Let’s solve each problem step by step. We’re subtracting fractions, so we need to make sure the denominators (bottom numbers) are the same before we subtract. If they’re already the same, just subtract the top numbers. If not, find a common denominator.
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1. ½ - ¹⁄₁₁
Denominators: 2 and 11 → LCM = 22
Convert:
½ = 11/22
¹⁄₁₁ = 2/22
Subtract: 11/22 - 2/22 =
9/22
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2. ⁴⁄₆ - ²⁄₆
Same denominator! Just subtract tops:
4 - 2 = 2 →
2/6
Simplify: divide top and bottom by 2 →
1/3
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3. ⁷⁄₉ - ³⁄₄
Denominators: 9 and 4 → LCM = 36
Convert:
⁷⁄ = 28/36
³⁄₄ = 27/36
Subtract: 28/36 - 27/36 =
1/36
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4. ¹⁶⁄₃₀ - ⁹⁄₂₀
Denominators: 30 and 20 → LCM = 60
Convert:
¹⁶⁄₃₀ = 32/60
⁹⁄₂₀ = 27/60
Subtract: 32/60 - 27/60 =
5/60
Simplify: divide by 5 →
1/12
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5. ⅓ - ¹⁄₁₇
Denominators: 3 and 17 → LCM = 51
Convert:
⅓ = 17/51
¹⁄₁₇ = 3/51
Subtract: 17/51 - 3/51 =
14/51
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6. ²⁄₄ - ²⁄₈
First, simplify ²⁄₄ = ½
Now: ½ - ²⁄₈
But ²⁄₈ = ¼
So: ½ - ¼ = 2/4 - 1/4 =
1/4
*(Alternatively, use LCD of 4 and 8 = 8)*
²⁄₄ = 4/8
²⁄₈ = 2/8
4/8 - 2/8 = 2/8 =
1/4
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7. ⁶⁄₂₀ - ²⁄₇
Denominators: 20 and 7 → LCM = 140
Convert:
⁶⁄₂₀ = 42/140
²⁄₇ = 40/140
Subtract: 42/140 - 40/140 =
2/140
Simplify: divide by 2 →
1/70
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8. ¹⁰⁄₁₆ - ²⁄₇
Denominators: 16 and 7 → LCM = 112
Convert:
¹⁰⁄₁₆ = 70/112
²⁄₇ = 32/112
Subtract: 70/112 - 32/112 =
38/112
Simplify: divide by 2 →
19/56
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9. ⁷⁄ - ¹³⁄₂₁
Denominators: 9 and 21 → LCM = 63
Convert:
⁷⁄₉ = 49/63
¹³⁄₂₁ = 39/63
Subtract: 49/63 - 39/63 =
10/63
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10. ⁹⁄₁₅ - ½
First, simplify ⁹⁄₁₅ = ³⁄₅
Now: ³⁄₅ - ½
LCD of 5 and 2 = 10
³⁄₅ = 6/10
½ = 5/10
Subtract: 6/10 - 5/10 =
1/10
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Final Answer:
1. 9/22
2. 1/3
3. 1/36
4. 1/12
5. 14/51
6. 1/4
7. 1/70
8. 19/56
9. 10/63
10. 1/10
Parent Tip: Review the logic above to help your child master the concept of hard addition fractions worksheet.
