Pin on Fractions - Free Printable

Here's the step-by-step solution to all 12 problems on the worksheet “Multiplication and Division of Fractions”.

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📌 General Rules:

- Multiplying fractions: Multiply numerators together, denominators together. Simplify if possible.
- Dividing fractions: Multiply by the reciprocal (flip the second fraction), then multiply as usual. Simplify.

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## ✔ Problem 1:
$\frac{2}{6} \times \frac{15}{13}$

- Multiply numerators: $2 \times 15 = 30$
- Multiply denominators: $6 \times 13 = 78$
→ $\frac{30}{78}$

- Simplify: Divide numerator and denominator by 6 → $\frac{5}{13}$

✔ Answer: $\boxed{\frac{5}{13}}$

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## ✔ Problem 2:
$\frac{10}{24} \div \frac{36}{40}$

- Flip the second fraction: $\frac{10}{24} \times \frac{40}{36}$

- Multiply: $\frac{10 \times 40}{24 \times 36} = \frac{400}{864}$

- Simplify: Divide numerator and denominator by 16 → $\frac{25}{54}$

✔ Answer: $\boxed{\frac{25}{54}}$

*(Note: GCF of 400 and 864 is 16 → 400 ÷ 16 = 25, 864 ÷ 16 = 54)*

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## ✔ Problem 3:
$\frac{9}{10} \times \frac{21}{63}$

- Notice: $\frac{21}{63} = \frac{1}{3}$ (simplify first!)

→ $\frac{9}{10} \times \frac{1}{3} = \frac{9 \times 1}{10 \times 3} = \frac{9}{30}$

- Simplify: Divide by 3 → $\frac{3}{10}$

✔ Answer: $\boxed{\frac{3}{10}}$

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## ✔ Problem 4:
$\frac{4}{3} \div \frac{20}{27}$

- Flip: $\frac{4}{3} \times \frac{27}{20}$

- Multiply: $\frac{4 \times 27}{3 \times 20} = \frac{108}{60}$

- Simplify: Divide by 12 → $\frac{9}{5}$ or $1\frac{4}{5}$

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

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## ✔ Problem 5:
$\frac{14}{33} \div \frac{56}{99}$

- Flip: $\frac{14}{33} \times \frac{99}{56}$

- Cross-simplify before multiplying:

- 14 and 56 → 14 ÷ 14 = 1, 56 ÷ 14 = 4
- 33 and 99 → 99 ÷ 33 = 3, 33 ÷ 33 = 1

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

✔ Answer: $\boxed{\frac{3}{4}}$

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## ✔ Problem 6:
$\frac{8}{3} \times \frac{14}{64}$

- Simplify before multiplying:

- 8 and 64 → 8 ÷ 8 = 1, 64 ÷ 8 = 8
- 14 and 3 → no common factors

→ $\frac{1}{3} \times \frac{14}{8} = \frac{14}{24}$

- Simplify: Divide by 2 → $\frac{7}{12}$

✔ Answer: $\boxed{\frac{7}{12}}$

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## ✔ Problem 7:
$\frac{20}{3} \times \frac{11}{9}$

- Multiply: $\frac{20 \times 11}{3 \times 9} = \frac{220}{27}$

- Already simplified (220 and 27 share no common factors)

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

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## ✔ Problem 8:
$\frac{3}{9} \times \frac{7}{14}$

- Simplify each fraction first:

- $\frac{3}{9} = \frac{1}{3}$
- $\frac{7}{14} = \frac{1}{2}$

→ $\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

✔ Answer: $\boxed{\frac{1}{6}}$

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## ✔ Problem 9:
$\frac{5}{3} \div \frac{2}{8}$

- Flip: $\frac{5}{3} \times \frac{8}{2}$

- Simplify: $\frac{8}{2} = 4$, so → $\frac{5}{3} \times 4 = \frac{20}{3}$

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

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## ✔ Problem 10:
$\frac{6}{4} \div \frac{9}{15}$

- Flip: $\frac{6}{4} \times \frac{15}{9}$

- Simplify before multiplying:

- $\frac{6}{4} = \frac{3}{2}$
- $\frac{15}{9} = \frac{5}{3}$

→ $\frac{3}{2} \times \frac{5}{3} = \frac{15}{6}$

- Simplify: Divide by 3 → $\frac{5}{2}$

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

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## ✔ Problem 11:
$\frac{17}{12} \div \frac{8}{16}$

- Flip: $\frac{17}{12} \times \frac{16}{8}$

- Simplify: $\frac{16}{8} = 2$

→ $\frac{17}{12} \times 2 = \frac{34}{12}$

- Simplify: Divide by 2 → $\frac{17}{6}$

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

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## ✔ Problem 12:
$\frac{5}{6} \times \frac{21}{5}$

- Cancel 5 in numerator and denominator:
→ $\frac{1}{6} \times \frac{21}{1} = \frac{21}{6}$

- Simplify: Divide by 3 → $\frac{7}{2}$

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

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## 🎉 Final Answers Summary:

| 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 | $\frac{220}{27}$ |
| ⑧ | $\frac{1}{6}$ |
| ⑨ | $\frac{20}{3}$ |
| ⑩ | $\frac{5}{2}$ |
| ⑪ | $\frac{17}{6}$ |
| ⑫ | $\frac{7}{2}$ |

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