Worksheet for practicing multiplication of fractions, provided by Math Center.

Problem: Multiplying Fractions by Fractions

The task involves solving a series of fraction multiplication problems. Below is the step-by-step solution for each problem, along with explanations.

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#### 1. \( \frac{2}{3} \times \frac{1}{4} \)

- Step 1: Multiply the numerators: \( 2 \times 1 = 2 \).
- Step 2: Multiply the denominators: \( 3 \times 4 = 12 \).
- Step 3: Write the result as a fraction: \( \frac{2}{12} \).
- Step 4: Simplify the fraction: \( \frac{2}{12} = \frac{1}{6} \).

Answer: \( \frac{1}{6} \)

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#### 2. \( \frac{2}{3} \times \frac{3}{4} \)

- Step 1: Multiply the numerators: \( 2 \times 3 = 6 \).
- Step 2: Multiply the denominators: \( 3 \times 4 = 12 \).
- Step 3: Write the result as a fraction: \( \frac{6}{12} \).
- Step 4: Simplify the fraction: \( \frac{6}{12} = \frac{1}{2} \).

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

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#### 3. \( \frac{2}{3} \times \frac{1}{3} \)

- Step 1: Multiply the numerators: \( 2 \times 1 = 2 \).
- Step 2: Multiply the denominators: \( 3 \times 3 = 9 \).
- Step 3: Write the result as a fraction: \( \frac{2}{9} \).

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

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#### 4. \( \frac{2}{3} \times \frac{2}{3} \)

- Step 1: Multiply the numerators: \( 2 \times 2 = 4 \).
- Step 2: Multiply the denominators: \( 3 \times 3 = 9 \).
- Step 3: Write the result as a fraction: \( \frac{4}{9} \).

Answer: \( \frac{4}{9} \)

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#### 5. \( \frac{3}{4} \times \frac{1}{5} \)

- Step 1: Multiply the numerators: \( 3 \times 1 = 3 \).
- Step 2: Multiply the denominators: \( 4 \times 5 = 20 \).
- Step 3: Write the result as a fraction: \( \frac{3}{20} \).

Answer: \( \frac{3}{20} \)

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#### 6. \( \frac{3}{4} \times \frac{4}{5} \)

- Step 1: Multiply the numerators: \( 3 \times 4 = 12 \).
- Step 2: Multiply the denominators: \( 4 \times 5 = 20 \).
- Step 3: Write the result as a fraction: \( \frac{12}{20} \).
- Step 4: Simplify the fraction: \( \frac{12}{20} = \frac{3}{5} \).

Answer: \( \frac{3}{5} \)

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#### 7. \( \frac{3}{4} \times \frac{1}{4} \)

- Step 1: Multiply the numerators: \( 3 \times 1 = 3 \).
- Step 2: Multiply the denominators: \( 4 \times 4 = 16 \).
- Step 3: Write the result as a fraction: \( \frac{3}{16} \).

Answer: \( \frac{3}{16} \)

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#### 8. \( \frac{3}{4} \times \frac{3}{4} \)

- Step 1: Multiply the numerators: \( 3 \times 3 = 9 \).
- Step 2: Multiply the denominators: \( 4 \times 4 = 16 \).
- Step 3: Write the result as a fraction: \( \frac{9}{16} \).

Answer: \( \frac{9}{16} \)

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#### 9. \( \frac{4}{9} \times \frac{1}{6} \)

- Step 1: Multiply the numerators: \( 4 \times 1 = 4 \).
- Step 2: Multiply the denominators: \( 9 \times 6 = 54 \).
- Step 3: Write the result as a fraction: \( \frac{4}{54} \).
- Step 4: Simplify the fraction: \( \frac{4}{54} = \frac{2}{27} \).

Answer: \( \frac{2}{27} \)

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#### 10. \( \frac{4}{9} \times \frac{5}{6} \)

- Step 1: Multiply the numerators: \( 4 \times 5 = 20 \).
- Step 2: Multiply the denominators: \( 9 \times 6 = 54 \).
- Step 3: Write the result as a fraction: \( \frac{20}{54} \).
- Step 4: Simplify the fraction: \( \frac{20}{54} = \frac{10}{27} \).

Answer: \( \frac{10}{27} \)

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#### 11. \( \frac{9}{10} \times \frac{1}{5} \)

- Step 1: Multiply the numerators: \( 9 \times 1 = 9 \).
- Step 2: Multiply the denominators: \( 10 \times 5 = 50 \).
- Step 3: Write the result as a fraction: \( \frac{9}{50} \).

Answer: \( \frac{9}{50} \)

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#### 12. \( \frac{9}{10} \times \frac{3}{5} \)

- Step 1: Multiply the numerators: \( 9 \times 3 = 27 \).
- Step 2: Multiply the denominators: \( 10 \times 5 = 50 \).
- Step 3: Write the result as a fraction: \( \frac{27}{50} \).

Answer: \( \frac{27}{50} \)

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#### 13. \( \frac{7}{8} \times \frac{1}{7} \)

- Step 1: Multiply the numerators: \( 7 \times 1 = 7 \).
- Step 2: Multiply the denominators: \( 8 \times 7 = 56 \).
- Step 3: Write the result as a fraction: \( \frac{7}{56} \).
- Step 4: Simplify the fraction: \( \frac{7}{56} = \frac{1}{8} \).

Answer: \( \frac{1}{8} \)

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#### 14. \( \frac{7}{8} \times \frac{2}{7} \)

- Step 1: Multiply the numerators: \( 7 \times 2 = 14 \).
- Step 2: Multiply the denominators: \( 8 \times 7 = 56 \).
- Step 3: Write the result as a fraction: \( \frac{14}{56} \).
- Step 4: Simplify the fraction: \( \frac{14}{56} = \frac{1}{4} \).

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

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#### 15. \( \frac{10}{11} \times \frac{1}{10} \)

- Step 1: Multiply the numerators: \( 10 \times 1 = 10 \).
- Step 2: Multiply the denominators: \( 11 \times 10 = 110 \).
- Step 3: Write the result as a fraction: \( \frac{10}{110} \).
- Step 4: Simplify the fraction: \( \frac{10}{110} = \frac{1}{11} \).

Answer: \( \frac{1}{11} \)

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#### 16. \( \frac{10}{11} \times \frac{3}{10} \)

- Step 1: Multiply the numerators: \( 10 \times 3 = 30 \).
- Step 2: Multiply the denominators: \( 11 \times 10 = 110 \).
- Step 3: Write the result as a fraction: \( \frac{30}{110} \).
- Step 4: Simplify the fraction: \( \frac{30}{110} = \frac{3}{11} \).

Answer: \( \frac{3}{11} \)

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Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ \frac{1}{6} \\
2. & \ \frac{1}{2} \\
3. & \ \frac{2}{9} \\
4. & \ \frac{4}{9} \\
5. & \ \frac{3}{20} \\
6. & \ \frac{3}{5} \\
7. & \ \frac{3}{16} \\
8. & \ \frac{9}{16} \\
9. & \ \frac{2}{27} \\
10. & \ \frac{10}{27} \\
11. & \ \frac{9}{50} \\
12. & \ \frac{27}{50} \\
13. & \ \frac{1}{8} \\
14. & \ \frac{1}{4} \\
15. & \ \frac{1}{11} \\
16. & \ \frac{3}{11}
\end{aligned}
}
\]