Mixed Operations - Fractions worksheet for practicing arithmetic with mixed numbers.

Let's solve each problem step by step. These are mixed operations with fractions, involving addition, subtraction, multiplication, and division of mixed numbers.

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Step-by-step Solutions:

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1. $ 9\frac{3}{5} - 4\frac{4}{5} $

Convert to improper fractions:
- $ 9\frac{3}{5} = \frac{48}{5} $
- $ 4\frac{4}{5} = \frac{24}{5} $

Now subtract:
- $ \frac{48}{5} - \frac{24}{5} = \frac{24}{5} = 4\frac{4}{5} $

✔ Answer: $ 4\frac{4}{5} $

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

Add whole numbers and fractions separately:
- $ 9 + 3 = 12 $
- $ \frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1 $

Total: $ 12 + 1 = 13 $

✔ Answer: $ 13 $

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

- $ 2 + 5 = 7 $
- $ \frac{1}{3} + \frac{1}{3} = \frac{2}{3} $

✔ Answer: $ 7\frac{2}{3} $

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4. $ 9\frac{2}{4} + 1\frac{2}{4} $

Simplify fractions first:
- $ \frac{2}{4} = \frac{1}{2} $, so $ 9\frac{2}{4} = 9\frac{1}{2} $
- $ 1\frac{2}{4} = 1\frac{1}{2} $

Now add:
- $ 9 + 1 = 10 $
- $ \frac{1}{2} + \frac{1}{2} = 1 $

Total: $ 10 + 1 = 11 $

✔ Answer: $ 11 $

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5. $ 6\frac{4}{6} \div 4\frac{1}{6} $

Simplify:
- $ \frac{4}{6} = \frac{2}{3} $, so $ 6\frac{4}{6} = 6\frac{2}{3} $
- $ 4\frac{1}{6} $ stays as is

Convert to improper fractions:
- $ 6\frac{2}{3} = \frac{20}{3} $
- $ 4\frac{1}{6} = \frac{25}{6} $

Now divide:
- $ \frac{20}{3} \div \frac{25}{6} = \frac{20}{3} \times \frac{6}{25} = \frac{120}{75} $

Simplify:
- $ \frac{120}{75} = \frac{8}{5} = 1\frac{3}{5} $

✔ Answer: $ 1\frac{3}{5} $

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6. $ 4\frac{1}{8} \div 3\frac{5}{8} $

Convert to improper fractions:
- $ 4\frac{1}{8} = \frac{33}{8} $
- $ 3\frac{5}{8} = \frac{29}{8} $

Divide:
- $ \frac{33}{8} \div \frac{29}{8} = \frac{33}{8} \times \frac{8}{29} = \frac{33}{29} = 1\frac{4}{29} $

✔ Answer: $ 1\frac{4}{29} $

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7. $ 5\frac{2}{5} \times 5\frac{4}{5} $

Convert to improper fractions:
- $ 5\frac{2}{5} = \frac{27}{5} $
- $ 5\frac{4}{5} = \frac{29}{5} $

Multiply:
- $ \frac{27}{5} \times \frac{29}{5} = \frac{783}{25} $

Convert to mixed number:
- $ 783 \div 25 = 31 $ remainder $ 8 $ → $ 31\frac{8}{25} $

✔ Answer: $ 31\frac{8}{25} $

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8. $ 3\frac{4}{6} \div 6\frac{3}{6} $

Simplify:
- $ \frac{4}{6} = \frac{2}{3} $, so $ 3\frac{4}{6} = 3\frac{2}{3} $
- $ \frac{3}{6} = \frac{1}{2} $, so $ 6\frac{3}{6} = 6\frac{1}{2} $

Convert:
- $ 3\frac{2}{3} = \frac{11}{3} $
- $ 6\frac{1}{2} = \frac{13}{2} $

Divide:
- $ \frac{11}{3} \div \frac{13}{2} = \frac{11}{3} \times \frac{2}{13} = \frac{22}{39} $

✔ Answer: $ \frac{22}{39} $

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9. $ 3\frac{3}{4} \times 9\frac{3}{4} $

Convert:
- $ 3\frac{3}{4} = \frac{15}{4} $
- $ 9\frac{3}{4} = \frac{39}{4} $

Multiply:
- $ \frac{15}{4} \times \frac{39}{4} = \frac{585}{16} $

Convert:
- $ 585 \div 16 = 36 $ remainder $ 9 $ → $ 36\frac{9}{16} $

✔ Answer: $ 36\frac{9}{16} $

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10. $ 1\frac{6}{8} \times 8\frac{2}{8} $

Simplify:
- $ \frac{6}{8} = \frac{3}{4} $, so $ 1\frac{6}{8} = 1\frac{3}{4} $
- $ \frac{2}{8} = \frac{1}{4} $, so $ 8\frac{2}{8} = 8\frac{1}{4} $

Convert:
- $ 1\frac{3}{4} = \frac{7}{4} $
- $ 8\frac{1}{4} = \frac{33}{4} $

Multiply:
- $ \frac{7}{4} \times \frac{33}{4} = \frac{231}{16} $

Convert:
- $ 231 \div 16 = 14 $ remainder $ 7 $ → $ 14\frac{7}{16} $

✔ Answer: $ 14\frac{7}{16} $

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11. $ 2\frac{3}{5} + 7\frac{2}{5} $

- $ 2 + 7 = 9 $
- $ \frac{3}{5} + \frac{2}{5} = \frac{5}{5} = 1 $

Total: $ 9 + 1 = 10 $

✔ Answer: $ 10 $

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12. $ 4\frac{1}{3} \times 8\frac{1}{3} $

Convert:
- $ 4\frac{1}{3} = \frac{13}{3} $
- $ 8\frac{1}{3} = \frac{25}{3} $

Multiply:
- $ \frac{13}{3} \times \frac{25}{3} = \frac{325}{9} $

Convert:
- $ 325 \div 9 = 36 $ remainder $ 1 $ → $ 36\frac{1}{9} $

✔ Answer: $ 36\frac{1}{9} $

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13. $ 8\frac{1}{3} \times 7\frac{1}{3} $

Convert:
- $ 8\frac{1}{3} = \frac{25}{3} $
- $ 7\frac{1}{3} = \frac{22}{3} $

Multiply:
- $ \frac{25}{3} \times \frac{22}{3} = \frac{550}{9} $

Convert:
- $ 550 \div 9 = 61 $ remainder $ 1 $ → $ 61\frac{1}{9} $

✔ Answer: $ 61\frac{1}{9} $

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14. $ 8\frac{1}{8} + 9\frac{1}{8} $

- $ 8 + 9 = 17 $
- $ \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4} $

✔ Answer: $ 17\frac{1}{4} $

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15. $ 9\frac{4}{5} + 3\frac{2}{5} $

- $ 9 + 3 = 12 $
- $ \frac{4}{5} + \frac{2}{5} = \frac{6}{5} = 1\frac{1}{5} $

Total: $ 12 + 1\frac{1}{5} = 13\frac{1}{5} $

✔ Answer: $ 13\frac{1}{5} $

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16. $ 9\frac{1}{4} - 8\frac{3}{4} $

Convert to improper fractions:
- $ 9\frac{1}{4} = \frac{37}{4} $
- $ 8\frac{3}{4} = \frac{35}{4} $

Subtract:
- $ \frac{37}{4} - \frac{35}{4} = \frac{2}{4} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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17. $ 9\frac{1}{6} - 6\frac{2}{6} $

Simplify:
- $ \frac{2}{6} = \frac{1}{3} $, so $ 6\frac{2}{6} = 6\frac{1}{3} $

But better to keep denominator same:

- $ 9\frac{1}{6} = \frac{55}{6} $
- $ 6\frac{2}{6} = \frac{38}{6} $

Subtract:
- $ \frac{55}{6} - \frac{38}{6} = \frac{17}{6} = 2\frac{5}{6} $

✔ Answer: $ 2\frac{5}{6} $

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18. $ 1\frac{4}{8} \times 7\frac{6}{8} $

Simplify:
- $ \frac{4}{8} = \frac{1}{2} $, so $ 1\frac{4}{8} = 1\frac{1}{2} $
- $ \frac{6}{8} = \frac{3}{4} $, so $ 7\frac{6}{8} = 7\frac{3}{4} $

Convert:
- $ 1\frac{1}{2} = \frac{3}{2} $
- $ 7\frac{3}{4} = \frac{31}{4} $

Multiply:
- $ \frac{3}{2} \times \frac{31}{4} = \frac{93}{8} $

Convert:
- $ 93 \div 8 = 11 $ remainder $ 5 $ → $ 11\frac{5}{8} $

✔ Answer: $ 11\frac{5}{8} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 4\frac{4}{5} $ |
| 2 | $ 13 $ |
| 3 | $ 7\frac{2}{3} $ |
| 4 | $ 11 $ |
| 5 | $ 1\frac{3}{5} $ |
| 6 | $ 1\frac{4}{29} $ |
| 7 | $ 31\frac{8}{25} $ |
| 8 | $ \frac{22}{39} $ |
| 9 | $ 36\frac{9}{16} $ |
| 10 | $ 14\frac{7}{16} $ |
| 11 | $ 10 $ |
| 12 | $ 36\frac{1}{9} $ |
| 13 | $ 61\frac{1}{9} $ |
| 14 | $ 17\frac{1}{4} $ |
| 15 | $ 13\frac{1}{5} $ |
| 16 | $ \frac{1}{2} $ |
| 17 | $ 2\frac{5}{6} $ |
| 18 | $ 11\frac{5}{8} $ |

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