

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89. $ \frac{5}{6} \quad \text{vs} \quad \frac{2}{3} $

Convert $ \frac{2}{3} = \frac{4}{6} $, so $ \frac{5}{6} > \frac{4}{6} $

✔ Answer: $ > $

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90. $ \frac{2}{8} \quad \text{vs} \quad \frac{2}{6} $

Simplify: $ \frac{2}{8} = \frac{1}{4} $, $ \frac{2}{6} = \frac{1}{3} $, and $ \frac{1}{4} < \frac{1}{3} $

✔ Answer: $ < $

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91. $ \frac{2}{4} \quad \text{vs} \quad \frac{1}{5} $

$ \frac{2}{4} = \frac{1}{2} = 0.5 $, $ \frac{1}{5} = 0.2 $ → $ \frac{2}{4} > \frac{1}{5} $

✔ Answer: $ > $

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92. $ \frac{3}{4} \quad \text{vs} \quad \frac{1}{3} $

$ \frac{3}{4} = 0.75 $, $ \frac{1}{3} \approx 0.333 $ → $ \frac{3}{4} > \frac{1}{3} $

✔ Answer: $ > $

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93. $ \frac{5}{8} \quad \text{vs} \quad \frac{2}{6} $

Simplify $ \frac{2}{6} = \frac{1}{3} \approx 0.333 $, $ \frac{5}{8} = 0.625 $ → $ \frac{5}{8} > \frac{2}{6} $

✔ Answer: $ > $

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94. $ \frac{3}{5} \quad \text{vs} \quad \frac{5}{8} $

Cross multiply: $ 3 \times 8 = 24 $, $ 5 \times 5 = 25 $ → $ 24 < 25 $ → $ \frac{3}{5} < \frac{5}{8} $

✔ Answer: $ < $

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95. $ \frac{2}{4} \quad \text{vs} \quad \frac{3}{6} $

Simplify both: $ \frac{2}{4} = \frac{1}{2} $, $ \frac{3}{6} = \frac{1}{2} $ → equal

✔ Answer: $ = $

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Section 4: Divide

To divide a fraction by a whole number:
$$
\frac{a}{b} \div c = \frac{a}{b \times c}
$$

Or: $ \frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c} $

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96. $ \frac{2}{8} \div 1 = \frac{2}{8} = \frac{1}{4} $

✔ Answer: $ \frac{1}{4} $

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97. $ 4 \div \frac{1}{5} = 4 \times 5 = 20 $

✔ Answer: $ 20 $

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98. $ \frac{5}{6} \div 5 = \frac{5}{6} \times \frac{1}{5} = \frac{5}{30} = \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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99. $ \frac{2}{4} \div 5 = \frac{1}{2} \div 5 = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10} $

✔ Answer: $ \frac{1}{10} $

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100. $ \frac{6}{8} \div 8 = \frac{3}{4} \div 8 = \frac{3}{4} \times \frac{1}{8} = \frac{3}{32} $

✔ Answer: $ \frac{3}{32} $

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101. $ 5 \div \frac{3}{6} = 5 \div \frac{1}{2} = 5 \times 2 = 10 $

✔ Answer: $ 10 $

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102. $ \frac{2}{4} \div 8 = \frac{1}{2} \div 8 = \frac{1}{2} \times \frac{1}{8} = \frac{1}{16} $

✔ Answer: $ \frac{1}{16} $

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103. $ 9 \div \frac{2}{3} = 9 \times \frac{3}{2} = \frac{27}{2} = 13 \frac{1}{2} $

✔ Answer: $ 13 \frac{1}{2} $

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104. $ 6 \div \frac{2}{5} = 6 \times \frac{5}{2} = \frac{30}{2} = 15 $

✔ Answer: $ 15 $

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105. $ \frac{1}{4} \div 4 = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} $

✔ Answer: $ \frac{1}{16} $

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106. $ \frac{1}{8} \div 8 = \frac{1}{8} \times \frac{1}{8} = \frac{1}{64} $

✔ Answer: $ \frac{1}{64} $

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107. $ \frac{4}{6} \div 3 = \frac{2}{3} \div 3 = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9} $

✔ Answer: $ \frac{2}{9} $

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✔ Final Answers Summary

#### Convert:
54. $ \frac{23}{3} $
55. $ \frac{11}{5} $
56. $ \frac{33}{4} $
57. $ \frac{17}{3} $
58. $ \frac{42}{5} $
59. $ \frac{23}{6} $
60. $ \frac{22}{3} $
61. $ \frac{9}{4} $
62. $ \frac{3}{2} $
63. $ \frac{22}{5} $
64. $ \frac{26}{3} $
65. $ \frac{65}{8} $
66. $ \frac{15}{4} $
67. $ \frac{28}{5} $
68. $ \frac{25}{3} $
69. $ \frac{47}{6} $
70. $ \frac{37}{4} $
71. $ \frac{5}{3} $
72. $ \frac{39}{8} $
73. $ \frac{28}{3} $

#### Calculate:
74. $ \frac{3}{5} $
75. $ 10 \frac{3}{5} $
76. $ 11 \frac{5}{9} $
77. $ 5 \frac{5}{9} $
78. $ 14 \frac{16}{21} $
79. $ 4 \frac{1}{2} $
80. $ 10 \frac{1}{10} $
81. $ 15 \frac{4}{7} $
82. $ 3 \frac{21}{23} $
83. $ 12 \frac{1}{11} $

#### Compare:
84. <
85. >
86. <
87. >
88. >
89. >
90. <
91. >
92. >
93. >
94. <
95. =

#### Divide:
96. $ \frac{1}{4} $
97. $ 20 $
98. $ \frac{1}{6} $
99. $ \frac{1}{10} $
100. $ \frac{3}{32} $
101. $ 10 $
102. $ \frac{1}{16} $
103. $ 13 \frac{1}{2} $
104. $ 15 $
105. $ \frac{1}{16} $
106. $ \frac{1}{64} $
107. $ \frac{2}{9} $

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