Free educational worksheet for practicing multiplying fractions, with step-by-step instructions and 20 problems.

Problem: Multiply the fractions and simplify the results.

The worksheet provides a list of fraction multiplication problems. We will solve each problem step by step, following the guidelines for multiplying fractions:

1. Simplify the fractions if not in lowest terms.
2. Multiply the numerators to get the new numerator.
3. Multiply the denominators to get the new denominator.
4. Simplify the resulting fraction if possible.

Let's solve each problem:

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#### Problem 1: $\frac{1}{2} \times \frac{2}{4}$

- Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
- Multiply the numerators: $1 \times 1 = 1$.
- Multiply the denominators: $2 \times 2 = 4$.
- Result: $\frac{1}{4}$.

Answer: $\frac{1}{4}$

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#### Problem 2: $\frac{2}{6} \times \frac{1}{6}$

- Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
- Multiply the numerators: $1 \times 1 = 1$.
- Multiply the denominators: $3 \times 6 = 18$.
- Result: $\frac{1}{18}$.

Answer: $\frac{1}{18}$

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#### Problem 3: $\frac{4}{5} \times \frac{1}{7}$

- The fractions are already in simplest form.
- Multiply the numerators: $4 \times 1 = 4$.
- Multiply the denominators: $5 \times 7 = 35$.
- Result: $\frac{4}{35}$.

Answer: $\frac{4}{35}$

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#### Problem 4: $\frac{2}{3} \times \frac{2}{5}$

- The fractions are already in simplest form.
- Multiply the numerators: $2 \times 2 = 4$.
- Multiply the denominators: $3 \times 5 = 15$.
- Result: $\frac{4}{15}$.

Answer: $\frac{4}{15}$

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#### Problem 5: $\frac{2}{3} \times \frac{1}{2}$

- The fractions are already in simplest form.
- Multiply the numerators: $2 \times 1 = 2$.
- Multiply the denominators: $3 \times 2 = 6$.
- Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
- Result: $\frac{1}{3}$.

Answer: $\frac{1}{3}$

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#### Problem 6: $\frac{2}{8} \times \frac{2}{4}$

- Simplify $\frac{2}{8}$ to $\frac{1}{4}$ and $\frac{2}{4}$ to $\frac{1}{2}$.
- Multiply the numerators: $1 \times 1 = 1$.
- Multiply the denominators: $4 \times 2 = 8$.
- Result: $\frac{1}{8}$.

Answer: $\frac{1}{8}$

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#### Problem 7: $\frac{1}{3} \times \frac{1}{3}$

- The fractions are already in simplest form.
- Multiply the numerators: $1 \times 1 = 1$.
- Multiply the denominators: $3 \times 3 = 9$.
- Result: $\frac{1}{9}$.

Answer: $\frac{1}{9}$

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#### Problem 8: $\frac{3}{6} \times \frac{4}{6}$

- Simplify $\frac{3}{6}$ to $\frac{1}{2}$ and $\frac{4}{6}$ to $\frac{2}{3}$.
- Multiply the numerators: $1 \times 2 = 2$.
- Multiply the denominators: $2 \times 3 = 6$.
- Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
- Result: $\frac{1}{3}$.

Answer: $\frac{1}{3}$

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#### Problem 9: $\frac{1}{2} \times \frac{5}{8}$

- The fractions are already in simplest form.
- Multiply the numerators: $1 \times 5 = 5$.
- Multiply the denominators: $2 \times 8 = 16$.
- Result: $\frac{5}{16}$.

Answer: $\frac{5}{16}$

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#### Problem 10: $\frac{3}{9} \times \frac{5}{8}$

- Simplify $\frac{3}{9}$ to $\frac{1}{3}$.
- Multiply the numerators: $1 \times 5 = 5$.
- Multiply the denominators: $3 \times 8 = 24$.
- Result: $\frac{5}{24}$.

Answer: $\frac{5}{24}$

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#### Problem 11: $\frac{1}{2} \times \frac{3}{4}$

- The fractions are already in simplest form.
- Multiply the numerators: $1 \times 3 = 3$.
- Multiply the denominators: $2 \times 4 = 8$.
- Result: $\frac{3}{8}$.

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

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#### Problem 12: $\frac{3}{4} \times \frac{3}{7}$

- The fractions are already in simplest form.
- Multiply the numerators: $3 \times 3 = 9$.
- Multiply the denominators: $4 \times 7 = 28$.
- Result: $\frac{9}{28}$.

Answer: $\frac{9}{28}$

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#### Problem 13: $\frac{3}{4} \times \frac{1}{3}$

- The fractions are already in simplest form.
- Multiply the numerators: $3 \times 1 = 3$.
- Multiply the denominators: $4 \times 3 = 12$.
- Simplify $\frac{3}{12}$ to $\frac{1}{4}$.
- Result: $\frac{1}{4}$.

Answer: $\frac{1}{4}$

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#### Problem 14: $\frac{1}{2} \times \frac{1}{3}$

- The fractions are already in simplest form.
- Multiply the numerators: $1 \times 1 = 1$.
- Multiply the denominators: $2 \times 3 = 6$.
- Result: $\frac{1}{6}$.

Answer: $\frac{1}{6}$

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#### Problem 15: $\frac{1}{3} \times \frac{2}{3}$

- The fractions are already in simplest form.
- Multiply the numerators: $1 \times 2 = 2$.
- Multiply the denominators: $3 \times 3 = 9$.
- Result: $\frac{2}{9}$.

Answer: $\frac{2}{9}$

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#### Problem 16: $\frac{2}{4} \times \frac{5}{6}$

- Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
- Multiply the numerators: $1 \times 5 = 5$.
- Multiply the denominators: $2 \times 6 = 12$.
- Result: $\frac{5}{12}$.

Answer: $\frac{5}{12}$

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#### Problem 17: $\frac{4}{5} \times \frac{1}{4}$

- The fractions are already in simplest form.
- Multiply the numerators: $4 \times 1 = 4$.
- Multiply the denominators: $5 \times 4 = 20$.
- Simplify $\frac{4}{20}$ to $\frac{1}{5}$.
- Result: $\frac{1}{5}$.

Answer: $\frac{1}{5}$

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#### Problem 18: $\frac{5}{6} \times \frac{1}{3}$

- The fractions are already in simplest form.
- Multiply the numerators: $5 \times 1 = 5$.
- Multiply the denominators: $6 \times 3 = 18$.
- Result: $\frac{5}{18}$.

Answer: $\frac{5}{18}$

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#### Problem 19: $\frac{1}{3} \times \frac{2}{7}$

- The fractions are already in simplest form.
- Multiply the numerators: $1 \times 2 = 2$.
- Multiply the denominators: $3 \times 7 = 21$.
- Result: $\frac{2}{21}$.

Answer: $\frac{2}{21}$

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#### Problem 20: $\frac{6}{9} \times \frac{5}{7}$

- Simplify $\frac{6}{9}$ to $\frac{2}{3}$.
- Multiply the numerators: $2 \times 5 = 10$.
- Multiply the denominators: $3 \times 7 = 21$.
- Result: $\frac{10}{21}$.

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

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Final Answers:

1. $\frac{1}{4}$
2. $\frac{1}{18}$
3. $\frac{4}{35}$
4. $\frac{4}{15}$
5. $\frac{1}{3}$
6. $\frac{1}{8}$
7. $\frac{1}{9}$
8. $\frac{1}{3}$
9. $\frac{5}{16}$
10. $\frac{5}{24}$
11. $\frac{3}{8}$
12. $\frac{9}{28}$
13. $\frac{1}{4}$
14. $\frac{1}{6}$
15. $\frac{2}{9}$
16. $\frac{5}{12}$
17. $\frac{1}{5}$
18. $\frac{5}{18}$
19. $\frac{2}{21}$
20. $\frac{10}{21}$

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1. \frac{1}{4} & 2. \frac{1}{18} \\
3. \frac{4}{35} & 4. \frac{4}{15} \\
5. \frac{1}{3} & 6. \frac{1}{8} \\
7. \frac{1}{9} & 8. \frac{1}{3} \\
9. \frac{5}{16} & 10. \frac{5}{24} \\
11. \frac{3}{8} & 12. \frac{9}{28} \\
13. \frac{1}{4} & 14. \frac{1}{6} \\
15. \frac{2}{9} & 16. \frac{5}{12} \\
17. \frac{1}{5} & 18. \frac{5}{18} \\
19. \frac{2}{21} & 20. \frac{10}{21} \\
\end{array}
}
\]