Dividing Fractions Worksheets - 15 Worksheets Library - Free Printable

Let's solve each of the dividing fractions 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 go through each problem one by one.

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1.) $ 3 \div \frac{1}{8} $

Convert 3 to a fraction: $ \frac{3}{1} $

Now:
$$
\frac{3}{1} \div \frac{1}{8} = \frac{3}{1} \times \frac{8}{1} = 24
$$

✔ Answer: 24

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

Write 7 as $ \frac{7}{1} $

$$
\frac{1}{4} \div \frac{7}{1} = \frac{1}{4} \times \frac{1}{7} = \frac{1}{28}
$$

✔ Answer: $ \frac{1}{28} $

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

Convert mixed number to improper fraction:
$ 2\frac{1}{3} = \frac{7}{3} $

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

✔ Answer: $ \frac{6}{35} $

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4.) $ \frac{11}{9} \div \frac{2}{12} $

Simplify $ \frac{2}{12} = \frac{1}{6} $

Now:
$$
\frac{11}{9} \div \frac{1}{6} = \frac{11}{9} \times \frac{6}{1} = \frac{66}{9} = \frac{22}{3} = 7\frac{1}{3}
$$

✔ Answer: $ 7\frac{1}{3} $

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5.) $ 6 \div \frac{3}{8} $

Write 6 as $ \frac{6}{1} $

$$
\frac{6}{1} \div \frac{3}{8} = \frac{6}{1} \times \frac{8}{3} = \frac{48}{3} = 16
$$

✔ Answer: 16

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6.) $ 1\frac{1}{5} \div 2\frac{4}{10} $

Convert both to improper fractions:

- $ 1\frac{1}{5} = \frac{6}{5} $
- $ 2\frac{4}{10} = 2\frac{2}{5} = \frac{12}{5} $

Now:
$$
\frac{6}{5} \div \frac{12}{5} = \frac{6}{5} \times \frac{5}{12} = \frac{30}{60} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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7.) $ \frac{3}{8} \div 1\frac{6}{12} $

Simplify $ 1\frac{6}{12} = 1\frac{1}{2} = \frac{3}{2} $

Now:
$$
\frac{3}{8} \div \frac{3}{2} = \frac{3}{8} \times \frac{2}{3} = \frac{6}{24} = \frac{1}{4}
$$

✔ Answer: $ \frac{1}{4} $

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8.) $ \frac{5}{4} \div 8 $

Write 8 as $ \frac{8}{1} $

$$
\frac{5}{4} \div \frac{8}{1} = \frac{5}{4} \times \frac{1}{8} = \frac{5}{32}
$$

✔ Answer: $ \frac{5}{32} $

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9.) $ \frac{6}{7} \div \frac{4}{14} $

Simplify $ \frac{4}{14} = \frac{2}{7} $

Now:
$$
\frac{6}{7} \div \frac{2}{7} = \frac{6}{7} \times \frac{7}{2} = \frac{42}{14} = 3
$$

✔ Answer: 3

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10.) $ 2\frac{2}{4} \div 3\frac{1}{6} $

Simplify and convert:

- $ 2\frac{2}{4} = 2\frac{1}{2} = \frac{5}{2} $
- $ 3\frac{1}{6} = \frac{19}{6} $

Now:
$$
\frac{5}{2} \div \frac{19}{6} = \frac{5}{2} \times \frac{6}{19} = \frac{30}{38} = \frac{15}{19}
$$

✔ Answer: $ \frac{15}{19} $

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11.) $ \frac{2}{6} \div \frac{4}{4} $

Simplify:
- $ \frac{2}{6} = \frac{1}{3} $
- $ \frac{4}{4} = 1 $

So:
$$
\frac{1}{3} \div 1 = \frac{1}{3}
$$

✔ Answer: $ \frac{1}{3} $

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12.) $ 3\frac{1}{2} \div \frac{2}{3} $

Convert mixed number:
- $ 3\frac{1}{2} = \frac{7}{2} $

Now:
$$
\frac{7}{2} \div \frac{2}{3} = \frac{7}{2} \times \frac{3}{2} = \frac{21}{4} = 5\frac{1}{4}
$$

✔ Answer: $ 5\frac{1}{4} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | 24 |
| 2) | $ \frac{1}{28} $ |
| 3) | $ \frac{6}{35} $ |
| 4) | $ 7\frac{1}{3} $ |
| 5) | 16 |
| 6) | $ \frac{1}{2} $ |
| 7) | $ \frac{1}{4} $ |
| 8) | $ \frac{5}{32} $ |
| 9) | 3 |
| 10) | $ \frac{15}{19} $ |
| 11) | $ \frac{1}{3} $ |
| 12) | $ 5\frac{1}{4} $ |

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📝 Summary Tips:

- Always convert mixed numbers to improper fractions.
- Flip the second fraction (reciprocal) and multiply.
- Simplify before or after multiplying.
- Reduce final answers to lowest terms.

Let me know if you'd like this in printable format! 😊