Worksheet featuring fraction arithmetic problems involving addition and subtraction.

Let's solve each of the fraction arithmetic problems step by step. The goal is to perform the operations (addition or subtraction) with fractions, which often requires finding a common denominator.

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1. $ \frac{5}{6} - \frac{2}{5} $

- Find the least common denominator (LCD) of 6 and 5 → 30
- Convert:
$$
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30},\quad
\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
$$
- Subtract:
$$
\frac{25}{30} - \frac{12}{30} = \frac{13}{30}
$$

✔ Answer: $ \frac{13}{30} $

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2. $ \frac{5}{6} - \frac{1}{4} $

- LCD of 6 and 4 → 12
- Convert:
$$
\frac{5}{6} = \frac{10}{12},\quad
\frac{1}{4} = \frac{3}{12}
$$
- Subtract:
$$
\frac{10}{12} - \frac{3}{12} = \frac{7}{12}
$$

✔ Answer: $ \frac{7}{12} $

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3. $ \frac{11}{12} - \frac{5}{6} $

- LCD of 12 and 6 → 12
- Convert:
$$
\frac{5}{6} = \frac{10}{12}
$$
- Subtract:
$$
\frac{11}{12} - \frac{10}{12} = \frac{1}{12}
$$

✔ Answer: $ \frac{1}{12} $

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4. $ \frac{5}{6} - \frac{5}{9} $

- LCD of 6 and 9 → 18
- Convert:
$$
\frac{5}{6} = \frac{15}{18},\quad
\frac{5}{9} = \frac{10}{18}
$$
- Subtract:
$$
\frac{15}{18} - \frac{10}{18} = \frac{5}{18}
$$

✔ Answer: $ \frac{5}{18} $

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

- LCD of 3 and 2 → 6
- Convert:
$$
\frac{2}{3} = \frac{4}{6},\quad
\frac{1}{2} = \frac{3}{6}
$$
- Add:
$$
\frac{4}{6} + \frac{3}{6} = \frac{7}{6}
$$
- Simplify: $ \frac{7}{6} = 1\frac{1}{6} $

✔ Answer: $ \frac{7}{6} $ or $ 1\frac{1}{6} $

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6. $ \frac{5}{8} - \frac{5}{8} $

- Same denominator → subtract numerators:
$$
\frac{5 - 5}{8} = \frac{0}{8} = 0
$$

✔ Answer: $ 0 $

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

- LCD of 5 and 9 → 45
- Convert:
$$
\frac{4}{5} = \frac{36}{45},\quad
\frac{4}{9} = \frac{20}{45}
$$
- Add:
$$
\frac{36}{45} + \frac{20}{45} = \frac{56}{45}
$$
- Simplify: $ \frac{56}{45} = 1\frac{11}{45} $

✔ Answer: $ \frac{56}{45} $ or $ 1\frac{11}{45} $

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8. $ \frac{5}{8} + \frac{3}{10} $

- LCD of 8 and 10 → 40
- Convert:
$$
\frac{5}{8} = \frac{25}{40},\quad
\frac{3}{10} = \frac{12}{40}
$$
- Add:
$$
\frac{25}{40} + \frac{12}{40} = \frac{37}{40}
$$

✔ Answer: $ \frac{37}{40} $

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9. $ \frac{2}{3} - \frac{1}{4} $

- LCD of 3 and 4 → 12
- Convert:
$$
\frac{2}{3} = \frac{8}{12},\quad
\frac{1}{4} = \frac{3}{12}
$$
- Subtract:
$$
\frac{8}{12} - \frac{3}{12} = \frac{5}{12}
$$

✔ Answer: $ \frac{5}{12} $

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10. $ \frac{3}{4} + \frac{7}{12} $

- LCD of 4 and 12 → 12
- Convert:
$$
\frac{3}{4} = \frac{9}{12}
$$
- Add:
$$
\frac{9}{12} + \frac{7}{12} = \frac{16}{12} = \frac{4}{3} = 1\frac{1}{3}
$$

✔ Answer: $ \frac{4}{3} $ or $ 1\frac{1}{3} $

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11. $ \frac{3}{8} - \frac{1}{9} $

- LCD of 8 and 9 → 72
- Convert:
$$
\frac{3}{8} = \frac{27}{72},\quad
\frac{1}{9} = \frac{8}{72}
$$
- Subtract:
$$
\frac{27}{72} - \frac{8}{72} = \frac{19}{72}
$$

✔ Answer: $ \frac{19}{72} $

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12. $ \frac{3}{8} + \frac{3}{4} $

- LCD of 8 and 4 → 8
- Convert:
$$
\frac{3}{4} = \frac{6}{8}
$$
- Add:
$$
\frac{3}{8} + \frac{6}{8} = \frac{9}{8} = 1\frac{1}{8}
$$

✔ Answer: $ \frac{9}{8} $ or $ 1\frac{1}{8} $

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13. $ \frac{7}{8} - \frac{5}{9} $

- LCD of 8 and 9 → 72
- Convert:
$$
\frac{7}{8} = \frac{63}{72},\quad
\frac{5}{9} = \frac{40}{72}
$$
- Subtract:
$$
\frac{63}{72} - \frac{40}{72} = \frac{23}{72}
$$

✔ Answer: $ \frac{23}{72} $

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14. $ \frac{7}{8} + \frac{8}{9} $

- LCD of 8 and 9 → 72
- Convert:
$$
\frac{7}{8} = \frac{63}{72},\quad
\frac{8}{9} = \frac{64}{72}
$$
- Add:
$$
\frac{63}{72} + \frac{64}{72} = \frac{127}{72}
$$
- Simplify: $ \frac{127}{72} = 1\frac{55}{72} $

✔ Answer: $ \frac{127}{72} $ or $ 1\frac{55}{72} $

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15. $ \frac{1}{2} - \frac{3}{8} $

- LCD of 2 and 8 → 8
- Convert:
$$
\frac{1}{2} = \frac{4}{8}
$$
- Subtract:
$$
\frac{4}{8} - \frac{3}{8} = \frac{1}{8}
$$

✔ Answer: $ \frac{1}{8} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| $ \frac{5}{6} - \frac{2}{5} $ | $ \frac{13}{30} $ |
| $ \frac{5}{6} - \frac{1}{4} $ | $ \frac{7}{12} $ |
| $ \frac{11}{12} - \frac{5}{6} $ | $ \frac{1}{12} $ |
| $ \frac{5}{6} - \frac{5}{9} $ | $ \frac{5}{18} $ |
| $ \frac{2}{3} + \frac{1}{2} $ | $ \frac{7}{6} $ or $ 1\frac{1}{6} $ |
| $ \frac{5}{8} - \frac{5}{8} $ | $ 0 $ |
| $ \frac{4}{5} + \frac{4}{9} $ | $ \frac{56}{45} $ or $ 1\frac{11}{45} $ |
| $ \frac{5}{8} + \frac{3}{10} $ | $ \frac{37}{40} $ |
| $ \frac{2}{3} - \frac{1}{4} $ | $ \frac{5}{12} $ |
| $ \frac{3}{4} + \frac{7}{12} $ | $ \frac{4}{3} $ or $ 1\frac{1}{3} $ |
| $ \frac{3}{8} - \frac{1}{9} $ | $ \frac{19}{72} $ |
| $ \frac{3}{8} + \frac{3}{4} $ | $ \frac{9}{8} $ or $ 1\frac{1}{8} $ |
| $ \frac{7}{8} - \frac{5}{9} $ | $ \frac{23}{72} $ |
| $ \frac{7}{8} + \frac{8}{9} $ | $ \frac{127}{72} $ or $ 1\frac{55}{72} $ |
| $ \frac{1}{2} - \frac{3}{8} $ | $ \frac{1}{8} $ |

Let me know if you'd like these in decimal form or need further explanation!