Dividing Fractions Worksheet - Free Printable

It looks like you've uploaded a worksheet titled "Dividing Fractions Sheet 1", which contains a series of fraction division problems. The instructions say:

> Work out these fraction divisions. Give your answer as a mixed number or simplified fraction.

Let's go through each problem step by step and solve them.

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🔷 How to Divide Fractions:

To divide fractions, follow the rule:

> Keep, Change, Flip
> - Keep the first fraction
> - Change the division sign to multiplication
> - Flip (invert) the second fraction

Then multiply the numerators and denominators, simplify, and convert to a mixed number if needed.

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Now, let’s solve each problem:

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

$$
= \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2} = 1\frac{1}{2}
$$

✔ Answer: $ 1\frac{1}{2} $

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2. $ \frac{5}{6} \div \frac{1}{3} $

$$
= \frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2}
$$

✔ Answer: $ 2\frac{1}{2} $

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3. $ \frac{2}{5} \div \frac{1}{4} $

$$
= \frac{2}{5} \times \frac{4}{1} = \frac{8}{5} = 1\frac{3}{5}
$$

✔ Answer: $ 1\frac{3}{5} $

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4. $ \frac{7}{8} \div \frac{1}{2} $

$$
= \frac{7}{8} \times \frac{2}{1} = \frac{14}{8} = \frac{7}{4} = 1\frac{3}{4}
$$

✔ Answer: $ 1\frac{3}{4} $

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5. $ \frac{3}{10} \div \frac{1}{5} $

$$
= \frac{3}{10} \times \frac{5}{1} = \frac{15}{10} = \frac{3}{2} = 1\frac{1}{2}
$$

✔ Answer: $ 1\frac{1}{2} $

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

$$
= \frac{4}{9} \times \frac{3}{1} = \frac{12}{9} = \frac{4}{3} = 1\frac{1}{3}
$$

✔ Answer: $ 1\frac{1}{3} $

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

$$
= \frac{5}{7} \times \frac{2}{1} = \frac{10}{7} = 1\frac{3}{7}
$$

✔ Answer: $ 1\frac{3}{7} $

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

$$
= \frac{2}{3} \times \frac{6}{1} = \frac{12}{3} = 4
$$

✔ Answer: $ 4 $

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9. $ \frac{9}{10} \div \frac{1}{5} $

$$
= \frac{9}{10} \times \frac{5}{1} = \frac{45}{10} = \frac{9}{2} = 4\frac{1}{2}
$$

✔ Answer: $ 4\frac{1}{2} $

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10. $ \frac{7}{12} \div \frac{1}{4} $

$$
= \frac{7}{12} \times \frac{4}{1} = \frac{28}{12} = \frac{7}{3} = 2\frac{1}{3}
$$

✔ Answer: $ 2\frac{1}{3} $

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11. $ \frac{5}{8} \div \frac{1}{4} $

$$
= \frac{5}{8} \times \frac{4}{1} = \frac{20}{8} = \frac{5}{2} = 2\frac{1}{2}
$$

✔ Answer: $ 2\frac{1}{2} $

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12. $ \frac{11}{15} \div \frac{1}{3} $

$$
= \frac{11}{15} \times \frac{3}{1} = \frac{33}{15} = \frac{11}{5} = 2\frac{1}{5}
$$

✔ Answer: $ 2\frac{1}{5} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ 1\frac{1}{2} $ |
| 2 | $ 2\frac{1}{2} $ |
| 3 | $ 1\frac{3}{5} $ |
| 4 | $ 1\frac{3}{4} $ |
| 5 | $ 1\frac{1}{2} $ |
| 6 | $ 1\frac{1}{3} $ |
| 7 | $ 1\frac{3}{7} $ |
| 8 | $ 4 $ |
| 9 | $ 4\frac{1}{2} $ |
| 10 | $ 2\frac{1}{3} $ |
| 11 | $ 2\frac{1}{2} $ |
| 12 | $ 2\frac{1}{5} $ |

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📝 Explanation:

Each problem involves dividing a fraction by a unit fraction (like $ \frac{1}{2}, \frac{1}{3}, \frac{1}{4} $). The key is remembering to multiply by the reciprocal. Since the second fraction is always $ \frac{1}{n} $, its reciprocal is $ n $, so the result becomes:

$$
\frac{a}{b} \div \frac{1}{n} = \frac{a}{b} \times n = \frac{a \cdot n}{b}
$$

This simplifies quickly, and then we just reduce and convert to a mixed number if needed.

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Let me know if you'd like this as a printable PDF or want to practice more!