Math worksheet for practicing addition and subtraction of mixed numbers with 14 problems.

Let's solve each problem step by step. The task is to add or subtract mixed numbers, which involves working with both whole numbers and fractions.

We'll follow these steps for each problem:

1. Convert mixed numbers to improper fractions (if needed).
2. Find a common denominator.
3. Add or subtract the fractions.
4. Simplify the result.
5. Convert back to a mixed number if necessary.

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Problem 1: $ 9\frac{6}{8} + 2\frac{1}{4} $

- Simplify $ \frac{6}{8} = \frac{3}{4} $
- So, $ 9\frac{3}{4} + 2\frac{1}{4} $
- Add whole numbers: $ 9 + 2 = 11 $
- Add fractions: $ \frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1 $
- Total: $ 11 + 1 = 12 $

✔ Answer: 12

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Problem 2: $ 7\frac{1}{4} + 5\frac{3}{4} $

- Whole numbers: $ 7 + 5 = 12 $
- Fractions: $ \frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1 $
- Total: $ 12 + 1 = 13 $

✔ Answer: 13

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Problem 3: $ 6\frac{4}{5} + 3\frac{1}{2} $

- Find common denominator: LCD of 5 and 2 is 10
- Convert:
- $ \frac{4}{5} = \frac{8}{10} $
- $ \frac{1}{2} = \frac{5}{10} $
- Add whole numbers: $ 6 + 3 = 9 $
- Add fractions: $ \frac{8}{10} + \frac{5}{10} = \frac{13}{10} = 1\frac{3}{10} $
- Total: $ 9 + 1\frac{3}{10} = 10\frac{3}{10} $

✔ Answer: $ 10\frac{3}{10} $

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Problem 4: $ 3\frac{1}{4} + 1\frac{3}{8} $

- LCD of 4 and 8 is 8
- Convert:
- $ \frac{1}{4} = \frac{2}{8} $
- $ \frac{3}{8} $ stays
- Whole numbers: $ 3 + 1 = 4 $
- Fractions: $ \frac{2}{8} + \frac{3}{8} = \frac{5}{8} $
- Total: $ 4\frac{5}{8} $

✔ Answer: $ 4\frac{5}{8} $

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

- Whole numbers: $ 2 + 1 = 3 $
- Fractions: $ \frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1 $
- Total: $ 3 + 1 = 4 $

✔ Answer: 4

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Problem 6: $ 2\frac{1}{4} + 1\frac{3}{8} $

- LCD of 4 and 8 is 8
- $ \frac{1}{4} = \frac{2}{8} $
- Whole numbers: $ 2 + 1 = 3 $
- Fractions: $ \frac{2}{8} + \frac{3}{8} = \frac{5}{8} $
- Total: $ 3\frac{5}{8} $

✔ Answer: $ 3\frac{5}{8} $

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Problem 7: $ 3\frac{4}{5} + 2\frac{4}{5} $

- Whole numbers: $ 3 + 2 = 5 $
- Fractions: $ \frac{4}{5} + \frac{4}{5} = \frac{8}{5} = 1\frac{3}{5} $
- Total: $ 5 + 1\frac{3}{5} = 6\frac{3}{5} $

✔ Answer: $ 6\frac{3}{5} $

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Problem 8: $ 9\frac{2}{3} - 5\frac{2}{4} $

- Simplify $ \frac{2}{4} = \frac{1}{2} $
- So: $ 9\frac{2}{3} - 5\frac{1}{2} $
- LCD of 3 and 2 is 6
- Convert:
- $ \frac{2}{3} = \frac{4}{6} $
- $ \frac{1}{2} = \frac{3}{6} $
- Whole numbers: $ 9 - 5 = 4 $
- Fractions: $ \frac{4}{6} - \frac{3}{6} = \frac{1}{6} $
- Total: $ 4\frac{1}{6} $

✔ Answer: $ 4\frac{1}{6} $

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Problem 9: $ 8\frac{1}{4} - 7\frac{3}{4} $

- Whole numbers: $ 8 - 7 = 1 $
- But $ \frac{1}{4} - \frac{3}{4} $ → can't do directly
- Borrow 1 from 8: $ 8\frac{1}{4} = 7 + 1 + \frac{1}{4} = 7\frac{5}{4} $
- Now: $ 7\frac{5}{4} - 7\frac{3}{4} = (7 - 7) + (\frac{5}{4} - \frac{3}{4}) = 0 + \frac{2}{4} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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Problem 10: $ 9\frac{2}{3} - 7\frac{2}{8} $

- Simplify $ \frac{2}{8} = \frac{1}{4} $
- So: $ 9\frac{2}{3} - 7\frac{1}{4} $
- LCD of 3 and 4 is 12
- Convert:
- $ \frac{2}{3} = \frac{8}{12} $
- $ \frac{1}{4} = \frac{3}{12} $
- Whole numbers: $ 9 - 7 = 2 $
- Fractions: $ \frac{8}{12} - \frac{3}{12} = \frac{5}{12} $
- Total: $ 2\frac{5}{12} $

✔ Answer: $ 2\frac{5}{12} $

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Problem 11: $ 8\frac{5}{6} - 1\frac{1}{4} $

- LCD of 6 and 4 is 12
- Convert:
- $ \frac{5}{6} = \frac{10}{12} $
- $ \frac{1}{4} = \frac{3}{12} $
- Whole numbers: $ 8 - 1 = 7 $
- Fractions: $ \frac{10}{12} - \frac{3}{12} = \frac{7}{12} $
- Total: $ 7\frac{7}{12} $

✔ Answer: $ 7\frac{7}{12} $

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Problem 12: $ 3\frac{3}{4} - 1\frac{2}{8} $

- Simplify $ \frac{2}{8} = \frac{1}{4} $
- So: $ 3\frac{3}{4} - 1\frac{1}{4} $
- Whole numbers: $ 3 - 1 = 2 $
- Fractions: $ \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $
- Total: $ 2\frac{1}{2} $

✔ Answer: $ 2\frac{1}{2} $

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Problem 13: $ 5\frac{1}{2} - 2\frac{1}{4} $

- LCD of 2 and 4 is 4
- $ \frac{1}{2} = \frac{2}{4} $
- Whole numbers: $ 5 - 2 = 3 $
- Fractions: $ \frac{2}{4} - \frac{1}{4} = \frac{1}{4} $
- Total: $ 3\frac{1}{4} $

✔ Answer: $ 3\frac{1}{4} $

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Problem 14: $ 1\frac{1}{4} - 3\frac{4}{4} $

Wait — $ 3\frac{4}{4} = 3 + 1 = 4 $

So: $ 1\frac{1}{4} - 4 $

This is negative:
- $ 1\frac{1}{4} = \frac{5}{4} $
- $ 4 = \frac{16}{4} $
- $ \frac{5}{4} - \frac{16}{4} = -\frac{11}{4} = -2\frac{3}{4} $

✔ Answer: $ -2\frac{3}{4} $

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Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 12 |
| 2 | 13 |
| 3 | $ 10\frac{3}{10} $ |
| 4 | $ 4\frac{5}{8} $ |
| 5 | 4 |
| 6 | $ 3\frac{5}{8} $ |
| 7 | $ 6\frac{3}{5} $ |
| 8 | $ 4\frac{1}{6} $ |
| 9 | $ \frac{1}{2} $ |
| 10 | $ 2\frac{5}{12} $ |
| 11 | $ 7\frac{7}{12} $ |
| 12 | $ 2\frac{1}{2} $ |
| 13 | $ 3\frac{1}{4} $ |
| 14 | $ -2\frac{3}{4} $ |

> ⚠️ Note: Problem 14 results in a negative number, which may be unusual depending on grade level. Double-check if the original problem was written correctly (e.g., maybe it's $ 3\frac{4}{4} - 1\frac{1}{4} $?). But based on what's shown, this is correct.

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