Adding Fractions with Unlike Denominators - Free Math Worksheet for Practice

Let's solve each of these fraction addition problems step by step. The key concept is adding fractions with unlike denominators, which requires finding a common denominator (preferably the least common denominator, or LCD), converting each fraction to an equivalent fraction with that denominator, and then adding the numerators.

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1. $ \frac{3}{5} + \frac{1}{10} $

- LCD of 5 and 10 is 10
- Convert $ \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} $
- Now: $ \frac{6}{10} + \frac{1}{10} = \frac{7}{10} $

✔ Answer: $ \frac{7}{10} $

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

- LCD of 4 and 2 is 4
- Convert $ \frac{1}{2} = \frac{2}{4} $
- Now: $ \frac{1}{4} + \frac{2}{4} = \frac{3}{4} $

✔ Answer: $ \frac{3}{4} $

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3. $ \frac{2}{5} + \frac{4}{15} $

- LCD of 5 and 15 is 15
- Convert $ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} $
- Now: $ \frac{6}{15} + \frac{4}{15} = \frac{10}{15} $
- Simplify: $ \frac{10}{15} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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4. $ \frac{3}{7} + \frac{1}{14} $

- LCD of 7 and 14 is 14
- Convert $ \frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14} $
- Now: $ \frac{6}{14} + \frac{1}{14} = \frac{7}{14} $
- Simplify: $ \frac{7}{14} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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

- LCD of 3 and 9 is 9
- Convert $ \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9} $
- Now: $ \frac{6}{9} + \frac{2}{9} = \frac{8}{9} $

✔ Answer: $ \frac{8}{9} $

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6. $ \frac{4}{5} + \frac{3}{20} $

- LCD of 5 and 20 is 20
- Convert $ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} $
- Now: $ \frac{16}{20} + \frac{3}{20} = \frac{19}{20} $

✔ Answer: $ \frac{19}{20} $

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7. $ \frac{1}{4} + \frac{1}{8} $

- LCD of 4 and 8 is 8
- Convert $ \frac{1}{4} = \frac{2}{8} $
- Now: $ \frac{2}{8} + \frac{1}{8} = \frac{3}{8} $

✔ Answer: $ \frac{3}{8} $

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8. $ \frac{1}{9} + \frac{1}{18} $

- LCD of 9 and 18 is 18
- Convert $ \frac{1}{9} = \frac{2}{18} $
- Now: $ \frac{2}{18} + \frac{1}{18} = \frac{3}{18} $
- Simplify: $ \frac{3}{18} = \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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9. $ \frac{3}{4} + \frac{1}{12} $

- LCD of 4 and 12 is 12
- Convert $ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $
- Now: $ \frac{9}{12} + \frac{1}{12} = \frac{10}{12} $
- Simplify: $ \frac{10}{12} = \frac{5}{6} $

✔ Answer: $ \frac{5}{6} $

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10. $ \frac{3}{6} + \frac{1}{3} $

- First simplify $ \frac{3}{6} = \frac{1}{2} $
- Now: $ \frac{1}{2} + \frac{1}{3} $
- LCD of 2 and 3 is 6
- Convert: $ \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6} $
- Add: $ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} $

✔ Answer: $ \frac{5}{6} $

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✔ Final Answers:

1. $ \frac{7}{10} $
2. $ \frac{3}{4} $
3. $ \frac{2}{3} $
4. $ \frac{1}{2} $
5. $ \frac{8}{9} $
6. $ \frac{19}{20} $
7. $ \frac{3}{8} $
8. $ \frac{1}{6} $
9. $ \frac{5}{6} $
10. $ \frac{5}{6} $

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