Multiplying Fractions Worksheets with Answer Key - Free Printable

Let's solve each of these multiplication of fractions problems step by step.

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🔷 Rule for Multiplying Fractions:

To multiply two fractions:
$$
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
$$
Then simplify the result if possible.

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We’ll go through each problem:

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1. $\frac{3}{10} \times \frac{2}{9}$

$$
= \frac{3 \times 2}{10 \times 9} = \frac{6}{90}
$$
Simplify: divide numerator and denominator by 6:
$$
\frac{6 \div 6}{90 \div 6} = \frac{1}{15}
$$
✔ Answer: $\boxed{\frac{1}{15}}$

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

$$
= \frac{1 \times 3}{3 \times 5} = \frac{3}{15}
$$
Simplify: divide by 3:
$$
\frac{3 \div 3}{15 \div 3} = \frac{1}{5}
$$
✔ Answer: $\boxed{\frac{1}{5}}$

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3. $\frac{4}{5} \times \frac{5}{8}$

$$
= \frac{4 \times 5}{5 \times 8} = \frac{20}{40}
$$
Simplify: divide by 20:
$$
\frac{20 \div 20}{40 \div 20} = \frac{1}{2}
$$
✔ Answer: $\boxed{\frac{1}{2}}$

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4. $\frac{7}{10} \times \frac{2}{14}$

First simplify $\frac{2}{14} = \frac{1}{7}$

Now:
$$
\frac{7}{10} \times \frac{1}{7} = \frac{7 \times 1}{10 \times 7} = \frac{7}{70}
$$
Simplify: divide by 7:
$$
\frac{1}{10}
$$
✔ Answer: $\boxed{\frac{1}{10}}$

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

$$
= \frac{3 \times 2}{7 \times 3} = \frac{6}{21}
$$
Simplify: divide by 3:
$$
\frac{2}{7}
$$
✔ Answer: $\boxed{\frac{2}{7}}$

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

$$
= \frac{3 \times 1}{4 \times 9} = \frac{3}{36}
$$
Simplify: divide by 3:
$$
\frac{1}{12}
$$
✔ Answer: $\boxed{\frac{1}{12}}$

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7. $\frac{2}{15} \times \frac{5}{6}$

$$
= \frac{2 \times 5}{15 \times 6} = \frac{10}{90}
$$
Simplify: divide by 10:
$$
\frac{1}{9}
$$
✔ Answer: $\boxed{\frac{1}{9}}$

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8. $\frac{4}{5} \times \frac{1}{6}$

$$
= \frac{4 \times 1}{5 \times 6} = \frac{4}{30}
$$
Simplify: divide by 2:
$$
\frac{2}{15}
$$
✔ Answer: $\boxed{\frac{2}{15}}$

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9. $\frac{3}{4} \times \frac{2}{3}$

$$
= \frac{3 \times 2}{4 \times 3} = \frac{6}{12}
$$
Simplify: divide by 6:
$$
\frac{1}{2}
$$
✔ Answer: $\boxed{\frac{1}{2}}$

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10. $\frac{5}{8} \times \frac{2}{25}$

$$
= \frac{5 \times 2}{8 \times 25} = \frac{10}{200}
$$
Simplify: divide by 10:
$$
\frac{1}{20}
$$
✔ Answer: $\boxed{\frac{1}{20}}$

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11. $\frac{4}{6} \times \frac{3}{8}$

First simplify $\frac{4}{6} = \frac{2}{3}$

Now:
$$
\frac{2}{3} \times \frac{3}{8} = \frac{2 \times 3}{3 \times 8} = \frac{6}{24}
$$
Simplify: divide by 6:
$$
\frac{1}{4}
$$
✔ Answer: $\boxed{\frac{1}{4}}$

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12. $\frac{5}{7} \times \frac{3}{6}$

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

Now:
$$
\frac{5}{7} \times \frac{1}{2} = \frac{5 \times 1}{7 \times 2} = \frac{5}{14}
$$
✔ Answer: $\boxed{\frac{5}{14}}$

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13. $\frac{2}{7} \times \frac{21}{14}$

Simplify $\frac{21}{14} = \frac{3}{2}$ (divide numerator and denominator by 7)

Now:
$$
\frac{2}{7} \times \frac{3}{2} = \frac{2 \times 3}{7 \times 2} = \frac{6}{14}
$$
Simplify: divide by 2:
$$
\frac{3}{7}
$$
✔ Answer: $\boxed{\frac{3}{7}}$

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14. $\frac{15}{8} \times \frac{2}{5}$

$$
= \frac{15 \times 2}{8 \times 5} = \frac{30}{40}
$$
Simplify: divide by 10:
$$
\frac{3}{4}
$$
✔ Answer: $\boxed{\frac{3}{4}}$

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15. $\frac{4}{6} \times \frac{3}{9}$

Simplify:
- $\frac{4}{6} = \frac{2}{3}$
- $\frac{3}{9} = \frac{1}{3}$

Now:
$$
\frac{2}{3} \times \frac{1}{3} = \frac{2}{9}
$$
✔ Answer: $\boxed{\frac{2}{9}}$

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16. $\frac{6}{8} \times \frac{1}{12}$

Simplify $\frac{6}{8} = \frac{3}{4}$

Now:
$$
\frac{3}{4} \times \frac{1}{12} = \frac{3 \times 1}{4 \times 12} = \frac{3}{48}
$$
Simplify: divide by 3:
$$
\frac{1}{16}
$$
✔ Answer: $\boxed{\frac{1}{16}}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{1}{15}$ |
| 2 | $\frac{1}{5}$ |
| 3 | $\frac{1}{2}$ |
| 4 | $\frac{1}{10}$ |
| 5 | $\frac{2}{7}$ |
| 6 | $\frac{1}{12}$ |
| 7 | $\frac{1}{9}$ |
| 8 | $\frac{2}{15}$ |
| 9 | $\frac{1}{2}$ |
| 10 | $\frac{1}{20}$ |
| 11 | $\frac{1}{4}$ |
| 12 | $\frac{5}{14}$ |
| 13 | $\frac{3}{7}$ |
| 14 | $\frac{3}{4}$ |
| 15 | $\frac{2}{9}$ |
| 16 | $\frac{1}{16}$ |

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