Practice worksheet for dividing fractions, including proper fractions, improper fractions, and mixed numbers.

Let's solve each of these division of fractions problems step by step.

The general rule for dividing fractions is:

> To divide two fractions, multiply the first fraction by the reciprocal of the second.

That is:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$

We'll apply this rule to each problem.

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1. $ \frac{15}{10} \div \frac{6}{5} $

First simplify $ \frac{15}{10} = \frac{3}{2} $

Now:
$$
\frac{3}{2} \div \frac{6}{5} = \frac{3}{2} \times \frac{5}{6} = \frac{15}{12} = \frac{5}{4}
$$

✔ Answer: $ \frac{5}{4} $

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2. $ \frac{11}{4} \div \frac{8}{16} $

Simplify $ \frac{8}{16} = \frac{1}{2} $

Now:
$$
\frac{11}{4} \div \frac{1}{2} = \frac{11}{4} \times \frac{2}{1} = \frac{22}{4} = \frac{11}{2}
$$

✔ Answer: $ \frac{11}{2} $

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3. $ \frac{5}{4} \div \frac{15}{11} $

$$
\frac{5}{4} \times \frac{11}{15} = \frac{55}{60} = \frac{11}{12}
$$

✔ Answer: $ \frac{11}{12} $

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4. $ 6\frac{2}{3} \div 2\frac{1}{3} $

Convert mixed numbers to improper fractions:

- $ 6\frac{2}{3} = \frac{20}{3} $
- $ 2\frac{1}{3} = \frac{7}{3} $

Now:
$$
\frac{20}{3} \div \frac{7}{3} = \frac{20}{3} \times \frac{3}{7} = \frac{60}{21} = \frac{20}{7} = 2\frac{6}{7}
$$

✔ Answer: $ \frac{20}{7} $ or $ 2\frac{6}{7} $

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5. $ 2\frac{1}{2} \div 2\frac{1}{7} $

Convert:

- $ 2\frac{1}{2} = \frac{5}{2} $
- $ 2\frac{1}{7} = \frac{15}{7} $

$$
\frac{5}{2} \div \frac{15}{7} = \frac{5}{2} \times \frac{7}{15} = \frac{35}{30} = \frac{7}{6} = 1\frac{1}{6}
$$

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

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6. $ \frac{11}{2} \div \frac{10}{8} $

Simplify $ \frac{10}{8} = \frac{5}{4} $

$$
\frac{11}{2} \div \frac{5}{4} = \frac{11}{2} \times \frac{4}{5} = \frac{44}{10} = \frac{22}{5} = 4\frac{2}{5}
$$

✔ Answer: $ \frac{22}{5} $ or $ 4\frac{2}{5} $

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7. $ \frac{9}{4} \div \frac{31}{12} $

$$
\frac{9}{4} \times \frac{12}{31} = \frac{108}{124} = \frac{27}{31}
$$

✔ Answer: $ \frac{27}{31} $

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8. $ \frac{3}{8} \div \frac{2}{5} $

$$
\frac{3}{8} \times \frac{5}{2} = \frac{15}{16}
$$

✔ Answer: $ \frac{15}{16} $

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9. $ \frac{3}{10} \div \frac{2}{9} $

$$
\frac{3}{10} \times \frac{9}{2} = \frac{27}{20} = 1\frac{7}{20}
$$

✔ Answer: $ \frac{27}{20} $ or $ 1\frac{7}{20} $

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10. $ \frac{6}{11} \div \frac{2}{5} $

$$
\frac{6}{11} \times \frac{5}{2} = \frac{30}{22} = \frac{15}{11} = 1\frac{4}{11}
$$

✔ Answer: $ \frac{15}{11} $ or $ 1\frac{4}{11} $

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11. $ \frac{5}{3} \div \frac{3}{14} $

$$
\frac{5}{3} \times \frac{14}{3} = \frac{70}{9} = 7\frac{7}{9}
$$

✔ Answer: $ \frac{70}{9} $ or $ 7\frac{7}{9} $

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12. $ \frac{15}{5} \div \frac{12}{26} $

Simplify $ \frac{15}{5} = 3 $, and $ \frac{12}{26} = \frac{6}{13} $

So:
$$
3 \div \frac{6}{13} = 3 \times \frac{13}{6} = \frac{39}{6} = \frac{13}{2} = 6\frac{1}{2}
$$

✔ Answer: $ \frac{13}{2} $ or $ 6\frac{1}{2} $

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13. $ \frac{21}{10} \div \frac{3}{8} $

$$
\frac{21}{10} \times \frac{8}{3} = \frac{168}{30} = \frac{28}{5} = 5\frac{3}{5}
$$

✔ Answer: $ \frac{28}{5} $ or $ 5\frac{3}{5} $

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14. $ \frac{2}{3} \div \frac{4}{5} $

$$
\frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}
$$

✔ Answer: $ \frac{5}{6} $

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15. $ \frac{2}{5} \div \frac{16}{15} $

$$
\frac{2}{5} \times \frac{15}{16} = \frac{30}{80} = \frac{3}{8}
$$

✔ Answer: $ \frac{3}{8} $

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16. $ \frac{3}{5} \div \frac{12}{17} $

$$
\frac{3}{5} \times \frac{17}{12} = \frac{51}{60} = \frac{17}{20}
$$

✔ Answer: $ \frac{17}{20} $

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{5}{4} $ |
| 2 | $ \frac{11}{2} $ |
| 3 | $ \frac{11}{12} $ |
| 4 | $ \frac{20}{7} $ or $ 2\frac{6}{7} $ |
| 5 | $ \frac{7}{6} $ or $ 1\frac{1}{6} $ |
| 6 | $ \frac{22}{5} $ or $ 4\frac{2}{5} $ |
| 7 | $ \frac{27}{31} $ |
| 8 | $ \frac{15}{16} $ |
| 9 | $ \frac{27}{20} $ or $ 1\frac{7}{20} $ |
| 10 | $ \frac{15}{11} $ or $ 1\frac{4}{11} $ |
| 11 | $ \frac{70}{9} $ or $ 7\frac{7}{9} $ |
| 12 | $ \frac{13}{2} $ or $ 6\frac{1}{2} $ |
| 13 | $ \frac{28}{5} $ or $ 5\frac{3}{5} $ |
| 14 | $ \frac{5}{6} $ |
| 15 | $ \frac{3}{8} $ |
| 16 | $ \frac{17}{20} $ |

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