Math worksheet for practicing adding and subtracting fractions with unlike denominators.

Let’s solve each problem step by step. We’ll find a common denominator for each pair of fractions, then add or subtract the numerators.

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Problem 1: 4/3 + 2/5

Common denominator of 3 and 5 is 15.
4/3 = (4×5)/(3×5) = 20/15
2/5 = (2×3)/(5×3) = 6/15
20/15 + 6/15 = 26/15 → 26/15

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Problem 2: 7/10 - 2/5

Common denominator of 10 and 5 is 10.
2/5 = (2×2)/(5×2) = 4/10
7/10 - 4/10 = 3/10 → 3/10

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Problem 3: 5/9 + 2/7

Common denominator of 9 and 7 is 63.
5/9 = (5×7)/(9×7) = 35/63
2/7 = (2×9)/(7×9) = 18/63
35/63 + 18/63 = 53/63 → 53/63

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Problem 4: 4/8 - 1/4

Simplify 4/8 first → 1/2
Now: 1/2 - 1/4
Common denominator is 4.
1/2 = 2/4
2/4 - 1/4 = 1/4 → 1/4

*(Alternatively, without simplifying: 4/8 = 4/8, 1/4 = 2/8 → 4/8 - 2/8 = 2/8 = 1/4)*

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Problem 5: 3/9 + 1/3

Simplify 3/9 → 1/3
So: 1/3 + 1/3 = 2/3 → 2/3

*(Or: 3/9 + 3/9 = 6/9 = 2/3 — same result)*

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Problem 6: 2/5 + 1/10

Common denominator is 10.
2/5 = 4/10
4/10 + 1/10 = 5/10 = 1/2 → 1/2

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Problem 7: 4/5 + 9/10

Common denominator is 10.
4/5 = 8/10
8/10 + 9/10 = 17/10 → 17/10

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Problem 8: 4/6 - 1/3

Simplify 4/6 → 2/3
2/3 - 1/3 = 1/3 → 1/3

*(Or: 4/6 - 2/6 = 2/6 = 1/3)*

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Problem 9: 3/12 + 2/4

Simplify both:
3/12 = 1/4
2/4 = 1/2
Now: 1/4 + 1/2 = 1/4 + 2/4 = 3/4 → 3/4

*(Or keep as is: 3/12 + 6/12 = 9/12 = 3/4)*

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Problem 10: 5/12 - 1/6

Common denominator is 12.
1/6 = 2/12
5/12 - 2/12 = 3/12 = 1/4 → 1/4

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Problem 11: 2/8 + 3/9

Simplify:
2/8 = 1/4
3/9 = 1/3
Common denominator of 4 and 3 is 12.
1/4 = 3/12
1/3 = 4/12
3/12 + 4/12 = 7/12 → 7/12

*(Without simplifying: 2/8 = 18/72? Wait — better to use LCD of 8 and 9 = 72? But that’s messy. Better to simplify first. Let’s check: 2/8 = 1/4, 3/9=1/3 → yes, 7/12 is correct.)*

Wait — let me double-check with original denominators:

LCD of 8 and 9 is 72.
2/8 = 18/72
3/9 = 24/72
18+24=42 → 42/72 = 7/12 → Same answer. Good.

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Problem 12: 1/4 - 1/8

Common denominator is 8.
1/4 = 2/8
2/8 - 1/8 = 1/8 → 1/8

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Problem 13: 6/7 + 2/6

Simplify 2/6 → 1/3
Now: 6/7 + 1/3
LCD of 7 and 3 is 21.
6/7 = 18/21
1/3 = 7/21
18/21 + 7/21 = 25/21 → 25/21

*(Without simplifying: 6/7 + 2/6 → LCD 42: 36/42 + 14/42 = 50/42 = 25/21 — same)*

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Problem 14: 1/3 - 1/7

LCD of 3 and 7 is 21.
1/3 = 7/21
1/7 = 3/21
7/21 - 3/21 = 4/21 → 4/21

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Problem 15: 7/8 + 4/5

LCD of 8 and 5 is 40.
7/8 = 35/40
4/5 = 32/40
35/40 + 32/40 = 67/40 → 67/40

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Final Answer:
1. 26/15
2. 3/10
3. 53/63
4. 1/4
5. 2/3
6. 1/2
7. 17/10
8. 1/3
9. 3/4
10. 1/4
11. 7/12
12. 1/8
13. 25/21
14. 4/21
15. 67/40