GRADE 6 TERM 4 MATHEMATICS WORKSHEET 5 (Q& A) • Teacha! - Free Printable
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Step-by-step solution for: GRADE 6 TERM 4 MATHEMATICS WORKSHEET 5 (Q& A) • Teacha!
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Show Answer Key & Explanations
Step-by-step solution for: GRADE 6 TERM 4 MATHEMATICS WORKSHEET 5 (Q& A) • Teacha!
Of course! I'll solve each section of the worksheet step-by-step and explain the reasoning behind each answer.
---
## Section 1: Convert (Mixed Numbers to Improper Fractions)
To convert a mixed number `a b/c` to an improper fraction:
> Multiply the whole number `a` by the denominator `c`, then add the numerator `b`. The result becomes the new numerator, with the same denominator `c`.
Formula: `(a × c + b) / c`
---
54. `7 2/3` = `(7×3 + 2)/3` = `(21+2)/3` = 23/3
55. `2 1/5` = `(2×5 + 1)/5` = `(10+1)/5` = 11/5
56. `8 1/4` = `(8×4 + 1)/4` = `(32+1)/4` = 33/4
57. `5 2/3` = `(5×3 + 2)/3` = `(15+2)/3` = 17/3
58. `8 2/5` = `(8×5 + 2)/5` = `(40+2)/5` = 42/5
59. `3 5/6` = `(3×6 + 5)/6` = `(18+5)/6` = 23/6
60. `7 1/3` = `(7×3 + 1)/3` = `(21+1)/3` = 22/3
61. `2 1/4` = `(2×4 + 1)/4` = `(8+1)/4` = 9/4
62. `1 3/6` = `(1×6 + 3)/6` = `(6+3)/6` = 9/6 → *Simplify*: Divide numerator and denominator by 3 → 3/2
*(Note: Some teachers prefer simplified form; others accept unsimplified. Since 3/2 is simpler, we’ll use that.)*
63. `4 2/5` = `(4×5 + 2)/5` = `(20+2)/5` = 22/5
64. `8 2/3` = `(8×3 + 2)/3` = `(24+2)/3` = 26/3
65. `8 1/8` = `(8×8 + 1)/8` = `(64+1)/8` = 65/8
66. `3 3/4` = `(3×4 + 3)/4` = `(12+3)/4` = 15/4
67. `5 3/5` = `(5×5 + 3)/5` = `(25+3)/5` = 28/5
68. `8 2/6` = `(8×6 + 2)/6` = `(48+2)/6` = 50/6 → *Simplify*: Divide by 2 → 25/3
69. `7 5/6` = `(7×6 + 5)/6` = `(42+5)/6` = 47/6
70. `9 1/4` = `(9×4 + 1)/4` = `(36+1)/4` = 37/4
71. `1 4/6` = `(1×6 + 4)/6` = `(6+4)/6` = 10/6 → *Simplify*: Divide by 2 → 5/3
72. `4 7/8` = `(4×8 + 7)/8` = `(32+7)/8` = 39/8
73. `9 1/3` = `(9×3 + 1)/3` = `(27+1)/3` = 28/3
---
## Section 2: Calculate (Addition & Subtraction of Mixed Numbers)
When adding or subtracting mixed numbers:
1. Add/subtract the whole numbers.
2. Add/subtract the fractions.
3. If the fraction part is improper, convert it to a mixed number and add the whole number part to the total.
4. If subtracting and the top fraction is smaller, borrow 1 from the whole number (convert to equivalent fraction).
---
74. `9 2/5 - 8 4/5`
- Whole numbers: 9 - 8 = 1
- Fractions: 2/5 - 4/5 → Can’t do! Borrow 1 from 9 → becomes 8 + 7/5 (since 1 = 5/5, so 2/5 + 5/5 = 7/5)
- Now: 8 7/5 - 8 4/5 = (8-8) + (7/5 - 4/5) = 0 + 3/5 = 3/5
✔ Answer: 3/5
---
75. `5 1/10 + 5 5/10`
- Whole: 5 + 5 = 10
- Fraction: 1/10 + 5/10 = 6/10 → Simplify to 3/5
- Total: 10 3/5
✔ Answer: 10 3/5
---
76. `7 9/18 + 4 1/18`
- Whole: 7 + 4 = 11
- Fraction: 9/18 + 1/18 = 10/18 → Simplify: divide by 2 → 5/9
- Total: 11 5/9
✔ Answer: 11 5/9
---
77. `7 1/9 - 1 5/9`
- Whole: 7 - 1 = 6
- Fraction: 1/9 - 5/9 → Can’t do! Borrow 1 → 6 + 10/9 (since 1 = 9/9 → 1/9 + 9/9 = 10/9)
- Now: 6 10/9 - 1 5/9 = (6-1) + (10/9 - 5/9) = 5 + 5/9 = 5 5/9
✔ Answer: 5 5/9
---
78. `6 2/21 + 8 14/21`
- Whole: 6 + 8 = 14
- Fraction: 2/21 + 14/21 = 16/21
- Total: 14 16/21
✔ Answer: 14 16/21
---
79. `2 3/4 + 1 3/4`
- Whole: 2 + 1 = 3
- Fraction: 3/4 + 3/4 = 6/4 = 1 2/4 = 1 1/2
- Total: 3 + 1 1/2 = 4 1/2
✔ Answer: 4 1/2
---
80. `4 3/10 + 5 8/10`
- Whole: 4 + 5 = 9
- Fraction: 3/10 + 8/10 = 11/10 = 1 1/10
- Total: 9 + 1 1/10 = 10 1/10
✔ Answer: 10 1/10
---
81. `7 5/7 + 7 6/7`
- Whole: 7 + 7 = 14
- Fraction: 5/7 + 6/7 = 11/7 = 1 4/7
- Total: 14 + 1 4/7 = 15 4/7
✔ Answer: 15 4/7
---
82. `7 12/23 - 3 14/23`
- Whole: 7 - 3 = 4
- Fraction: 12/23 - 14/23 → Can’t do! Borrow 1 → 3 + 35/23 (since 1 = 23/23 → 12/23 + 23/23 = 35/23)
- Now: 6 35/23 - 3 14/23 = (6-3) + (35/23 - 14/23) = 3 + 21/23 = 3 21/23
✔ Answer: 3 21/23
---
83. `3 8/11 + 8 4/11`
- Whole: 3 + 8 = 11
- Fraction: 8/11 + 4/11 = 12/11 = 1 1/11
- Total: 11 + 1 1/11 = 12 1/11
✔ Answer: 12 1/11
---
## Section 3: Compare the Fractions (Use <, >, or =)
To compare two fractions:
- If denominators are the same → compare numerators.
- If numerators are the same → compare denominators (smaller denominator = larger fraction).
- Otherwise, find common denominators or cross-multiply.
---
84. `1/4 ___ 1/3`
- Same numerator → smaller denominator is bigger → 1/3 > 1/4 → <
✔ Answer: <
---
85. `1/4 ___ 1/6`
- Same numerator → 1/4 > 1/6 → >
✔ Answer: >
---
86. `3/8 ___ 3/5`
- Same numerator → 3/5 > 3/8 → <
✔ Answer: <
---
87. `1/3 ___ 1/4`
- Same numerator → 1/3 > 1/4 → >
✔ Answer: >
---
88. `5/6 ___ 1/5`
- Cross multiply: 5×5 = 25, 1×6 = 6 → 25 > 6 → 5/6 > 1/5 → >
✔ Answer: >
---
89. `5/6 ___ 2/3`
- Common denominator: 6 → 5/6 vs 4/6 → 5/6 > 4/6 → >
✔ Answer: >
---
90. `2/8 ___ 2/6`
- Same numerator → 2/6 > 2/8 → <
✔ Answer: <
---
91. `2/4 ___ 1/5`
- Simplify 2/4 = 1/2 → 1/2 vs 1/5 → 1/2 > 1/5 → >
✔ Answer: >
---
92. `3/4 ___ 1/3`
- Cross multiply: 3×3=9, 1×4=4 → 9 > 4 → 3/4 > 1/3 → >
✔ Answer: >
---
93. `5/8 ___ 2/6`
- Simplify 2/6 = 1/3 → Compare 5/8 vs 1/3 → Cross multiply: 5×3=15, 1×8=8 → 15>8 → 5/8 > 1/3 → >
✔ Answer: >
---
94. `3/5 ___ 5/8`
- Cross multiply: 3×8=24, 5×5=25 → 24 < 25 → 3/5 < 5/8 → <
✔ Answer: <
---
95. `2/4 ___ 3/6`
- Simplify both: 2/4 = 1/2, 3/6 = 1/2 → =
✔ Answer: =
---
## Section 4: Divide (Fraction Division)
Rule: To divide fractions → Multiply by the reciprocal
`a/b ÷ c/d = a/b × d/c`
Also, dividing by a whole number: `a/b ÷ c = a/b × 1/c`
---
96. `2/8 ÷ 1` = `2/8 × 1/1` = 2/8 → Simplify → 1/4
✔ Answer: 1/4
---
97. `4 ÷ 1/5` = `4 × 5/1` = 20
✔ Answer: 20
---
98. `5/6 ÷ 5` = `5/6 × 1/5` = `(5×1)/(6×5)` = 5/30 → Simplify → 1/6
✔ Answer: 1/6
---
99. `2/4 ÷ 5` = `2/4 × 1/5` = `2/20` → Simplify → 1/10
✔ Answer: 1/10
---
100. `6/8 ÷ 8` = `6/8 × 1/8` = `6/64` → Simplify (÷2) → 3/32
✔ Answer: 3/32
---
101. `5 ÷ 3/6` = `5 × 6/3` = `5 × 2` = 10
*(Note: 3/6 = 1/2, so 5 ÷ 1/2 = 5 × 2 = 10)*
✔ Answer: 10
---
102. `2/4 ÷ 8` = `2/4 × 1/8` = `2/32` → Simplify → 1/16
✔ Answer: 1/16
---
103. `9 ÷ 2/3` = `9 × 3/2` = `27/2` = 13 1/2
✔ Answer: 13 1/2
---
104. `6 ÷ 2/5` = `6 × 5/2` = `30/2` = 15
✔ Answer: 15
---
105. `1/4 ÷ 4` = `1/4 × 1/4` = 1/16
✔ Answer: 1/16
---
106. `1/8 ÷ 8` = `1/8 × 1/8` = 1/64
✔ Answer: 1/64
---
107. `4/6 ÷ 3` = `4/6 × 1/3` = `4/18` → Simplify → 2/9
✔ Answer: 2/9
---
## ✔ Final Answers Summary:
54. 23/3
55. 11/5
56. 33/4
57. 17/3
58. 42/5
59. 23/6
60. 22/3
61. 9/4
62. 3/2
63. 22/5
64. 26/3
65. 65/8
66. 15/4
67. 28/5
68. 25/3
69. 47/6
70. 37/4
71. 5/3
72. 39/8
73. 28/3
74. 3/5
75. 10 3/5
76. 11 5/9
77. 5 5/9
78. 14 16/21
79. 4 1/2
80. 10 1/10
81. 15 4/7
82. 3 21/23
83. 12 1/11
84. <
85. >
86. <
87. >
88. >
89. >
90. <
91. >
92. >
93. >
94. <
95. =
96. 1/4
97. 20
98. 1/6
99. 1/10
100. 3/32
101. 10
102. 1/16
103. 13 1/2
104. 15
105. 1/16
106. 1/64
107. 2/9
---
Let me know if you’d like this in printable format or need help with any step again! 😊
---
## Section 1: Convert (Mixed Numbers to Improper Fractions)
To convert a mixed number `a b/c` to an improper fraction:
> Multiply the whole number `a` by the denominator `c`, then add the numerator `b`. The result becomes the new numerator, with the same denominator `c`.
Formula: `(a × c + b) / c`
---
54. `7 2/3` = `(7×3 + 2)/3` = `(21+2)/3` = 23/3
55. `2 1/5` = `(2×5 + 1)/5` = `(10+1)/5` = 11/5
56. `8 1/4` = `(8×4 + 1)/4` = `(32+1)/4` = 33/4
57. `5 2/3` = `(5×3 + 2)/3` = `(15+2)/3` = 17/3
58. `8 2/5` = `(8×5 + 2)/5` = `(40+2)/5` = 42/5
59. `3 5/6` = `(3×6 + 5)/6` = `(18+5)/6` = 23/6
60. `7 1/3` = `(7×3 + 1)/3` = `(21+1)/3` = 22/3
61. `2 1/4` = `(2×4 + 1)/4` = `(8+1)/4` = 9/4
62. `1 3/6` = `(1×6 + 3)/6` = `(6+3)/6` = 9/6 → *Simplify*: Divide numerator and denominator by 3 → 3/2
*(Note: Some teachers prefer simplified form; others accept unsimplified. Since 3/2 is simpler, we’ll use that.)*
63. `4 2/5` = `(4×5 + 2)/5` = `(20+2)/5` = 22/5
64. `8 2/3` = `(8×3 + 2)/3` = `(24+2)/3` = 26/3
65. `8 1/8` = `(8×8 + 1)/8` = `(64+1)/8` = 65/8
66. `3 3/4` = `(3×4 + 3)/4` = `(12+3)/4` = 15/4
67. `5 3/5` = `(5×5 + 3)/5` = `(25+3)/5` = 28/5
68. `8 2/6` = `(8×6 + 2)/6` = `(48+2)/6` = 50/6 → *Simplify*: Divide by 2 → 25/3
69. `7 5/6` = `(7×6 + 5)/6` = `(42+5)/6` = 47/6
70. `9 1/4` = `(9×4 + 1)/4` = `(36+1)/4` = 37/4
71. `1 4/6` = `(1×6 + 4)/6` = `(6+4)/6` = 10/6 → *Simplify*: Divide by 2 → 5/3
72. `4 7/8` = `(4×8 + 7)/8` = `(32+7)/8` = 39/8
73. `9 1/3` = `(9×3 + 1)/3` = `(27+1)/3` = 28/3
---
## Section 2: Calculate (Addition & Subtraction of Mixed Numbers)
When adding or subtracting mixed numbers:
1. Add/subtract the whole numbers.
2. Add/subtract the fractions.
3. If the fraction part is improper, convert it to a mixed number and add the whole number part to the total.
4. If subtracting and the top fraction is smaller, borrow 1 from the whole number (convert to equivalent fraction).
---
74. `9 2/5 - 8 4/5`
- Whole numbers: 9 - 8 = 1
- Fractions: 2/5 - 4/5 → Can’t do! Borrow 1 from 9 → becomes 8 + 7/5 (since 1 = 5/5, so 2/5 + 5/5 = 7/5)
- Now: 8 7/5 - 8 4/5 = (8-8) + (7/5 - 4/5) = 0 + 3/5 = 3/5
✔ Answer: 3/5
---
75. `5 1/10 + 5 5/10`
- Whole: 5 + 5 = 10
- Fraction: 1/10 + 5/10 = 6/10 → Simplify to 3/5
- Total: 10 3/5
✔ Answer: 10 3/5
---
76. `7 9/18 + 4 1/18`
- Whole: 7 + 4 = 11
- Fraction: 9/18 + 1/18 = 10/18 → Simplify: divide by 2 → 5/9
- Total: 11 5/9
✔ Answer: 11 5/9
---
77. `7 1/9 - 1 5/9`
- Whole: 7 - 1 = 6
- Fraction: 1/9 - 5/9 → Can’t do! Borrow 1 → 6 + 10/9 (since 1 = 9/9 → 1/9 + 9/9 = 10/9)
- Now: 6 10/9 - 1 5/9 = (6-1) + (10/9 - 5/9) = 5 + 5/9 = 5 5/9
✔ Answer: 5 5/9
---
78. `6 2/21 + 8 14/21`
- Whole: 6 + 8 = 14
- Fraction: 2/21 + 14/21 = 16/21
- Total: 14 16/21
✔ Answer: 14 16/21
---
79. `2 3/4 + 1 3/4`
- Whole: 2 + 1 = 3
- Fraction: 3/4 + 3/4 = 6/4 = 1 2/4 = 1 1/2
- Total: 3 + 1 1/2 = 4 1/2
✔ Answer: 4 1/2
---
80. `4 3/10 + 5 8/10`
- Whole: 4 + 5 = 9
- Fraction: 3/10 + 8/10 = 11/10 = 1 1/10
- Total: 9 + 1 1/10 = 10 1/10
✔ Answer: 10 1/10
---
81. `7 5/7 + 7 6/7`
- Whole: 7 + 7 = 14
- Fraction: 5/7 + 6/7 = 11/7 = 1 4/7
- Total: 14 + 1 4/7 = 15 4/7
✔ Answer: 15 4/7
---
82. `7 12/23 - 3 14/23`
- Whole: 7 - 3 = 4
- Fraction: 12/23 - 14/23 → Can’t do! Borrow 1 → 3 + 35/23 (since 1 = 23/23 → 12/23 + 23/23 = 35/23)
- Now: 6 35/23 - 3 14/23 = (6-3) + (35/23 - 14/23) = 3 + 21/23 = 3 21/23
✔ Answer: 3 21/23
---
83. `3 8/11 + 8 4/11`
- Whole: 3 + 8 = 11
- Fraction: 8/11 + 4/11 = 12/11 = 1 1/11
- Total: 11 + 1 1/11 = 12 1/11
✔ Answer: 12 1/11
---
## Section 3: Compare the Fractions (Use <, >, or =)
To compare two fractions:
- If denominators are the same → compare numerators.
- If numerators are the same → compare denominators (smaller denominator = larger fraction).
- Otherwise, find common denominators or cross-multiply.
---
84. `1/4 ___ 1/3`
- Same numerator → smaller denominator is bigger → 1/3 > 1/4 → <
✔ Answer: <
---
85. `1/4 ___ 1/6`
- Same numerator → 1/4 > 1/6 → >
✔ Answer: >
---
86. `3/8 ___ 3/5`
- Same numerator → 3/5 > 3/8 → <
✔ Answer: <
---
87. `1/3 ___ 1/4`
- Same numerator → 1/3 > 1/4 → >
✔ Answer: >
---
88. `5/6 ___ 1/5`
- Cross multiply: 5×5 = 25, 1×6 = 6 → 25 > 6 → 5/6 > 1/5 → >
✔ Answer: >
---
89. `5/6 ___ 2/3`
- Common denominator: 6 → 5/6 vs 4/6 → 5/6 > 4/6 → >
✔ Answer: >
---
90. `2/8 ___ 2/6`
- Same numerator → 2/6 > 2/8 → <
✔ Answer: <
---
91. `2/4 ___ 1/5`
- Simplify 2/4 = 1/2 → 1/2 vs 1/5 → 1/2 > 1/5 → >
✔ Answer: >
---
92. `3/4 ___ 1/3`
- Cross multiply: 3×3=9, 1×4=4 → 9 > 4 → 3/4 > 1/3 → >
✔ Answer: >
---
93. `5/8 ___ 2/6`
- Simplify 2/6 = 1/3 → Compare 5/8 vs 1/3 → Cross multiply: 5×3=15, 1×8=8 → 15>8 → 5/8 > 1/3 → >
✔ Answer: >
---
94. `3/5 ___ 5/8`
- Cross multiply: 3×8=24, 5×5=25 → 24 < 25 → 3/5 < 5/8 → <
✔ Answer: <
---
95. `2/4 ___ 3/6`
- Simplify both: 2/4 = 1/2, 3/6 = 1/2 → =
✔ Answer: =
---
## Section 4: Divide (Fraction Division)
Rule: To divide fractions → Multiply by the reciprocal
`a/b ÷ c/d = a/b × d/c`
Also, dividing by a whole number: `a/b ÷ c = a/b × 1/c`
---
96. `2/8 ÷ 1` = `2/8 × 1/1` = 2/8 → Simplify → 1/4
✔ Answer: 1/4
---
97. `4 ÷ 1/5` = `4 × 5/1` = 20
✔ Answer: 20
---
98. `5/6 ÷ 5` = `5/6 × 1/5` = `(5×1)/(6×5)` = 5/30 → Simplify → 1/6
✔ Answer: 1/6
---
99. `2/4 ÷ 5` = `2/4 × 1/5` = `2/20` → Simplify → 1/10
✔ Answer: 1/10
---
100. `6/8 ÷ 8` = `6/8 × 1/8` = `6/64` → Simplify (÷2) → 3/32
✔ Answer: 3/32
---
101. `5 ÷ 3/6` = `5 × 6/3` = `5 × 2` = 10
*(Note: 3/6 = 1/2, so 5 ÷ 1/2 = 5 × 2 = 10)*
✔ Answer: 10
---
102. `2/4 ÷ 8` = `2/4 × 1/8` = `2/32` → Simplify → 1/16
✔ Answer: 1/16
---
103. `9 ÷ 2/3` = `9 × 3/2` = `27/2` = 13 1/2
✔ Answer: 13 1/2
---
104. `6 ÷ 2/5` = `6 × 5/2` = `30/2` = 15
✔ Answer: 15
---
105. `1/4 ÷ 4` = `1/4 × 1/4` = 1/16
✔ Answer: 1/16
---
106. `1/8 ÷ 8` = `1/8 × 1/8` = 1/64
✔ Answer: 1/64
---
107. `4/6 ÷ 3` = `4/6 × 1/3` = `4/18` → Simplify → 2/9
✔ Answer: 2/9
---
## ✔ Final Answers Summary:
Convert:
54. 23/3
55. 11/5
56. 33/4
57. 17/3
58. 42/5
59. 23/6
60. 22/3
61. 9/4
62. 3/2
63. 22/5
64. 26/3
65. 65/8
66. 15/4
67. 28/5
68. 25/3
69. 47/6
70. 37/4
71. 5/3
72. 39/8
73. 28/3
Calculate:
74. 3/5
75. 10 3/5
76. 11 5/9
77. 5 5/9
78. 14 16/21
79. 4 1/2
80. 10 1/10
81. 15 4/7
82. 3 21/23
83. 12 1/11
Compare:
84. <
85. >
86. <
87. >
88. >
89. >
90. <
91. >
92. >
93. >
94. <
95. =
Divide:
96. 1/4
97. 20
98. 1/6
99. 1/10
100. 3/32
101. 10
102. 1/16
103. 13 1/2
104. 15
105. 1/16
106. 1/64
107. 2/9
---
Let me know if you’d like this in printable format or need help with any step again! 😊
Parent Tip: Review the logic above to help your child master the concept of math exercises for grade 6.
