Multiplying Fractions Worksheets with Answer Key - Free Printable

To solve the problems involving the multiplication of fractions, we follow these steps:

1. Multiply the numerators together to get the new numerator.
2. Multiply the denominators together to get the new denominator.
3. Simplify the resulting fraction if possible.

Let's solve each problem step by step.

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Problem 1: \( \frac{3}{10} \times \frac{2}{9} \)

- Multiply the numerators: \( 3 \times 2 = 6 \)
- Multiply the denominators: \( 10 \times 9 = 90 \)
- Result: \( \frac{6}{90} \)
- Simplify: \( \frac{6}{90} = \frac{1}{15} \) (divide numerator and denominator by 6)

Answer: \( \frac{1}{15} \)

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Problem 2: \( \frac{1}{3} \times \frac{3}{5} \)

- Multiply the numerators: \( 1 \times 3 = 3 \)
- Multiply the denominators: \( 3 \times 5 = 15 \)
- Result: \( \frac{3}{15} \)
- Simplify: \( \frac{3}{15} = \frac{1}{5} \) (divide numerator and denominator by 3)

Answer: \( \frac{1}{5} \)

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Problem 3: \( \frac{4}{5} \times \frac{5}{8} \)

- Multiply the numerators: \( 4 \times 5 = 20 \)
- Multiply the denominators: \( 5 \times 8 = 40 \)
- Result: \( \frac{20}{40} \)
- Simplify: \( \frac{20}{40} = \frac{1}{2} \) (divide numerator and denominator by 20)

Answer: \( \frac{1}{2} \)

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Problem 4: \( \frac{7}{10} \times \frac{2}{14} \)

- Multiply the numerators: \( 7 \times 2 = 14 \)
- Multiply the denominators: \( 10 \times 14 = 140 \)
- Result: \( \frac{14}{140} \)
- Simplify: \( \frac{14}{140} = \frac{1}{10} \) (divide numerator and denominator by 14)

Answer: \( \frac{1}{10} \)

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Problem 5: \( \frac{3}{7} \times \frac{2}{3} \)

- Multiply the numerators: \( 3 \times 2 = 6 \)
- Multiply the denominators: \( 7 \times 3 = 21 \)
- Result: \( \frac{6}{21} \)
- Simplify: \( \frac{6}{21} = \frac{2}{7} \) (divide numerator and denominator by 3)

Answer: \( \frac{2}{7} \)

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Problem 6: \( \frac{3}{4} \times \frac{1}{9} \)

- Multiply the numerators: \( 3 \times 1 = 3 \)
- Multiply the denominators: \( 4 \times 9 = 36 \)
- Result: \( \frac{3}{36} \)
- Simplify: \( \frac{3}{36} = \frac{1}{12} \) (divide numerator and denominator by 3)

Answer: \( \frac{1}{12} \)

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Problem 7: \( \frac{2}{15} \times \frac{5}{6} \)

- Multiply the numerators: \( 2 \times 5 = 10 \)
- Multiply the denominators: \( 15 \times 6 = 90 \)
- Result: \( \frac{10}{90} \)
- Simplify: \( \frac{10}{90} = \frac{1}{9} \) (divide numerator and denominator by 10)

Answer: \( \frac{1}{9} \)

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Problem 8: \( \frac{4}{5} \times \frac{1}{6} \)

- Multiply the numerators: \( 4 \times 1 = 4 \)
- Multiply the denominators: \( 5 \times 6 = 30 \)
- Result: \( \frac{4}{30} \)
- Simplify: \( \frac{4}{30} = \frac{2}{15} \) (divide numerator and denominator by 2)

Answer: \( \frac{2}{15} \)

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Problem 9: \( \frac{3}{4} \times \frac{2}{3} \)

- Multiply the numerators: \( 3 \times 2 = 6 \)
- Multiply the denominators: \( 4 \times 3 = 12 \)
- Result: \( \frac{6}{12} \)
- Simplify: \( \frac{6}{12} = \frac{1}{2} \) (divide numerator and denominator by 6)

Answer: \( \frac{1}{2} \)

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Problem 10: \( \frac{5}{8} \times \frac{2}{25} \)

- Multiply the numerators: \( 5 \times 2 = 10 \)
- Multiply the denominators: \( 8 \times 25 = 200 \)
- Result: \( \frac{10}{200} \)
- Simplify: \( \frac{10}{200} = \frac{1}{20} \) (divide numerator and denominator by 10)

Answer: \( \frac{1}{20} \)

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Problem 11: \( \frac{4}{6} \times \frac{3}{8} \)

- Multiply the numerators: \( 4 \times 3 = 12 \)
- Multiply the denominators: \( 6 \times 8 = 48 \)
- Result: \( \frac{12}{48} \)
- Simplify: \( \frac{12}{48} = \frac{1}{4} \) (divide numerator and denominator by 12)

Answer: \( \frac{1}{4} \)

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Problem 12: \( \frac{5}{7} \times \frac{3}{6} \)

- Multiply the numerators: \( 5 \times 3 = 15 \)
- Multiply the denominators: \( 7 \times 6 = 42 \)
- Result: \( \frac{15}{42} \)
- Simplify: \( \frac{15}{42} = \frac{5}{14} \) (divide numerator and denominator by 3)

Answer: \( \frac{5}{14} \)

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Problem 13: \( \frac{2}{7} \times \frac{21}{14} \)

- Multiply the numerators: \( 2 \times 21 = 42 \)
- Multiply the denominators: \( 7 \times 14 = 98 \)
- Result: \( \frac{42}{98} \)
- Simplify: \( \frac{42}{98} = \frac{3}{7} \) (divide numerator and denominator by 14)

Answer: \( \frac{3}{7} \)

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Problem 14: \( \frac{15}{8} \times \frac{2}{5} \)

- Multiply the numerators: \( 15 \times 2 = 30 \)
- Multiply the denominators: \( 8 \times 5 = 40 \)
- Result: \( \frac{30}{40} \)
- Simplify: \( \frac{30}{40} = \frac{3}{4} \) (divide numerator and denominator by 10)

Answer: \( \frac{3}{4} \)

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Problem 15: \( \frac{4}{6} \times \frac{3}{9} \)

- Multiply the numerators: \( 4 \times 3 = 12 \)
- Multiply the denominators: \( 6 \times 9 = 54 \)
- Result: \( \frac{12}{54} \)
- Simplify: \( \frac{12}{54} = \frac{2}{9} \) (divide numerator and denominator by 6)

Answer: \( \frac{2}{9} \)

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Problem 16: \( \frac{6}{8} \times \frac{1}{12} \)

- Multiply the numerators: \( 6 \times 1 = 6 \)
- Multiply the denominators: \( 8 \times 12 = 96 \)
- Result: \( \frac{6}{96} \)
- Simplify: \( \frac{6}{96} = \frac{1}{16} \) (divide numerator and denominator by 6)

Answer: \( \frac{1}{16} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{1}{15} \\
2. & \frac{1}{5} \\
3. & \frac{1}{2} \\
4. & \frac{1}{10} \\
5. & \frac{2}{7} \\
6. & \frac{1}{12} \\
7. & \frac{1}{9} \\
8. & \frac{2}{15} \\
9. & \frac{1}{2} \\
10. & \frac{1}{20} \\
11. & \frac{1}{4} \\
12. & \frac{5}{14} \\
13. & \frac{3}{7} \\
14. & \frac{3}{4} \\
15. & \frac{2}{9} \\
16. & \frac{1}{16} \\
\end{array}
}
\]