Dividing Fractions (A) worksheet with 20 fraction division problems for practice.

Let's solve the Dividing Fractions (A) worksheet step by step. The key rule for dividing fractions is:

> To divide fractions, multiply by the reciprocal (invert) 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 and show the steps.

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

- Invert the second fraction: $ \frac{2}{3} \to \frac{3}{2} $
- Multiply: $ \frac{1}{4} \times \frac{3}{2} = \frac{3}{8} $

✔ Answer: $ \frac{1}{4} \div \frac{2}{3} = \frac{1}{4} \times \frac{3}{2} = \frac{3}{8} $

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

- Invert: $ \frac{2}{3} \to \frac{3}{2} $
- Multiply: $ \frac{1}{8} \times \frac{3}{2} = \frac{3}{16} $

✔ Answer: $ \frac{1}{8} \div \frac{2}{3} = \frac{1}{8} \times \frac{3}{2} = \frac{3}{16} $

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3. $ \frac{1}{5} \div \frac{4}{9} $

- Invert: $ \frac{4}{9} \to \frac{9}{4} $
- Multiply: $ \frac{1}{5} \times \frac{9}{4} = \frac{9}{20} $

✔ Answer: $ \frac{1}{5} \div \frac{4}{9} = \frac{1}{5} \times \frac{9}{4} = \frac{9}{20} $

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

- Invert: $ \frac{2}{3} \to \frac{3}{2} $
- Multiply: $ \frac{3}{5} \times \frac{3}{2} = \frac{9}{10} $

✔ Answer: $ \frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2} = \frac{9}{10} $

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5. $ \frac{3}{7} \div \frac{2}{3} $

- Invert: $ \frac{2}{3} \to \frac{3}{2} $
- Multiply: $ \frac{3}{7} \times \frac{3}{2} = \frac{9}{14} $

✔ Answer: $ \frac{3}{7} \div \frac{2}{3} = \frac{3}{7} \times \frac{3}{2} = \frac{9}{14} $

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6. $ \frac{3}{4} \div \frac{8}{9} $

- Invert: $ \frac{8}{9} \to \frac{9}{8} $
- Multiply: $ \frac{3}{4} \times \frac{9}{8} = \frac{27}{32} $

✔ Answer: $ \frac{3}{4} \div \frac{8}{9} = \frac{3}{4} \times \frac{9}{8} = \frac{27}{32} $

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

- Invert: $ \frac{1}{2} \to \frac{2}{1} $
- Multiply: $ \frac{1}{3} \times \frac{2}{1} = \frac{2}{3} $

✔ Answer: $ \frac{1}{3} \div \frac{1}{2} = \frac{1}{3} \times \frac{2}{1} = \frac{2}{3} $

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

- Invert: $ \frac{3}{4} \to \frac{4}{3} $
- Multiply: $ \frac{2}{3} \times \frac{4}{3} = \frac{8}{9} $

✔ Answer: $ \frac{2}{3} \div \frac{3}{4} = \frac{2}{3} \times \frac{4}{3} = \frac{8}{9} $

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9. $ \frac{1}{3} \div \frac{5}{7} $

- Invert: $ \frac{5}{7} \to \frac{7}{5} $
- Multiply: $ \frac{1}{3} \times \frac{7}{5} = \frac{7}{15} $

✔ Answer: $ \frac{1}{3} \div \frac{5}{7} = \frac{1}{3} \times \frac{7}{5} = \frac{7}{15} $

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10. $ \frac{2}{9} \div \frac{1}{2} $

- Invert: $ \frac{1}{2} \to \frac{2}{1} $
- Multiply: $ \frac{2}{9} \times \frac{2}{1} = \frac{4}{9} $

✔ Answer: $ \frac{2}{9} \div \frac{1}{2} = \frac{2}{9} \times \frac{2}{1} = \frac{4}{9} $

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11. $ \frac{5}{6} \div \frac{6}{7} $

- Invert: $ \frac{6}{7} \to \frac{7}{6} $
- Multiply: $ \frac{5}{6} \times \frac{7}{6} = \frac{35}{36} $

✔ Answer: $ \frac{5}{6} \div \frac{6}{7} = \frac{5}{6} \times \frac{7}{6} = \frac{35}{36} $

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12. $ \frac{1}{4} \div \frac{4}{5} $

- Invert: $ \frac{4}{5} \to \frac{5}{4} $
- Multiply: $ \frac{1}{4} \times \frac{5}{4} = \frac{5}{16} $

✔ Answer: $ \frac{1}{4} \div \frac{4}{5} = \frac{1}{4} \times \frac{5}{4} = \frac{5}{16} $

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13. $ \frac{1}{8} \div \frac{2}{5} $

- Invert: $ \frac{2}{5} \to \frac{5}{2} $
- Multiply: $ \frac{1}{8} \times \frac{5}{2} = \frac{5}{16} $

✔ Answer: $ \frac{1}{8} \div \frac{2}{5} = \frac{1}{8} \times \frac{5}{2} = \frac{5}{16} $

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

- Invert: $ \frac{5}{7} \to \frac{7}{5} $
- Multiply: $ \frac{1}{2} \times \frac{7}{5} = \frac{7}{10} $

✔ Answer: $ \frac{1}{2} \div \frac{5}{7} = \frac{1}{2} \times \frac{7}{5} = \frac{7}{10} $

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

- Invert: $ \frac{1}{5} \to \frac{5}{1} $
- Multiply: $ \frac{1}{7} \times \frac{5}{1} = \frac{5}{7} $

✔ Answer: $ \frac{1}{7} \div \frac{1}{5} = \frac{1}{7} \times \frac{5}{1} = \frac{5}{7} $

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

- Invert: $ \frac{3}{5} \to \frac{5}{3} $
- Multiply: $ \frac{1}{2} \times \frac{5}{3} = \frac{5}{6} $

✔ Answer: $ \frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6} $

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

- Invert: $ \frac{2}{7} \to \frac{7}{2} $
- Multiply: $ \frac{1}{4} \times \frac{7}{2} = \frac{7}{8} $

✔ Answer: $ \frac{1}{4} \div \frac{2}{7} = \frac{1}{4} \times \frac{7}{2} = \frac{7}{8} $

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

- Invert: $ \frac{2}{3} \to \frac{3}{2} $
- Multiply: $ \frac{1}{5} \times \frac{3}{2} = \frac{3}{10} $

✔ Answer: $ \frac{1}{5} \div \frac{2}{3} = \frac{1}{5} \times \frac{3}{2} = \frac{3}{10} $

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

- Invert: $ \frac{7}{8} \to \frac{8}{7} $
- Multiply: $ \frac{6}{7} \times \frac{8}{7} = \frac{48}{49} $

✔ Answer: $ \frac{6}{7} \div \frac{7}{8} = \frac{6}{7} \times \frac{8}{7} = \frac{48}{49} $

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20. $ \frac{1}{5} \div \frac{1}{4} $

- Invert: $ \frac{1}{4} \to \frac{4}{1} $
- Multiply: $ \frac{1}{5} \times \frac{4}{1} = \frac{4}{5} $

✔ Answer: $ \frac{1}{5} \div \frac{1}{4} = \frac{1}{5} \times \frac{4}{1} = \frac{4}{5} $

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✔ Final Answers Summary:

| Problem | Inversion | Result |
|--------|-----------|--------|
| 1. | $ \frac{1}{4} \times \frac{3}{2} $ | $ \frac{3}{8} $ |
| 2. | $ \frac{1}{8} \times \frac{3}{2} $ | $ \frac{3}{16} $ |
| 3. | $ \frac{1}{5} \times \frac{9}{4} $ | $ \frac{9}{20} $ |
| 4. | $ \frac{3}{5} \times \frac{3}{2} $ | $ \frac{9}{10} $ |
| 5. | $ \frac{3}{7} \times \frac{3}{2} $ | $ \frac{9}{14} $ |
| 6. | $ \frac{3}{4} \times \frac{9}{8} $ | $ \frac{27}{32} $ |
| 7. | $ \frac{1}{3} \times \frac{2}{1} $ | $ \frac{2}{3} $ |
| 8. | $ \frac{2}{3} \times \frac{4}{3} $ | $ \frac{8}{9} $ |
| 9. | $ \frac{1}{3} \times \frac{7}{5} $ | $ \frac{7}{15} $ |
|10. | $ \frac{2}{9} \times \frac{2}{1} $ | $ \frac{4}{9} $ |
|11. | $ \frac{5}{6} \times \frac{7}{6} $ | $ \frac{35}{36} $ |
|12. | $ \frac{1}{4} \times \frac{5}{4} $ | $ \frac{5}{16} $ |
|13. | $ \frac{1}{8} \times \frac{5}{2} $ | $ \frac{5}{16} $ |
|14. | $ \frac{1}{2} \times \frac{7}{5} $ | $ \frac{7}{10} $ |
|15. | $ \frac{1}{7} \times \frac{5}{1} $ | $ \frac{5}{7} $ |
|16. | $ \frac{1}{2} \times \frac{5}{3} $ | $ \frac{5}{6} $ |
|17. | $ \frac{1}{4} \times \frac{7}{2} $ | $ \frac{7}{8} $ |
|18. | $ \frac{1}{5} \times \frac{3}{2} $ | $ \frac{3}{10} $ |
|19. | $ \frac{6}{7} \times \frac{8}{7} $ | $ \frac{48}{49} $ |
|20. | $ \frac{1}{5} \times \frac{4}{1} $ | $ \frac{4}{5} $ |

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🔍 Explanation Recap:

- To divide two fractions, invert the second fraction (the divisor) and then multiply.
- Simplify if possible (though in these problems, most answers are already in simplest form).
- Always check your multiplication of numerators and denominators.

Let me know if you'd like this formatted as a printable answer sheet!