Multiplication of Fractions Worksheet with 16 problems involving fractions and mixed numbers, ideal for math practice.

Let's solve each of these fraction multiplication problems step by step. The key steps are:

1. Convert any mixed numbers to improper fractions.
2. Multiply the numerators together and the denominators together.
3. Simplify the result, and convert back to a mixed number if needed.

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1. $\frac{3}{10} \times \frac{2}{10}$

$$
= \frac{3 \times 2}{10 \times 10} = \frac{6}{100} = \frac{3}{50}
$$

✔ Answer: $\boxed{\frac{3}{50}}$

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2. $2\frac{2}{3} \times 2\frac{2}{3}$

Convert mixed numbers:
- $2\frac{2}{3} = \frac{8}{3}$

Now multiply:
$$
\frac{8}{3} \times \frac{8}{3} = \frac{64}{9}
$$

Convert to mixed number:
$$
64 \div 9 = 7 \text{ R } 1 \Rightarrow 7\frac{1}{9}
$$

✔ Answer: $\boxed{7\frac{1}{9}}$

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3. $\frac{13}{20} \times 2\frac{5}{20}$

First simplify $2\frac{5}{20}$:
- $2\frac{5}{20} = 2\frac{1}{4} = \frac{9}{4}$ (since $5/20 = 1/4$)

Now multiply:
$$
\frac{13}{20} \times \frac{9}{4} = \frac{117}{80}
$$

Convert to mixed number:
$$
117 \div 80 = 1 \text{ R } 37 \Rightarrow 1\frac{37}{80}
$$

✔ Answer: $\boxed{1\frac{37}{80}}$

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4. $2\frac{2}{9} \times \frac{4}{9}$

Convert $2\frac{2}{9} = \frac{20}{9}$

Multiply:
$$
\frac{20}{9} \times \frac{4}{9} = \frac{80}{81}
$$

✔ Answer: $\boxed{\frac{80}{81}}$

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5. $\frac{3}{4} \times 2\frac{3}{4}$

Convert $2\frac{3}{4} = \frac{11}{4}$

Multiply:
$$
\frac{3}{4} \times \frac{11}{4} = \frac{33}{16}
$$

Convert to mixed number:
$$
33 \div 16 = 2 \text{ R } 1 \Rightarrow 2\frac{1}{16}
$$

✔ Answer: $\boxed{2\frac{1}{16}}$

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6. $2\frac{5}{8} \times 1\frac{4}{8}$

Simplify $1\frac{4}{8} = 1\frac{1}{2} = \frac{3}{2}$

Convert $2\frac{5}{8} = \frac{21}{8}$

Multiply:
$$
\frac{21}{8} \times \frac{3}{2} = \frac{63}{16}
$$

Convert to mixed number:
$$
63 \div 16 = 3 \text{ R } 15 \Rightarrow 3\frac{15}{16}
$$

✔ Answer: $\boxed{3\frac{15}{16}}$

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7. $2\frac{4}{25} \times \frac{20}{25}$

Convert $2\frac{4}{25} = \frac{54}{25}$

$\frac{20}{25} = \frac{4}{5}$ (simplified)

Now:
$$
\frac{54}{25} \times \frac{4}{5} = \frac{216}{125}
$$

Convert:
$$
216 \div 125 = 1 \text{ R } 91 \Rightarrow 1\frac{91}{125}
$$

✔ Answer: $\boxed{1\frac{91}{125}}$

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8. $\frac{1}{2} \times 1\frac{1}{2}$

$1\frac{1}{2} = \frac{3}{2}$

$$
\frac{1}{2} \times \frac{3}{2} = \frac{3}{4}
$$

✔ Answer: $\boxed{\frac{3}{4}}$

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9. $\frac{4}{12} \times 1\frac{10}{12}$

Simplify $\frac{4}{12} = \frac{1}{3}$

$1\frac{10}{12} = 1\frac{5}{6} = \frac{11}{6}$

Multiply:
$$
\frac{1}{3} \times \frac{11}{6} = \frac{11}{18}
$$

✔ Answer: $\boxed{\frac{11}{18}}$

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10. $2\frac{1}{6} \times 2\frac{4}{6}$

Simplify $2\frac{4}{6} = 2\frac{2}{3} = \frac{8}{3}$

$2\frac{1}{6} = \frac{13}{6}$

Multiply:
$$
\frac{13}{6} \times \frac{8}{3} = \frac{104}{18} = \frac{52}{9}
$$

Convert:
$$
52 \div 9 = 5 \text{ R } 7 \Rightarrow 5\frac{7}{9}
$$

✔ Answer: $\boxed{5\frac{7}{9}}$

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11. $2\frac{5}{15} \times 2\frac{5}{15}$

Simplify: $2\frac{5}{15} = 2\frac{1}{3} = \frac{7}{3}$

So:
$$
\frac{7}{3} \times \frac{7}{3} = \frac{49}{9}
$$

Convert:
$$
49 \div 9 = 5 \text{ R } 4 \Rightarrow 5\frac{4}{9}
$$

✔ Answer: $\boxed{5\frac{4}{9}}$

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12. $\frac{11}{15} \times 2\frac{7}{15}$

Convert $2\frac{7}{15} = \frac{37}{15}$

Multiply:
$$
\frac{11}{15} \times \frac{37}{15} = \frac{407}{225}
$$

Convert:
$$
407 \div 225 = 1 \text{ R } 182 \Rightarrow 1\frac{182}{225}
$$

✔ Answer: $\boxed{1\frac{182}{225}}$

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13. $1\frac{2}{25} \times \frac{6}{25}$

Convert $1\frac{2}{25} = \frac{27}{25}$

Multiply:
$$
\frac{27}{25} \times \frac{6}{25} = \frac{162}{625}
$$

✔ Answer: $\boxed{\frac{162}{625}}$

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14. $1\frac{1}{4} \times \frac{3}{4}$

Convert $1\frac{1}{4} = \frac{5}{4}$

Multiply:
$$
\frac{5}{4} \times \frac{3}{4} = \frac{15}{16}
$$

✔ Answer: $\boxed{\frac{15}{16}}$

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15. $1\frac{4}{16} \times 2\frac{6}{16}$

Simplify:
- $1\frac{4}{16} = 1\frac{1}{4} = \frac{5}{4}$
- $2\frac{6}{16} = 2\frac{3}{8} = \frac{19}{8}$

Multiply:
$$
\frac{5}{4} \times \frac{19}{8} = \frac{95}{32}
$$

Convert:
$$
95 \div 32 = 2 \text{ R } 31 \Rightarrow 2\frac{31}{32}
$$

✔ Answer: $\boxed{2\frac{31}{32}}$

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16. $1\frac{10}{12} \times 2\frac{9}{12}$

Simplify:
- $1\frac{10}{12} = 1\frac{5}{6} = \frac{11}{6}$
- $2\frac{9}{12} = 2\frac{3}{4} = \frac{11}{4}$

Multiply:
$$
\frac{11}{6} \times \frac{11}{4} = \frac{121}{24}
$$

Convert:
$$
121 \div 24 = 5 \text{ R } 1 \Rightarrow 5\frac{1}{24}
$$

✔ Answer: $\boxed{5\frac{1}{24}}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{3}{50}$ |
| 2 | $7\frac{1}{9}$ |
| 3 | $1\frac{37}{80}$ |
| 4 | $\frac{80}{81}$ |
| 5 | $2\frac{1}{16}$ |
| 6 | $3\frac{15}{16}$ |
| 7 | $1\frac{91}{125}$ |
| 8 | $\frac{3}{4}$ |
| 9 | $\frac{11}{18}$ |
| 10 | $5\frac{7}{9}$ |
| 11 | $5\frac{4}{9}$ |
| 12 | $1\frac{182}{225}$ |
| 13 | $\frac{162}{625}$ |
| 14 | $\frac{15}{16}$ |
| 15 | $2\frac{31}{32}$ |
| 16 | $5\frac{1}{24}$ |

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