Dividing Fractions Sheet 3 - Practice worksheet for solving fraction division problems.

Let's solve each of these fraction division problems step by step. The rule for dividing fractions is:

> To divide fractions, multiply by the reciprocal of the divisor.

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

Then simplify the result to its simplest form.

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

$$
= \frac{2}{3} \times \frac{5}{1} = \frac{10}{3} \quad \text{(already in simplest form)}
$$
✔ Answer: $\frac{10}{3}$

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

$$
= \frac{3}{8} \times \frac{7}{2} = \frac{21}{16} \quad \text{(no common factors)}
$$
✔ Answer: $\frac{21}{16}$

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

$$
= \frac{3}{2} \times \frac{9}{4} = \frac{27}{8} \quad \text{(no simplification needed)}
$$
✔ Answer: $\frac{27}{8}$

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

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

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

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

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

$$
= \frac{1}{6} \times \frac{15}{4} = \frac{15}{24} = \frac{5}{8} \quad \text{(divide numerator and denominator by 3)}
$$
✔ Answer: $\frac{5}{8}$

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

First simplify $\frac{10}{4} = \frac{5}{2}$, then:
$$
= \frac{3}{5} \div \frac{5}{2} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}
$$
✔ Answer: $\frac{6}{25}$

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

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

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

$$
= \frac{4}{11} \times \frac{9}{2} = \frac{36}{22} = \frac{18}{11} \quad \text{(divide by 2)}
$$
✔ Answer: $\frac{18}{11}$

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

$$
= \frac{7}{4} \times \frac{12}{5} = \frac{84}{20} = \frac{21}{5} \quad \text{(divide by 4)}
$$
✔ Answer: $\frac{21}{5}$

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

Simplify $\frac{6}{15} = \frac{2}{5}$, then:
$$
= \frac{2}{5} \div \frac{3}{10} = \frac{2}{5} \times \frac{10}{3} = \frac{20}{15} = \frac{4}{3}
$$
✔ Answer: $\frac{4}{3}$

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

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

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13) $\frac{2}{15} \div \frac{4}{7}$

$$
= \frac{2}{15} \times \frac{7}{4} = \frac{14}{60} = \frac{7}{30} \quad \text{(divide by 2)}
$$
✔ Answer: $\frac{7}{30}$

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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: $\frac{10}{9}$

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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: $\frac{7}{20}$

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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: $\frac{42}{25}$

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17) $\frac{10}{11} \div \frac{5}{8}$

$$
= \frac{10}{11} \times \frac{8}{5} = \frac{80}{55} = \frac{16}{11} \quad \text{(divide by 5)}
$$
✔ Answer: $\frac{16}{11}$

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

$$
= \frac{4}{13} \times \frac{14}{5} = \frac{56}{65}
$$
Check: 56 and 65 have no common factors (56 = 7×8, 65 = 5×13), so it's already simplified.
✔ Answer: $\frac{56}{65}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $\frac{10}{3}$ |
| 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) | $\frac{7}{30}$ |
| 14) | $\frac{10}{9}$ |
| 15) | $\frac{7}{20}$ |
| 16) | $\frac{42}{25}$ |
| 17) | $\frac{16}{11}$ |
| 18) | $\frac{56}{65}$ |

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💡 Tip: Always check if the final answer can be simplified by finding the greatest common divisor (GCD) of numerator and denominator.

Let me know if you'd like this as a printable PDF or with explanations for each step!