Practice your fraction skills with this worksheet featuring 15 addition and subtraction problems with unlike denominators.

Sure! Let’s solve each of the 15 problems step by step. The key to adding or subtracting fractions with unlike denominators is to:

1. Find a common denominator (usually the Least Common Denominator, LCD — the LCM of the denominators).
2. Rewrite each fraction with the common denominator.
3. Add or subtract the numerators, keeping the denominator the same.
4. Simplify the result if possible.

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Problem 1: $\frac{4}{3} + \frac{2}{5}$

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

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Problem 2: $\frac{7}{10} - \frac{2}{5}$

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

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Problem 3: $\frac{5}{9} + \frac{2}{7}$

- LCD of 9 and 7 = 63
- $\frac{5}{9} = \frac{35}{63}, \quad \frac{2}{7} = \frac{18}{63}$
- $\frac{35}{63} + \frac{18}{63} = \frac{53}{63} = \boxed{\frac{53}{63}}$ (already simplified)

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Problem 4: $\frac{4}{8} - \frac{1}{4}$

- Simplify $\frac{4}{8} = \frac{1}{2}$
- Now: $\frac{1}{2} - \frac{1}{4}$
- LCD = 4 → $\frac{2}{4} - \frac{1}{4} = \frac{1}{4} = \boxed{\frac{1}{4}}$

*(Alternatively, without simplifying first: LCD of 8 and 4 is 8 → $\frac{4}{8} - \frac{2}{8} = \frac{2}{8} = \frac{1}{4}$)*

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Problem 5: $\frac{3}{9} + \frac{1}{3}$

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

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Problem 6: $\frac{2}{5} + \frac{1}{10}$

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

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Problem 7: $\frac{4}{5} + \frac{9}{10}$

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

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Problem 8: $\frac{4}{6} - \frac{1}{3}$

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

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Problem 9: $\frac{3}{12} + \frac{2}{4}$

- Simplify: $\frac{3}{12} = \frac{1}{4}, \quad \frac{2}{4} = \frac{1}{2}$
- Now: $\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} = \boxed{\frac{3}{4}}$

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Problem 10: $\frac{5}{12} - \frac{1}{6}$

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

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Problem 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
- $\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12}$
- $\frac{3}{12} + \frac{4}{12} = \frac{7}{12} = \boxed{\frac{7}{12}}$

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Problem 12: $\frac{1}{4} - \frac{1}{8}$

- LCD = 8
- $\frac{1}{4} = \frac{2}{8}$
- $\frac{2}{8} - \frac{1}{8} = \frac{1}{8} = \boxed{\frac{1}{8}}$

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Problem 13: $\frac{6}{7} + \frac{2}{6}$

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

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Problem 14: $\frac{1}{3} - \frac{1}{7}$

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

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Problem 15: $\frac{7}{8} + \frac{4}{5}$

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

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## ✔ Final Answers:

1. $1\frac{11}{15}$
2. $\frac{3}{10}$
3. $\frac{53}{63}$
4. $\frac{1}{4}$
5. $\frac{2}{3}$
6. $\frac{1}{2}$
7. $1\frac{7}{10}$
8. $\frac{1}{3}$
9. $\frac{3}{4}$
10. $\frac{1}{4}$
11. $\frac{7}{12}$
12. $\frac{1}{8}$
13. $1\frac{4}{21}$
14. $\frac{4}{21}$
15. $1\frac{27}{40}$

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