Dividing Fractions Worksheets - 4th, 5th, 6th Grade - Includes ... - Free Printable

To solve the problems involving dividing fractions, we use the rule: Dividing by a fraction is the same as multiplying by its reciprocal. Here's how to approach each problem step by step.

General Steps:

1. Take the reciprocal of the divisor (the second fraction).
2. Multiply the first fraction by this reciprocal.
3. Simplify the resulting fraction if possible.

Let's solve each problem:

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1) $\frac{6}{9} \div \frac{1}{10}$

- Reciprocal of $\frac{1}{10}$ is $\frac{10}{1}$.
- Multiply: $\frac{6}{9} \times \frac{10}{1} = \frac{6 \times 10}{9 \times 1} = \frac{60}{9}$.
- Simplify: $\frac{60}{9} = \frac{20}{3}$.

Answer: $\boxed{\frac{20}{3}}$

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

- Reciprocal of $\frac{1}{10}$ is $\frac{10}{1}$.
- Multiply: $\frac{5}{6} \times \frac{10}{1} = \frac{5 \times 10}{6 \times 1} = \frac{50}{6}$.
- Simplify: $\frac{50}{6} = \frac{25}{3}$.

Answer: $\boxed{\frac{25}{3}}$

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

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

Answer: $\boxed{\frac{2}{3}}$

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4) $\frac{9}{10} \div \frac{2}{6}$

- Reciprocal of $\frac{2}{6}$ is $\frac{6}{2}$.
- Multiply: $\frac{9}{10} \times \frac{6}{2} = \frac{9 \times 6}{10 \times 2} = \frac{54}{20}$.
- Simplify: $\frac{54}{20} = \frac{27}{10}$.

Answer: $\boxed{\frac{27}{10}}$

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5) $\frac{4}{6} \div \frac{1}{4}$

- Reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$.
- Multiply: $\frac{4}{6} \times \frac{4}{1} = \frac{4 \times 4}{6 \times 1} = \frac{16}{6}$.
- Simplify: $\frac{16}{6} = \frac{8}{3}$.

Answer: $\boxed{\frac{8}{3}}$

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

- Reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$.
- Multiply: $\frac{4}{10} \times \frac{3}{1} = \frac{4 \times 3}{10 \times 1} = \frac{12}{10}$.
- Simplify: $\frac{12}{10} = \frac{6}{5}$.

Answer: $\boxed{\frac{6}{5}}$

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7) $\frac{3}{6} \div \frac{2}{3}$

- Reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
- Multiply: $\frac{3}{6} \times \frac{3}{2} = \frac{3 \times 3}{6 \times 2} = \frac{9}{12}$.
- Simplify: $\frac{9}{12} = \frac{3}{4}$.

Answer: $\boxed{\frac{3}{4}}$

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8) $\frac{1}{3} \div \frac{7}{9}$

- Reciprocal of $\frac{7}{9}$ is $\frac{9}{7}$.
- Multiply: $\frac{1}{3} \times \frac{9}{7} = \frac{1 \times 9}{3 \times 7} = \frac{9}{21}$.
- Simplify: $\frac{9}{21} = \frac{3}{7}$.

Answer: $\boxed{\frac{3}{7}}$

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9) $\frac{1}{2} \div \frac{5}{6}$

- Reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$.
- Multiply: $\frac{1}{2} \times \frac{6}{5} = \frac{1 \times 6}{2 \times 5} = \frac{6}{10}$.
- Simplify: $\frac{6}{10} = \frac{3}{5}$.

Answer: $\boxed{\frac{3}{5}}$

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10) $\frac{7}{10} \div \frac{1}{3}$

- Reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$.
- Multiply: $\frac{7}{10} \times \frac{3}{1} = \frac{7 \times 3}{10 \times 1} = \frac{21}{10}$.

Answer: $\boxed{\frac{21}{10}}$

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Final Answers:

1. $\boxed{\frac{20}{3}}$
2. $\boxed{\frac{25}{3}}$
3. $\boxed{\frac{2}{3}}$
4. $\boxed{\frac{27}{10}}$
5. $\boxed{\frac{8}{3}}$
6. $\boxed{\frac{6}{5}}$
7. $\boxed{\frac{3}{4}}$
8. $\boxed{\frac{3}{7}}$
9. $\boxed{\frac{3}{5}}$
10. $\boxed{\frac{21}{10}}$