Worksheets for fraction multiplication - Free Printable

Let's solve each problem on the Fractions Worksheet step by step.

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Problem 1a:

$$
\frac{3}{4} \times 4\frac{7}{12}
$$

Step 1: Convert the mixed number to an improper fraction.
$$
4\frac{7}{12} = \frac{4 \times 12 + 7}{12} = \frac{48 + 7}{12} = \frac{55}{12}
$$

Step 2: Multiply the fractions:
$$
\frac{3}{4} \times \frac{55}{12} = \frac{3 \times 55}{4 \times 12} = \frac{165}{48}
$$

Step 3: Simplify the fraction.
Find GCF of 165 and 48:
- 165 = 3 × 5 × 11
- 48 = 2⁴ × 3
GCF = 3
$$
\frac{165 ÷ 3}{48 ÷ 3} = \frac{55}{16}
$$

Step 4: Convert to a mixed number:
$$
\frac{55}{16} = 3\frac{7}{16}
$$

✔ Answer: $ 3\frac{7}{16} $

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Problem 1b:

$$
4\frac{1}{2} \times \frac{1}{6}
$$

Step 1: Convert mixed number to improper fraction:
$$
4\frac{1}{2} = \frac{9}{2}
$$

Step 2: Multiply:
$$
\frac{9}{2} \times \frac{1}{6} = \frac{9}{12} = \frac{3}{4}
$$

✔ Answer: $ \frac{3}{4} $

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Problem 2a:

$$
\frac{2}{12} \times 8\frac{2}{3}
$$

Step 1: Simplify $ \frac{2}{12} $ → $ \frac{1}{6} $

Step 2: Convert mixed number:
$$
8\frac{2}{3} = \frac{26}{3}
$$

Step 3: Multiply:
$$
\frac{1}{6} \times \frac{26}{3} = \frac{26}{18} = \frac{13}{9}
$$

Step 4: Convert to mixed number:
$$
\frac{13}{9} = 1\frac{4}{9}
$$

✔ Answer: $ 1\frac{4}{9} $

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Problem 2b:

$$
\frac{2}{10} \times 6\frac{3}{4}
$$

Step 1: Simplify $ \frac{2}{10} $ → $ \frac{1}{5} $

Step 2: Convert mixed number:
$$
6\frac{3}{4} = \frac{27}{4}
$$

Step 3: Multiply:
$$
\frac{1}{5} \times \frac{27}{4} = \frac{27}{20}
$$

Step 4: Convert to mixed number:
$$
\frac{27}{20} = 1\frac{7}{20}
$$

✔ Answer: $ 1\frac{7}{20} $

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Problem 3a:

$$
\frac{1}{3} \times 6\frac{1}{4}
$$

Step 1: Convert mixed number:
$$
6\frac{1}{4} = \frac{25}{4}
$$

Step 2: Multiply:
$$
\frac{1}{3} \times \frac{25}{4} = \frac{25}{12}
$$

Step 3: Convert to mixed number:
$$
\frac{25}{12} = 2\frac{1}{12}
$$

✔ Answer: $ 2\frac{1}{12} $

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Problem 3b:

$$
\frac{1}{5} \times 5\frac{4}{7}
$$

Step 1: Convert mixed number:
$$
5\frac{4}{7} = \frac{39}{7}
$$

Step 2: Multiply:
$$
\frac{1}{5} \times \frac{39}{7} = \frac{39}{35}
$$

Step 3: Convert to mixed number:
$$
\frac{39}{35} = 1\frac{4}{35}
$$

✔ Answer: $ 1\frac{4}{35} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1a | $ 3\frac{7}{16} $ |
| 1b | $ \frac{3}{4} $ |
| 2a | $ 1\frac{4}{9} $ |
| 2b | $ 1\frac{7}{20} $ |
| 3a | $ 2\frac{1}{12} $ |
| 3b | $ 1\frac{4}{35} $ |

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🔍 Summary of Steps:

1. Convert mixed numbers to improper fractions.
2. Multiply numerators and denominators.
3. Simplify the result (reduce fraction).
4. Convert back to mixed number if needed.

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