Multiplying Fractions Worksheets - Free Printable

Problem: Multiplying Fractions and Mixed Numbers

The task is to solve each multiplication problem involving fractions and mixed numbers, and write the answers in simplest form. Let's solve each part step by step.

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

1. Multiply the numerators: \( 1 \times 2 = 2 \).
2. Multiply the denominators: \( 8 \times 3 = 24 \).
3. The product is \( \frac{2}{24} \).
4. Simplify \( \frac{2}{24} \) by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{2 \div 2}{24 \div 2} = \frac{1}{12}
\]

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

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#### b. \( \frac{3}{5} \times \frac{10}{21} \)

1. Multiply the numerators: \( 3 \times 10 = 30 \).
2. Multiply the denominators: \( 5 \times 21 = 105 \).
3. The product is \( \frac{30}{105} \).
4. Simplify \( \frac{30}{105} \) by finding the GCD of 30 and 105, which is 15:
\[
\frac{30 \div 15}{105 \div 15} = \frac{2}{7}
\]

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

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

1. Multiply the numerators: \( 4 \times 3 = 12 \).
2. Multiply the denominators: \( 5 \times 6 = 30 \).
3. The product is \( \frac{12}{30} \).
4. Simplify \( \frac{12}{30} \) by finding the GCD of 12 and 30, which is 6:
\[
\frac{12 \div 6}{30 \div 6} = \frac{2}{5}
\]

Answer: \( \frac{2}{5} \)

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

1. Write 3 as a fraction: \( 3 = \frac{3}{1} \).
2. Multiply the numerators: \( 4 \times 3 = 12 \).
3. Multiply the denominators: \( 5 \times 1 = 5 \).
4. The product is \( \frac{12}{5} \).
5. Since \( \frac{12}{5} \) is an improper fraction, convert it to a mixed number:
\[
\frac{12}{5} = 2 \frac{2}{5}
\]

Answer: \( 2 \frac{2}{5} \)

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#### e. \( \frac{8}{9} \times 1 \frac{1}{4} \)

1. Convert the mixed number \( 1 \frac{1}{4} \) to an improper fraction:
\[
1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4}
\]
2. Multiply the fractions:
- Numerators: \( 8 \times 5 = 40 \).
- Denominators: \( 9 \times 4 = 36 \).
- The product is \( \frac{40}{36} \).
3. Simplify \( \frac{40}{36} \) by finding the GCD of 40 and 36, which is 4:
\[
\frac{40 \div 4}{36 \div 4} = \frac{10}{9}
\]
4. Convert \( \frac{10}{9} \) to a mixed number:
\[
\frac{10}{9} = 1 \frac{1}{9}
\]

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

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#### f. \( \frac{1}{8} \times 4 \frac{2}{3} \)

1. Convert the mixed number \( 4 \frac{2}{3} \) to an improper fraction:
\[
4 \frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{14}{3}
\]
2. Multiply the fractions:
- Numerators: \( 1 \times 14 = 14 \).
- Denominators: \( 8 \times 3 = 24 \).
- The product is \( \frac{14}{24} \).
3. Simplify \( \frac{14}{24} \) by finding the GCD of 14 and 24, which is 2:
\[
\frac{14 \div 2}{24 \div 2} = \frac{7}{12}
\]

Answer: \( \frac{7}{12} \)

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#### g. \( 5 \frac{1}{3} \times 2 \frac{1}{4} \)

1. Convert both mixed numbers to improper fractions:
- \( 5 \frac{1}{3} = \frac{3 \times 5 + 1}{3} = \frac{16}{3} \).
- \( 2 \frac{1}{4} = \frac{4 \times 2 + 1}{4} = \frac{9}{4} \).
2. Multiply the fractions:
- Numerators: \( 16 \times 9 = 144 \).
- Denominators: \( 3 \times 4 = 12 \).
- The product is \( \frac{144}{12} \).
3. Simplify \( \frac{144}{12} \):
\[
\frac{144 \div 12}{12 \div 12} = 12
\]

Answer: \( 12 \)

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#### h. \( 20 \times 3 \frac{1}{5} \)

1. Convert the mixed number \( 3 \frac{1}{5} \) to an improper fraction:
\[
3 \frac{1}{5} = \frac{5 \times 3 + 1}{5} = \frac{16}{5}
\]
2. Multiply:
- \( 20 \times \frac{16}{5} = \frac{20 \times 16}{5} = \frac{320}{5} \).
3. Simplify \( \frac{320}{5} \):
\[
\frac{320 \div 5}{5 \div 5} = 64
\]

Answer: \( 64 \)

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#### i. \( \frac{1}{4} \times 9 \frac{1}{2} \)

1. Convert the mixed number \( 9 \frac{1}{2} \) to an improper fraction:
\[
9 \frac{1}{2} = \frac{2 \times 9 + 1}{2} = \frac{19}{2}
\]
2. Multiply the fractions:
- Numerators: \( 1 \times 19 = 19 \).
- Denominators: \( 4 \times 2 = 8 \).
- The product is \( \frac{19}{8} \).
3. Convert \( \frac{19}{8} \) to a mixed number:
\[
\frac{19}{8} = 2 \frac{3}{8}
\]

Answer: \( 2 \frac{3}{8} \)

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

1. Convert both mixed numbers to improper fractions:
- \( 2 \frac{1}{3} = \frac{3 \times 2 + 1}{3} = \frac{7}{3} \).
2. Multiply the fractions:
- Numerators: \( 7 \times 7 = 49 \).
- Denominators: \( 3 \times 3 = 9 \).
- The product is \( \frac{49}{9} \).
3. Convert \( \frac{49}{9} \) to a mixed number:
\[
\frac{49}{9} = 5 \frac{4}{9}
\]

Answer: \( 5 \frac{4}{9} \)

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

1. Convert both mixed numbers to improper fractions:
- \( 5 \frac{1}{3} = \frac{3 \times 5 + 1}{3} = \frac{16}{3} \).
- \( 1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2} \).
2. Multiply the fractions:
- Numerators: \( 16 \times 3 = 48 \).
- Denominators: \( 3 \times 2 = 6 \).
- The product is \( \frac{48}{6} \).
3. Simplify \( \frac{48}{6} \):
\[
\frac{48 \div 6}{6 \div 6} = 8
\]

Answer: \( 8 \)

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

1. Convert both mixed numbers to improper fractions:
- \( 3 \frac{1}{2} = \frac{2 \times 3 + 1}{2} = \frac{7}{2} \).
- \( 1 \frac{2}{7} = \frac{7 \times 1 + 2}{7} = \frac{9}{7} \).
2. Multiply the fractions:
- Numerators: \( 7 \times 9 = 63 \).
- Denominators: \( 2 \times 7 = 14 \).
- The product is \( \frac{63}{14} \).
3. Simplify \( \frac{63}{14} \) by finding the GCD of 63 and 14, which is 7:
\[
\frac{63 \div 7}{14 \div 7} = \frac{9}{2}
\]
4. Convert \( \frac{9}{2} \) to a mixed number:
\[
\frac{9}{2} = 4 \frac{1}{2}
\]

Answer: \( 4 \frac{1}{2} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{a. } \frac{1}{12} & \text{b. } \frac{2}{7} \\
\text{c. } \frac{2}{5} & \text{d. } 2 \frac{2}{5} \\
\text{e. } 1 \frac{1}{9} & \text{f. } \frac{7}{12} \\
\text{g. } 12 & \text{h. } 64 \\
\text{i. } 2 \frac{3}{8} & \text{j. } 5 \frac{4}{9} \\
\text{k. } 8 & \text{l. } 4 \frac{1}{2}
\end{array}
}
\]