Multiplication and Division of Fractions worksheet with 12 problems for practice.

Let's solve each of the 12 problems step by step. We'll handle multiplication and division of fractions, simplifying where possible.

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① $\frac{2}{6} \times \frac{15}{13}$

- Simplify $\frac{2}{6} = \frac{1}{3}$
- Now: $\frac{1}{3} \times \frac{15}{13} = \frac{1 \times 15}{3 \times 13} = \frac{15}{39}$
- Simplify: $\frac{15}{39} = \frac{5}{13}$ (divide numerator and denominator by 3)

✔ Answer: $\boxed{\frac{5}{13}}$

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② $\frac{10}{24} \div \frac{36}{40}$

- First simplify both fractions:
- $\frac{10}{24} = \frac{5}{12}$
- $\frac{36}{40} = \frac{9}{10}$
- Division: $\frac{5}{12} \div \frac{9}{10} = \frac{5}{12} \times \frac{10}{9} = \frac{50}{108}$
- Simplify: divide numerator and denominator by 2 → $\frac{25}{54}$

✔ Answer: $\boxed{\frac{25}{54}}$

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③ $\frac{9}{10} \times \frac{21}{63}$

- Simplify $\frac{21}{63} = \frac{1}{3}$
- So: $\frac{9}{10} \times \frac{1}{3} = \frac{9}{30} = \frac{3}{10}$

✔ Answer: $\boxed{\frac{3}{10}}$

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④ $\frac{4}{3} \div \frac{20}{27}$

- Invert and multiply: $\frac{4}{3} \times \frac{27}{20} = \frac{4 \times 27}{3 \times 20} = \frac{108}{60}$
- Simplify: divide numerator and denominator by 12 → $\frac{9}{5}$

✔ Answer: $\boxed{\frac{9}{5}}$ or $1\frac{4}{5}$

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⑤ $\frac{14}{33} \div \frac{56}{99}$

- Invert and multiply: $\frac{14}{33} \times \frac{99}{56}$
- Simplify:
- 14 and 56: $14 \div 14 = 1$, $56 \div 14 = 4$
- 33 and 99: $33 \div 33 = 1$, $99 \div 33 = 3$
- So: $\frac{1}{1} \times \frac{3}{4} = \frac{3}{4}$

✔ Answer: $\boxed{\frac{3}{4}}$

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⑥ $\frac{8}{3} \times \frac{14}{64}$

- Simplify $\frac{14}{64} = \frac{7}{32}$
- Now: $\frac{8}{3} \times \frac{7}{32} = \frac{56}{96}$
- Simplify: divide numerator and denominator by 8 → $\frac{7}{12}$

✔ Answer: $\boxed{\frac{7}{12}}$

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⑦ $\frac{20}{3} \times \frac{11}{9}$

- Multiply: $\frac{20 \times 11}{3 \times 9} = \frac{220}{27}$
- Convert to mixed number: $220 \div 27 = 8$ remainder $4$, so $8\frac{4}{27}$

✔ Answer: $\boxed{\frac{220}{27}}$ or $8\frac{4}{27}$

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⑧ $\frac{3}{9} \times \frac{7}{14}$

- Simplify:
- $\frac{3}{9} = \frac{1}{3}$
- $\frac{7}{14} = \frac{1}{2}$
- So: $\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

✔ Answer: $\boxed{\frac{1}{6}}$

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⑨ $\frac{5}{3} \div \frac{2}{8}$

- Simplify $\frac{2}{8} = \frac{1}{4}$
- Now: $\frac{5}{3} \div \frac{1}{4} = \frac{5}{3} \times \frac{4}{1} = \frac{20}{3}$
- As mixed number: $6\frac{2}{3}$

✔ Answer: $\boxed{\frac{20}{3}}$ or $6\frac{2}{3}$

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⑩ $\frac{6}{4} \div \frac{9}{15}$

- Simplify:
- $\frac{6}{4} = \frac{3}{2}$
- $\frac{9}{15} = \frac{3}{5}$
- Now: $\frac{3}{2} \div \frac{3}{5} = \frac{3}{2} \times \frac{5}{3} = \frac{15}{6} = \frac{5}{2}$
- Or $2\frac{1}{2}$

✔ Answer: $\boxed{\frac{5}{2}}$ or $2\frac{1}{2}$

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⑪ $\frac{17}{12} \div \frac{8}{16}$

- Simplify $\frac{8}{16} = \frac{1}{2}$
- Now: $\frac{17}{12} \div \frac{1}{2} = \frac{17}{12} \times \frac{2}{1} = \frac{34}{12} = \frac{17}{6}$
- Mixed number: $2\frac{5}{6}$

✔ Answer: $\boxed{\frac{17}{6}}$ or $2\frac{5}{6}$

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⑫ $\frac{5}{6} \times \frac{21}{5}$

- Cancel common factors:
- 5 in numerator and denominator cancel
- So: $\frac{1}{6} \times \frac{21}{1} = \frac{21}{6} = \frac{7}{2}$
- Or $3\frac{1}{2}$

✔ Answer: $\boxed{\frac{7}{2}}$ or $3\frac{1}{2}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| ① | $\frac{5}{13}$ |
| ② | $\frac{25}{54}$ |
| ③ | $\frac{3}{10}$ |
| ④ | $\frac{9}{5}$ |
| ⑤ | $\frac{3}{4}$ |
| ⑥ | $\frac{7}{12}$ |
| ⑦ | $\frac{220}{27}$ or $8\frac{4}{27}$ |
| ⑧ | $\frac{1}{6}$ |
| ⑨ | $\frac{20}{3}$ or $6\frac{2}{3}$ |
| ⑩ | $\frac{5}{2}$ or $2\frac{1}{2}$ |
| ⑪ | $\frac{17}{6}$ or $2\frac{5}{6}$ |
| ⑫ | $\frac{7}{2}$ or $3\frac{1}{2}$ |

Let me know if you'd like these answers formatted neatly for printing!