Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

Let’s solve each problem step by step. We’re adding and subtracting fractions with unlike denominators, which means we need to find a common denominator first — usually the least common denominator (LCD) — then rewrite each fraction, do the math, and simplify if needed.

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Problem 1: 4/3 + 2/5

- LCD 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 → can’t simplify further → 26/15

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Problem 2: 7/10 - 2/5

- LCD of 10 and 5 is 10.
- 2/5 = (2×2)/(5×2) = 4/10
- 7/10 - 4/10 = 3/10 → already simplified → 3/10

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Problem 3: 5/9 + 2/7

- LCD 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 → already simplified → 53/63

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Problem 4: 4/8 - 1/4

- First, simplify 4/8 = 1/2
- Now: 1/2 - 1/4
- LCD of 2 and 4 is 4.
- 1/2 = 2/4
- 2/4 - 1/4 = 1/4 → 1/4

*(Alternatively, without simplifying first: 4/8 - 1/4 → LCD=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: LCD of 9 and 3 is 9 → 3/9 + 3/9 = 6/9 = 2/3)*

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Problem 6: 2/5 + 1/10

- LCD of 5 and 10 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

- LCD of 5 and 10 is 10.
- 4/5 = 8/10
- 8/10 + 9/10 = 17/10 → improper fraction → leave as is or write as mixed number? Since instructions don’t specify, we’ll keep as improper → 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: LCD=6 → 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 → LCD=4 → 1/4 + 2/4 = 3/4 → 3/4

*(Without simplifying: LCD of 12 and 4 is 12 → 3/12 + 6/12 = 9/12 = 3/4)*

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Problem 10: 5/12 - 1/6

- LCD of 12 and 6 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
- Now: 1/4 + 1/3 → LCD=12
- 1/4 = 3/12; 1/3 = 4/12 → 3/12 + 4/12 = 7/12 → 7/12

*(Without simplifying: LCD of 8 and 9 is 72 → 2/8=18/72, 3/9=24/72 → 42/72 = 7/12)*

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Problem 12: 1/4 - 1/8

- LCD of 4 and 8 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=21
- 6/7 = 18/21; 1/3 = 7/21 → 18/21 + 7/21 = 25/21 → 25/21

*(Without simplifying: LCD of 7 and 6 is 42 → 6/7=36/42, 2/6=14/42 → 50/42 = 25/21)*

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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