Dividing Fractions Worksheets | Grade1to6.com - Free Printable

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

To divide fractions, we use the rule:

> $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

That is, multiply by the reciprocal of the second fraction.

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i. $\frac{3}{4} \div \frac{2}{4}$

$$
= \frac{3}{4} \times \frac{4}{2}
= \frac{3 \times 4}{4 \times 2}
= \frac{12}{8}
= \frac{3}{2} \quad \text{(simplify by dividing numerator and denominator by 4)}
$$

✔ Answer: $\boxed{\frac{3}{2}}$

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ii. $\frac{5}{6} \div \frac{1}{7}$

$$
= \frac{5}{6} \times \frac{7}{1}
= \frac{5 \times 7}{6 \times 1}
= \frac{35}{6}
$$

✔ Answer: $\boxed{\frac{35}{6}}$ (or $5\frac{5}{6}$ as a mixed number)

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iii. $\frac{1}{7} \div \frac{5}{8}$

$$
= \frac{1}{7} \times \frac{8}{5}
= \frac{1 \times 8}{7 \times 5}
= \frac{8}{35}
$$

✔ Answer: $\boxed{\frac{8}{35}}$

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

$$
= \frac{5}{6} \times \frac{5}{1}
= \frac{5 \times 5}{6 \times 1}
= \frac{25}{6}
$$

✔ Answer: $\boxed{\frac{25}{6}}$ (or $4\frac{1}{6}$)

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v. $\frac{1}{7} \div \frac{2}{3}$

$$
= \frac{1}{7} \times \frac{3}{2}
= \frac{1 \times 3}{7 \times 2}
= \frac{3}{14}
$$

✔ Answer: $\boxed{\frac{3}{14}}$

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vi. $\frac{1}{6} \div \frac{1}{8}$

$$
= \frac{1}{6} \times \frac{8}{1}
= \frac{8}{6}
= \frac{4}{3} \quad \text{(simplify by dividing by 2)}
$$

✔ Answer: $\boxed{\frac{4}{3}}$ (or $1\frac{1}{3}$)

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vii. $\frac{2}{7} \div \frac{1}{9}$

$$
= \frac{2}{7} \times \frac{9}{1}
= \frac{2 \times 9}{7 \times 1}
= \frac{18}{7}
$$

✔ Answer: $\boxed{\frac{18}{7}}$ (or $2\frac{4}{7}$)

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viii. $\frac{1}{6} \div \frac{4}{9}$

$$
= \frac{1}{6} \times \frac{9}{4}
= \frac{1 \times 9}{6 \times 4}
= \frac{9}{24}
= \frac{3}{8} \quad \text{(simplify by dividing by 3)}
$$

✔ Answer: $\boxed{\frac{3}{8}}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| i. | $\frac{3}{2}$ |
| ii. | $\frac{35}{6}$ |
| iii. | $\frac{8}{35}$ |
| iv. | $\frac{25}{6}$ |
| v. | $\frac{3}{14}$ |
| vi. | $\frac{4}{3}$ |
| vii. | $\frac{18}{7}$ |
| viii. | $\frac{3}{8}$ |

Let me know if you'd like these answers in mixed number form or explained further!