Fraction multiplication practice worksheet with problems to solve and reduce to lowest terms.

Problem: Multiply the fractions and reduce your answer to lowest terms.

The task involves multiplying pairs of fractions and simplifying the results. Let's solve each problem step by step.

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#### 1. \( \frac{2}{3} \times \frac{1}{5} \)

- Step 1: Multiply the numerators: \( 2 \times 1 = 2 \).
- Step 2: Multiply the denominators: \( 3 \times 5 = 15 \).
- Step 3: Write the result as a fraction: \( \frac{2}{15} \).
- Step 4: Simplify (if possible): \( \frac{2}{15} \) is already in its simplest form.

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

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#### 2. \( \frac{5}{6} \times \frac{2}{7} \)

- Step 1: Multiply the numerators: \( 5 \times 2 = 10 \).
- Step 2: Multiply the denominators: \( 6 \times 7 = 42 \).
- Step 3: Write the result as a fraction: \( \frac{10}{42} \).
- Step 4: Simplify: The greatest common divisor (GCD) of 10 and 42 is 2. Divide both numerator and denominator by 2:
\[
\frac{10 \div 2}{42 \div 2} = \frac{5}{21}
\]

Answer: \( \frac{5}{21} \)

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#### 3. \( \frac{3}{4} \times \frac{4}{9} \)

- Step 1: Multiply the numerators: \( 3 \times 4 = 12 \).
- Step 2: Multiply the denominators: \( 4 \times 9 = 36 \).
- Step 3: Write the result as a fraction: \( \frac{12}{36} \).
- Step 4: Simplify: The GCD of 12 and 36 is 12. Divide both numerator and denominator by 12:
\[
\frac{12 \div 12}{36 \div 12} = \frac{1}{3}
\]

Answer: \( \frac{1}{3} \)

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#### 4. \( \frac{3}{5} \times \frac{3}{7} \)

- Step 1: Multiply the numerators: \( 3 \times 3 = 9 \).
- Step 2: Multiply the denominators: \( 5 \times 7 = 35 \).
- Step 3: Write the result as a fraction: \( \frac{9}{35} \).
- Step 4: Simplify: \( \frac{9}{35} \) is already in its simplest form.

Answer: \( \frac{9}{35} \)

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#### 5. \( \frac{1}{2} \times \frac{3}{7} \)

- Step 1: Multiply the numerators: \( 1 \times 3 = 3 \).
- Step 2: Multiply the denominators: \( 2 \times 7 = 14 \).
- Step 3: Write the result as a fraction: \( \frac{3}{14} \).
- Step 4: Simplify: \( \frac{3}{14} \) is already in its simplest form.

Answer: \( \frac{3}{14} \)

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#### 6. \( \frac{1}{8} \times \frac{2}{9} \)

- Step 1: Multiply the numerators: \( 1 \times 2 = 2 \).
- Step 2: Multiply the denominators: \( 8 \times 9 = 72 \).
- Step 3: Write the result as a fraction: \( \frac{2}{72} \).
- Step 4: Simplify: The GCD of 2 and 72 is 2. Divide both numerator and denominator by 2:
\[
\frac{2 \div 2}{72 \div 2} = \frac{1}{36}
\]

Answer: \( \frac{1}{36} \)

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#### 7. \( \frac{2}{7} \times \frac{3}{4} \)

- Step 1: Multiply the numerators: \( 2 \times 3 = 6 \).
- Step 2: Multiply the denominators: \( 7 \times 4 = 28 \).
- Step 3: Write the result as a fraction: \( \frac{6}{28} \).
- Step 4: Simplify: The GCD of 6 and 28 is 2. Divide both numerator and denominator by 2:
\[
\frac{6 \div 2}{28 \div 2} = \frac{3}{14}
\]

Answer: \( \frac{3}{14} \)

---

#### 8. \( \frac{1}{3} \times \frac{1}{6} \)

- Step 1: Multiply the numerators: \( 1 \times 1 = 1 \).
- Step 2: Multiply the denominators: \( 3 \times 6 = 18 \).
- Step 3: Write the result as a fraction: \( \frac{1}{18} \).
- Step 4: Simplify: \( \frac{1}{18} \) is already in its simplest form.

Answer: \( \frac{1}{18} \)

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

- Step 1: Multiply the numerators: \( 1 \times 3 = 3 \).
- Step 2: Multiply the denominators: \( 7 \times 4 = 28 \).
- Step 3: Write the result as a fraction: \( \frac{3}{28} \).
- Step 4: Simplify: \( \frac{3}{28} \) is already in its simplest form.

Answer: \( \frac{3}{28} \)

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#### 10. \( \frac{3}{4} \times \frac{2}{5} \)

- Step 1: Multiply the numerators: \( 3 \times 2 = 6 \).
- Step 2: Multiply the denominators: \( 4 \times 5 = 20 \).
- Step 3: Write the result as a fraction: \( \frac{6}{20} \).
- Step 4: Simplify: The GCD of 6 and 20 is 2. Divide both numerator and denominator by 2:
\[
\frac{6 \div 2}{20 \div 2} = \frac{3}{10}
\]

Answer: \( \frac{3}{10} \)

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#### 11. \( \frac{1}{8} \times \frac{2}{3} \)

- Step 1: Multiply the numerators: \( 1 \times 2 = 2 \).
- Step 2: Multiply the denominators: \( 8 \times 3 = 24 \).
- Step 3: Write the result as a fraction: \( \frac{2}{24} \).
- Step 4: Simplify: The GCD of 2 and 24 is 2. Divide both numerator and denominator by 2:
\[
\frac{2 \div 2}{24 \div 2} = \frac{1}{12}
\]

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

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#### 12. \( \frac{4}{9} \times \frac{3}{7} \)

- Step 1: Multiply the numerators: \( 4 \times 3 = 12 \).
- Step 2: Multiply the denominators: \( 9 \times 7 = 63 \).
- Step 3: Write the result as a fraction: \( \frac{12}{63} \).
- Step 4: Simplify: The GCD of 12 and 63 is 3. Divide both numerator and denominator by 3:
\[
\frac{12 \div 3}{63 \div 3} = \frac{4}{21}
\]

Answer: \( \frac{4}{21} \)

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#### 13. \( \frac{3}{8} \times \frac{5}{6} \)

- Step 1: Multiply the numerators: \( 3 \times 5 = 15 \).
- Step 2: Multiply the denominators: \( 8 \times 6 = 48 \).
- Step 3: Write the result as a fraction: \( \frac{15}{48} \).
- Step 4: Simplify: The GCD of 15 and 48 is 3. Divide both numerator and denominator by 3:
\[
\frac{15 \div 3}{48 \div 3} = \frac{5}{16}
\]

Answer: \( \frac{5}{16} \)

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#### 14. \( \frac{2}{9} \times \frac{5}{7} \)

- Step 1: Multiply the numerators: \( 2 \times 5 = 10 \).
- Step 2: Multiply the denominators: \( 9 \times 7 = 63 \).
- Step 3: Write the result as a fraction: \( \frac{10}{63} \).
- Step 4: Simplify: \( \frac{10}{63} \) is already in its simplest form.

Answer: \( \frac{10}{63} \)

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#### 15. \( \frac{2}{3} \times \frac{5}{9} \)

- Step 1: Multiply the numerators: \( 2 \times 5 = 10 \).
- Step 2: Multiply the denominators: \( 3 \times 9 = 27 \).
- Step 3: Write the result as a fraction: \( \frac{10}{27} \).
- Step 4: Simplify: \( \frac{10}{27} \) is already in its simplest form.

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

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#### 16. \( \frac{3}{5} \times \frac{3}{7} \)

- Step 1: Multiply the numerators: \( 3 \times 3 = 9 \).
- Step 2: Multiply the denominators: \( 5 \times 7 = 35 \).
- Step 3: Write the result as a fraction: \( \frac{9}{35} \).
- Step 4: Simplify: \( \frac{9}{35} \) is already in its simplest form.

Answer: \( \frac{9}{35} \)

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#### 17. \( \frac{5}{9} \times \frac{2}{5} \)

- Step 1: Multiply the numerators: \( 5 \times 2 = 10 \).
- Step 2: Multiply the denominators: \( 9 \times 5 = 45 \).
- Step 3: Write the result as a fraction: \( \frac{10}{45} \).
- Step 4: Simplify: The GCD of 10 and 45 is 5. Divide both numerator and denominator by 5:
\[
\frac{10 \div 5}{45 \div 5} = \frac{2}{9}
\]

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

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#### 18. \( \frac{5}{12} \times \frac{1}{3} \)

- Step 1: Multiply the numerators: \( 5 \times 1 = 5 \).
- Step 2: Multiply the denominators: \( 12 \times 3 = 36 \).
- Step 3: Write the result as a fraction: \( \frac{5}{36} \).
- Step 4: Simplify: \( \frac{5}{36} \) is already in its simplest form.

Answer: \( \frac{5}{36} \)

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Final Answers:

\[
\boxed{
\begin{array}{lll}
1. & \frac{2}{15} & 2. \frac{5}{21} & 3. \frac{1}{3} \\
4. & \frac{9}{35} & 5. \frac{3}{14} & 6. \frac{1}{36} \\
7. & \frac{3}{14} & 8. \frac{1}{18} & 9. \frac{3}{28} \\
10. & \frac{3}{10} & 11. \frac{1}{12} & 12. \frac{4}{21} \\
13. & \frac{5}{16} & 14. \frac{10}{63} & 15. \frac{10}{27} \\
16. & \frac{9}{35} & 17. \frac{2}{9} & 18. \frac{5}{36}
\end{array}
}
\]