Add Mixed Number Fractions-6 Worksheets - Free Printable

Let's solve each of the fraction addition problems and reduce them to lowest terms. We'll go step by step.

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1. $ 9\frac{6}{8} + \frac{8}{10} $

- Convert mixed numbers to improper fractions:
- $ 9\frac{6}{8} = \frac{9 \times 8 + 6}{8} = \frac{72 + 6}{8} = \frac{78}{8} $
- $ \frac{8}{10} $ stays as is.
- Find common denominator: LCM of 8 and 10 is 40.
- $ \frac{78}{8} = \frac{78 \times 5}{40} = \frac{390}{40} $
- $ \frac{8}{10} = \frac{8 \times 4}{40} = \frac{32}{40} $
- Add: $ \frac{390 + 32}{40} = \frac{422}{40} $
- Simplify: Divide numerator and denominator by 2 → $ \frac{211}{20} $
- Convert to mixed number: $ 10\frac{11}{20} $
✔ Answer: $ 10\frac{11}{20} $ — Yes, in lowest terms.

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2. $ 1\frac{2}{3} + \frac{2}{6} $

- Convert: $ 1\frac{2}{3} = \frac{5}{3} $
- $ \frac{2}{6} = \frac{1}{3} $
- Add: $ \frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2 $
✔ Answer: $ 2 $ — Yes, in lowest terms.

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

- $ 6\frac{1}{3} = \frac{19}{3} $
- Add: $ \frac{19}{3} + \frac{1}{3} = \frac{20}{3} $
- Mixed number: $ 6\frac{2}{3} $
✔ Answer: $ 6\frac{2}{3} $ — Yes, in lowest terms.

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4. $ 6\frac{1}{8} + \frac{7}{8} $

- $ 6\frac{1}{8} = \frac{49}{8} $
- Add: $ \frac{49}{8} + \frac{7}{8} = \frac{56}{8} = 7 $
✔ Answer: $ 7 $ — Yes, in lowest terms.

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

- Simplify $ \frac{2}{4} = \frac{1}{2} $, so $ 4\frac{2}{4} = 4\frac{1}{2} $
- But let’s work with original: $ 4\frac{2}{4} = \frac{18}{4} $
- Add: $ \frac{18}{4} + \frac{3}{4} = \frac{21}{4} $
- Convert: $ 5\frac{1}{4} $
✔ Answer: $ 5\frac{1}{4} $ — Yes, in lowest terms.

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6. $ 8\frac{1}{5} + \frac{2}{4} $

- $ 8\frac{1}{5} = \frac{41}{5} $
- $ \frac{2}{4} = \frac{1}{2} $
- Common denominator: 10
- $ \frac{41}{5} = \frac{82}{10} $
- $ \frac{1}{2} = \frac{5}{10} $
- Add: $ \frac{87}{10} = 8\frac{7}{10} $
✔ Answer: $ 8\frac{7}{10} $ — Yes, in lowest terms.

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7. $ 2\frac{3}{8} + \frac{7}{8} $

- $ 2\frac{3}{8} = \frac{19}{8} $
- Add: $ \frac{19}{8} + \frac{7}{8} = \frac{26}{8} = \frac{13}{4} = 3\frac{1}{4} $
✔ Answer: $ 3\frac{1}{4} $ — Yes, in lowest terms.

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8. $ 9\frac{2}{8} + \frac{1}{6} $

- Simplify $ \frac{2}{8} = \frac{1}{4} $, so $ 9\frac{2}{8} = 9\frac{1}{4} $
- $ 9\frac{1}{4} = \frac{37}{4} $
- $ \frac{1}{6} $ stays
- Common denominator: 12
- $ \frac{37}{4} = \frac{111}{12} $
- $ \frac{1}{6} = \frac{2}{12} $
- Add: $ \frac{113}{12} = 9\frac{5}{12} $
✔ Answer: $ 9\frac{5}{12} $ — Yes, in lowest terms.

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9. $ 8\frac{2}{5} + \frac{1}{3} $

- $ 8\frac{2}{5} = \frac{42}{5} $
- $ \frac{1}{3} $
- Common denominator: 15
- $ \frac{42}{5} = \frac{126}{15} $
- $ \frac{1}{3} = \frac{5}{15} $
- Add: $ \frac{131}{15} = 8\frac{11}{15} $
✔ Answer: $ 8\frac{11}{15} $ — Yes, in lowest terms.

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10. $ 7\frac{4}{6} + \frac{4}{6} $

- $ 7\frac{4}{6} = \frac{46}{6} $
- Add: $ \frac{46}{6} + \frac{4}{6} = \frac{50}{6} = \frac{25}{3} = 8\frac{1}{3} $
✔ Answer: $ 8\frac{1}{3} $ — Yes, in lowest terms.

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

- $ 9\frac{3}{8} = \frac{75}{8} $
- Add: $ \frac{75}{8} + \frac{2}{8} = \frac{77}{8} = 9\frac{5}{8} $
✔ Answer: $ 9\frac{5}{8} $ — Yes, in lowest terms.

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12. $ 8\frac{3}{4} + \frac{1}{5} $

- $ 8\frac{3}{4} = \frac{35}{4} $
- $ \frac{1}{5} $
- Common denominator: 20
- $ \frac{35}{4} = \frac{175}{20} $
- $ \frac{1}{5} = \frac{4}{20} $
- Add: $ \frac{179}{20} = 8\frac{19}{20} $
✔ Answer: $ 8\frac{19}{20} $ — Yes, in lowest terms.

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 10\frac{11}{20} $ |
| 2 | $ 2 $ |
| 3 | $ 6\frac{2}{3} $ |
| 4 | $ 7 $ |
| 5 | $ 5\frac{1}{4} $ |
| 6 | $ 8\frac{7}{10} $ |
| 7 | $ 3\frac{1}{4} $ |
| 8 | $ 9\frac{5}{12} $ |
| 9 | $ 8\frac{11}{15} $ |
| 10 | $ 8\frac{1}{3} $ |
| 11 | $ 9\frac{5}{8} $ |
| 12 | $ 8\frac{19}{20} $ |

All answers are in lowest terms.

✔ Final Check: All sums have been reduced correctly. ✔️

Let me know if you'd like a printable version or explanation for any specific problem!