Subtracting Fractions Worksheets - Free Printable

Let's solve each of these problems step by step. The key to adding or subtracting fractions with unlike denominators is to find a common denominator, convert the fractions, and then perform the operation.

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🔷 General Steps:

1. Find the Least Common Denominator (LCD).
2. Convert each fraction to an equivalent fraction with the LCD.
3. Add or subtract the numerators.
4. Simplify the result if needed.

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Let’s go through each problem:

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1. $ \frac{4}{3} + \frac{2}{5} $

- LCD of 3 and 5 = 15
- $ \frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15} $
- $ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} $
- $ \frac{20}{15} + \frac{6}{15} = \frac{26}{15} $
- Answer: $ \boxed{\frac{26}{15}} $ or $ 1\frac{11}{15} $

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2. $ \frac{7}{10} - \frac{2}{5} $

- LCD of 10 and 5 = 10
- $ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} $
- $ \frac{7}{10} - \frac{4}{10} = \frac{3}{10} $
- Answer: $ \boxed{\frac{3}{10}} $

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3. $ \frac{5}{9} + \frac{2}{7} $

- LCD of 9 and 7 = 63
- $ \frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63} $
- $ \frac{2}{7} = \frac{2 \times 9}{7 \times 9} = \frac{18}{63} $
- $ \frac{35}{63} + \frac{18}{63} = \frac{53}{63} $
- Answer: $ \boxed{\frac{53}{63}} $

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4. $ \frac{4}{8} - \frac{1}{4} $

- Simplify $ \frac{4}{8} = \frac{1}{2} $
- LCD of 2 and 4 = 4
- $ \frac{1}{2} = \frac{2}{4} $
- $ \frac{2}{4} - \frac{1}{4} = \frac{1}{4} $
- Answer: $ \boxed{\frac{1}{4}} $

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5. $ \frac{3}{9} + \frac{1}{3} $

- Simplify $ \frac{3}{9} = \frac{1}{3} $
- $ \frac{1}{3} + \frac{1}{3} = \frac{2}{3} $
- Answer: $ \boxed{\frac{2}{3}} $

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6. $ \frac{2}{5} + \frac{1}{10} $

- LCD of 5 and 10 = 10
- $ \frac{2}{5} = \frac{4}{10} $
- $ \frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2} $
- Answer: $ \boxed{\frac{1}{2}} $

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7. $ \frac{4}{5} + \frac{9}{10} $

- LCD of 5 and 10 = 10
- $ \frac{4}{5} = \frac{8}{10} $
- $ \frac{8}{10} + \frac{9}{10} = \frac{17}{10} $
- Answer: $ \boxed{\frac{17}{10}} $ or $ 1\frac{7}{10} $

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8. $ \frac{4}{6} - \frac{1}{3} $

- Simplify $ \frac{4}{6} = \frac{2}{3} $
- $ \frac{2}{3} - \frac{1}{3} = \frac{1}{3} $
- Answer: $ \boxed{\frac{1}{3}} $

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9. $ \frac{3}{12} + \frac{2}{4} $

- Simplify: $ \frac{3}{12} = \frac{1}{4}, \quad \frac{2}{4} = \frac{1}{2} $
- LCD of 4 and 2 = 4
- $ \frac{1}{4} + \frac{2}{4} = \frac{3}{4} $
- Answer: $ \boxed{\frac{3}{4}} $

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10. $ \frac{5}{12} - \frac{1}{6} $

- LCD of 12 and 6 = 12
- $ \frac{1}{6} = \frac{2}{12} $
- $ \frac{5}{12} - \frac{2}{12} = \frac{3}{12} = \frac{1}{4} $
- Answer: $ \boxed{\frac{1}{4}} $

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11. $ \frac{2}{8} + \frac{3}{9} $

- Simplify: $ \frac{2}{8} = \frac{1}{4}, \quad \frac{3}{9} = \frac{1}{3} $
- LCD of 4 and 3 = 12
- $ \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12} $
- $ \frac{3}{12} + \frac{4}{12} = \frac{7}{12} $
- Answer: $ \boxed{\frac{7}{12}} $

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12. $ \frac{1}{4} - \frac{1}{8} $

- LCD of 4 and 8 = 8
- $ \frac{1}{4} = \frac{2}{8} $
- $ \frac{2}{8} - \frac{1}{8} = \frac{1}{8} $
- Answer: $ \boxed{\frac{1}{8}} $

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13. $ \frac{6}{7} + \frac{2}{6} $

- Simplify $ \frac{2}{6} = \frac{1}{3} $
- LCD of 7 and 3 = 21
- $ \frac{6}{7} = \frac{18}{21}, \quad \frac{1}{3} = \frac{7}{21} $
- $ \frac{18}{21} + \frac{7}{21} = \frac{25}{21} $
- Answer: $ \boxed{\frac{25}{21}} $ or $ 1\frac{4}{21} $

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14. $ \frac{1}{3} - \frac{1}{7} $

- LCD of 3 and 7 = 21
- $ \frac{1}{3} = \frac{7}{21}, \quad \frac{1}{7} = \frac{3}{21} $
- $ \frac{7}{21} - \frac{3}{21} = \frac{4}{21} $
- Answer: $ \boxed{\frac{4}{21}} $

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15. $ \frac{7}{8} + \frac{4}{5} $

- LCD of 8 and 5 = 40
- $ \frac{7}{8} = \frac{35}{40}, \quad \frac{4}{5} = \frac{32}{40} $
- $ \frac{35}{40} + \frac{32}{40} = \frac{67}{40} $
- Answer: $ \boxed{\frac{67}{40}} $ or $ 1\frac{27}{40} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{26}{15} $ |
| 2 | $ \frac{3}{10} $ |
| 3 | $ \frac{53}{63} $ |
| 4 | $ \frac{1}{4} $ |
| 5 | $ \frac{2}{3} $ |
| 6 | $ \frac{1}{2} $ |
| 7 | $ \frac{17}{10} $ |
| 8 | $ \frac{1}{3} $ |
| 9 | $ \frac{3}{4} $ |
| 10 | $ \frac{1}{4} $ |
| 11 | $ \frac{7}{12} $ |
| 12 | $ \frac{1}{8} $ |
| 13 | $ \frac{25}{21} $ |
| 14 | $ \frac{4}{21} $ |
| 15 | $ \frac{67}{40} $ |

Let me know if you'd like this formatted as a printable answer sheet!