Dividing Fractions practice worksheet with 12 problems for math students.

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

> To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

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. $\frac{2}{10} \div \frac{3}{5}$

- Reciprocal of $\frac{3}{5}$ is $\frac{5}{3}$
- Multiply: $\frac{2}{10} \times \frac{5}{3} = \frac{10}{30} = \frac{1}{3}$

✔ Answer: $\frac{1}{3}$

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2. $\frac{25}{27} \div \frac{4}{3}$

- Reciprocal of $\frac{4}{3}$ is $\frac{3}{4}$
- Multiply: $\frac{25}{27} \times \frac{3}{4} = \frac{75}{108}$
- Simplify: Divide numerator and denominator by 3 → $\frac{25}{36}$

✔ Answer: $\frac{25}{36}$

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

- Reciprocal of $\frac{3}{2}$ is $\frac{2}{3}$
- Multiply: $\frac{1}{5} \times \frac{2}{3} = \frac{2}{15}$

✔ Answer: $\frac{2}{15}$

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4. $\frac{1}{2} \div \frac{9}{11}$

- Reciprocal of $\frac{9}{11}$ is $\frac{11}{9}$
- Multiply: $\frac{1}{2} \times \frac{11}{9} = \frac{11}{18}$

✔ Answer: $\frac{11}{18}$

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5. $\frac{5}{2} \div \frac{10}{7}$

- Reciprocal of $\frac{10}{7}$ is $\frac{7}{10}$
- Multiply: $\frac{5}{2} \times \frac{7}{10} = \frac{35}{20} = \frac{7}{4}$

✔ Answer: $\frac{7}{4}$ or $1\frac{3}{4}$

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6. $\frac{30}{42} \div \frac{5}{6}$

- First simplify $\frac{30}{42}$: divide numerator and denominator by 6 → $\frac{5}{7}$
- Now: $\frac{5}{7} \div \frac{5}{6}$
- Reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$
- Multiply: $\frac{5}{7} \times \frac{6}{5} = \frac{30}{35} = \frac{6}{7}$

✔ Answer: $\frac{6}{7}$

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7. $\frac{7}{25} \div \frac{13}{25}$

- Same denominator, so we can simplify:
- $\frac{7}{25} \times \frac{25}{13} = \frac{7 \times 25}{25 \times 13} = \frac{7}{13}$ (the 25s cancel)

✔ Answer: $\frac{7}{13}$

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8. $\frac{20}{125} \div \frac{5}{25}$

- Simplify both fractions:
- $\frac{20}{125} = \frac{4}{25}$ (divide by 5)
- $\frac{5}{25} = \frac{1}{5}$
- So: $\frac{4}{25} \div \frac{1}{5} = \frac{4}{25} \times \frac{5}{1} = \frac{20}{25} = \frac{4}{5}$

✔ Answer: $\frac{4}{5}$

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9. $\frac{36}{5} \div \frac{6}{5}$

- Same denominator, so:
- $\frac{36}{5} \times \frac{5}{6} = \frac{36 \times 5}{5 \times 6} = \frac{36}{6} = 6$ (5s cancel)

✔ Answer: $6$

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10. $\frac{12}{13} \div \frac{9}{7}$

- Reciprocal of $\frac{9}{7}$ is $\frac{7}{9}$
- Multiply: $\frac{12}{13} \times \frac{7}{9} = \frac{84}{117}$
- Simplify: divide numerator and denominator by 3 → $\frac{28}{39}$

✔ Answer: $\frac{28}{39}$

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11. $\frac{75}{19} \div \frac{100}{19}$

- Same denominator, so:
- $\frac{75}{19} \times \frac{19}{100} = \frac{75 \times 19}{19 \times 100} = \frac{75}{100} = \frac{3}{4}$ (19 cancels)

✔ Answer: $\frac{3}{4}$

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12. $\frac{100}{60} \div \frac{2}{30}$

- Simplify $\frac{100}{60} = \frac{5}{3}$ (divide by 20)
- Simplify $\frac{2}{30} = \frac{1}{15}$
- Now: $\frac{5}{3} \div \frac{1}{15} = \frac{5}{3} \times \frac{15}{1} = \frac{75}{3} = 25$

✔ Answer: $25$

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✔ Final Answers:

1. $\frac{1}{3}$
2. $\frac{25}{36}$
3. $\frac{2}{15}$
4. $\frac{11}{18}$
5. $\frac{7}{4}$
6. $\frac{6}{7}$
7. $\frac{7}{13}$
8. $\frac{4}{5}$
9. $6$
10. $\frac{28}{39}$
11. $\frac{3}{4}$
12. $25$

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📝 Summary of Key Steps:

- Always flip the second fraction (take reciprocal).
- Change division to multiplication.
- Simplify before multiplying if possible.
- Reduce final answer to lowest terms.

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