Multiplying and Dividing Fractions Worksheets with Answer Key - Free Printable

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 becomes multiplication by reciprocal:
- $\frac{5}{12} \div \frac{9}{10} = \frac{5}{12} \times \frac{10}{9} = \frac{5 \times 10}{12 \times 9} = \frac{50}{108}$
- 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 $\frac{21}{63} = \frac{1}{3}$
- Now: $\frac{9}{10} \times \frac{1}{3} = \frac{9}{30} = \frac{3}{10}$

✔ Answer: $\boxed{\frac{3}{10}}$

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④ $\frac{4}{3} \div \frac{20}{27}$

- Multiply by reciprocal: $\frac{4}{3} \times \frac{27}{20} = \frac{4 \times 27}{3 \times 20} = \frac{108}{60}$
- 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 $\frac{14}{33} \div \frac{56}{99}$

- Multiply by reciprocal: $\frac{14}{33} \times \frac{99}{56}$
- Simplify:
- 14 and 56: $14/56 = 1/4$
- 33 and 99: $99/33 = 3$, so $99/33 = 3$
- So: $\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}$? Wait — let's do it properly.

Better to cancel step-by-step:

$$
\frac{14}{33} \times \frac{99}{56} = \frac{14 \times 99}{33 \times 56}
$$

Now simplify:

- $14$ and $56$: $56 ÷ 14 = 4$, so reduce 14/56 → $1/4$
- $99$ and $33$: $99 ÷ 33 = 3$, so $99/33 = 3$

So now: $\frac{1 \times 3}{1 \times 4} = \frac{3}{4}$

Wait: Let’s write it clearly:

$$
\frac{14}{33} \times \frac{99}{56} = \frac{14 \times 99}{33 \times 56}
$$

Break down:

- $14 = 2 \times 7$
- $56 = 7 \times 8$
- $99 = 9 \times 11$
- $33 = 3 \times 11$

So:

$$
= \frac{(2 \times 7) \times (9 \times 11)}{(3 \times 11) \times (7 \times 8)} = \frac{2 \times 7 \times 9 \times 11}{3 \times 11 \times 7 \times 8}
$$

Cancel:
- 7 cancels
- 11 cancels
- 9 and 3: $9/3 = 3$
- So: $\frac{2 \times 3}{8} = \frac{6}{8} = \frac{3}{4}$

✔ 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: $\frac{8}{3} \times \frac{7}{32} = \frac{8 \times 7}{3 \times 32} = \frac{56}{96}$
- 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: $\frac{20 \times 11}{3 \times 9} = \frac{220}{27}$
- This is an improper fraction: $220 ÷ 27 = 8$ with remainder $4$, so $8\frac{4}{27}$

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

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⑧ $\frac{3}{9} \times \frac{7}{14}$

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

✔ 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 $\boxed{6\frac{2}{3}}$

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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: $\frac{3}{2} \div \frac{3}{5} = \frac{3}{2} \times \frac{5}{3} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2}$

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

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⑪ $\frac{17}{12} \div \frac{8}{16}$

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

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

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⑫ $\frac{5}{6} \times \frac{21}{5}$

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

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

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| ① | $\frac{5}{13}$ |
| ② | $\frac{25}{54}$ |
| ③ | $\frac{3}{10}$ |
| ④ | $\frac{9}{5}$ or $1\frac{4}{5}$ |
| 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 written on a printable answer sheet format!