Dividing Fractions worksheet with 12 equations for students to solve.

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

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

We'll apply this rule to each problem.

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

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

✔ Answer: $ \frac{7}{2} $ or $ 3\frac{1}{2} $

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

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

✔ Answer: $ \frac{3}{4} $

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3. $ \frac{1}{11} \div \frac{1}{9} $

$$
= \frac{1}{11} \times \frac{9}{1} = \frac{9}{11}
$$

✔ Answer: $ \frac{9}{11} $

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4. $ \frac{1}{3} \div \frac{16}{15} $

$$
= \frac{1}{3} \times \frac{15}{16} = \frac{15}{48} = \frac{5}{16}
$$

✔ Answer: $ \frac{5}{16} $

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5. $ \frac{1}{8} \div \frac{5}{16} $

$$
= \frac{1}{8} \times \frac{16}{5} = \frac{16}{40} = \frac{2}{5}
$$

✔ Answer: $ \frac{2}{5} $

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6. $ \frac{7}{9} \div \frac{8}{9} $

$$
= \frac{7}{9} \times \frac{9}{8} = \frac{63}{72} = \frac{7}{8}
$$

✔ Answer: $ \frac{7}{8} $

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7. $ \frac{6}{9} \div \frac{3}{9} $

First simplify both fractions:
- $ \frac{6}{9} = \frac{2}{3} $
- $ \frac{3}{9} = \frac{1}{3} $

Now:
$$
\frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times \frac{3}{1} = \frac{6}{3} = 2
$$

✔ Answer: $ 2 $

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8. $ \frac{1}{17} \div \frac{1}{8} $

$$
= \frac{1}{17} \times \frac{8}{1} = \frac{8}{17}
$$

✔ Answer: $ \frac{8}{17} $

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9. $ \frac{4}{15} \div \frac{1}{3} $

$$
= \frac{4}{15} \times \frac{3}{1} = \frac{12}{15} = \frac{4}{5}
$$

✔ Answer: $ \frac{4}{5} $

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10. $ \frac{9}{40} \div \frac{18}{30} $

Simplify $ \frac{18}{30} = \frac{3}{5} $

Now:
$$
\frac{9}{40} \div \frac{3}{5} = \frac{9}{40} \times \frac{5}{3} = \frac{45}{120} = \frac{3}{8}
$$

✔ Answer: $ \frac{3}{8} $

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11. $ \frac{5}{9} \div \frac{15}{27} $

Simplify $ \frac{15}{27} = \frac{5}{9} $

So:
$$
\frac{5}{9} \div \frac{5}{9} = \frac{5}{9} \times \frac{9}{5} = \frac{45}{45} = 1
$$

✔ Answer: $ 1 $

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12. $ \frac{13}{15} \div \frac{1}{45} $

$$
= \frac{13}{15} \times \frac{45}{1} = \frac{585}{15} = 39
$$

✔ Answer: $ 39 $

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✔ Final Answers:

1. $ \frac{7}{2} $
2. $ \frac{3}{4} $
3. $ \frac{9}{11} $
4. $ \frac{5}{16} $
5. $ \frac{2}{5} $
6. $ \frac{7}{8} $
7. $ 2 $
8. $ \frac{8}{17} $
9. $ \frac{4}{5} $
10. $ \frac{3}{8} $
11. $ 1 $
12. $ 39 $

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