Dividing Fractions Worksheets - 15 Worksheets Library - Free Printable

Let's solve each of the fraction division problems on the worksheet step by step.

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Rule for Dividing Fractions:

To divide fractions, multiply by the reciprocal of the divisor:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$

We’ll simplify the result to its simplest form (lowest terms), but improper fractions are acceptable.

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Solving Each Problem:

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1) $ \frac{2}{3} \div \frac{3}{5} $

$$
= \frac{2}{3} \times \frac{5}{3} = \frac{10}{9}
$$

✔ Answer: $ \boxed{\frac{10}{9}} $

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2) $ \frac{3}{8} \div \frac{2}{7} $

$$
= \frac{3}{8} \times \frac{7}{2} = \frac{21}{16}
$$

✔ Answer: $ \boxed{\frac{21}{16}} $

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3) $ \frac{3}{2} \div \frac{4}{9} $

$$
= \frac{3}{2} \times \frac{9}{4} = \frac{27}{8}
$$

✔ Answer: $ \boxed{\frac{27}{8}} $

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4) $ \frac{2}{7} \div \frac{5}{3} $

$$
= \frac{2}{7} \times \frac{3}{5} = \frac{6}{35}
$$

✔ Answer: $ \boxed{\frac{6}{35}} $

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5) $ \frac{5}{8} \div \frac{3}{7} $

$$
= \frac{5}{8} \times \frac{7}{3} = \frac{35}{24}
$$

✔ Answer: $ \boxed{\frac{35}{24}} $

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6) $ \frac{1}{6} \div \frac{4}{15} $

$$
= \frac{1}{6} \times \frac{15}{4} = \frac{15}{24} = \frac{5}{8} \quad \text{(simplify by dividing numerator and denominator by 3)}
$$

✔ Answer: $ \boxed{\frac{5}{8}} $

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7) $ \frac{3}{5} \div \frac{10}{4} $

First simplify $ \frac{10}{4} = \frac{5}{2} $

$$
= \frac{3}{5} \div \frac{5}{2} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}
$$

✔ Answer: $ \boxed{\frac{6}{25}} $

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8) $ \frac{5}{7} \div \frac{8}{3} $

$$
= \frac{5}{7} \times \frac{3}{8} = \frac{15}{56}
$$

✔ Answer: $ \boxed{\frac{15}{56}} $

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9) $ \frac{4}{11} \div \frac{2}{9} $

$$
= \frac{4}{11} \times \frac{9}{2} = \frac{36}{22} = \frac{18}{11} \quad \text{(simplify by dividing by 2)}
$$

✔ Answer: $ \boxed{\frac{18}{11}} $

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10) $ \frac{7}{4} \div \frac{5}{12} $

$$
= \frac{7}{4} \times \frac{12}{5} = \frac{84}{20} = \frac{21}{5} \quad \text{(divide numerator and denominator by 4)}
$$

✔ Answer: $ \boxed{\frac{21}{5}} $

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11) $ \frac{6}{15} \div \frac{3}{10} $

Simplify $ \frac{6}{15} = \frac{2}{5} $

$$
= \frac{2}{5} \div \frac{3}{10} = \frac{2}{5} \times \frac{10}{3} = \frac{20}{15} = \frac{4}{3}
$$

✔ Answer: $ \boxed{\frac{4}{3}} $

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12) $ \frac{7}{9} \div \frac{8}{5} $

$$
= \frac{7}{9} \times \frac{5}{8} = \frac{35}{72}
$$

✔ Answer: $ \boxed{\frac{35}{72}} $

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13) $ \frac{3}{15} \div \frac{4}{7} $

Simplify $ \frac{3}{15} = \frac{1}{5} $

$$
= \frac{1}{5} \div \frac{4}{7} = \frac{1}{5} \times \frac{7}{4} = \frac{7}{20}
$$

✔ Answer: $ \boxed{\frac{7}{20}} $

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14) $ \frac{5}{12} \div \frac{3}{8} $

$$
= \frac{5}{12} \times \frac{8}{3} = \frac{40}{36} = \frac{10}{9} \quad \text{(divide by 4)}
$$

✔ Answer: $ \boxed{\frac{10}{9}} $

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15) $ \frac{3}{5} \div \frac{12}{7} $

$$
= \frac{3}{5} \times \frac{7}{12} = \frac{21}{60} = \frac{7}{20} \quad \text{(divide by 3)}
$$

✔ Answer: $ \boxed{\frac{7}{20}} $

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16) $ \frac{7}{10} \div \frac{5}{12} $

$$
= \frac{7}{10} \times \frac{12}{5} = \frac{84}{50} = \frac{42}{25} \quad \text{(divide by 2)}
$$

✔ Answer: $ \boxed{\frac{42}{25}} $

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17) $ \frac{10}{11} \div \frac{5}{6} $

$$
= \frac{10}{11} \times \frac{6}{5} = \frac{60}{55} = \frac{12}{11} \quad \text{(divide by 5)}
$$

✔ Answer: $ \boxed{\frac{12}{11}} $

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18) $ \frac{4}{13} \div \frac{5}{14} $

$$
= \frac{4}{13} \times \frac{14}{5} = \frac{56}{65}
$$

(No common factors, so it’s already simplified.)

✔ Answer: $ \boxed{\frac{56}{65}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $ \frac{10}{9} $ |
| 2) | $ \frac{21}{16} $ |
| 3) | $ \frac{27}{8} $ |
| 4) | $ \frac{6}{35} $ |
| 5) | $ \frac{35}{24} $ |
| 6) | $ \frac{5}{8} $ |
| 7) | $ \frac{6}{25} $ |
| 8) | $ \frac{15}{56} $ |
| 9) | $ \frac{18}{11} $ |
| 10) | $ \frac{21}{5} $ |
| 11) | $ \frac{4}{3} $ |
| 12) | $ \frac{35}{72} $ |
| 13) | $ \frac{7}{20} $ |
| 14) | $ \frac{10}{9} $ |
| 15) | $ \frac{7}{20} $ |
| 16) | $ \frac{42}{25} $ |
| 17) | $ \frac{12}{11} $ |
| 18) | $ \frac{56}{65} $ |

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🔍 Explanation Summary:

- Always flip the second fraction (take the reciprocal) and change the division to multiplication.
- Multiply numerators and denominators.
- Simplify the result by finding the greatest common divisor (GCD).
- Leave answers as improper fractions unless otherwise instructed.

Let me know if you'd like this in a printable format or with visual steps!