Multiplying Fractions Worksheets with Answer Key - Free Printable

Let's solve each of these fraction multiplication problems using cross canceling (also known as simplifying before multiplying). This method involves reducing the fractions by dividing common factors across the numerator and denominator before multiplying.

We'll go step-by-step for each problem, showing cross-canceling and then multiplying.

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1. $ \frac{2}{12} \times \frac{3}{6} $

- Cross-cancel:
- 2 and 6: both divisible by 2 → $ \frac{1}{12} \times \frac{3}{3} $
- 3 and 12: both divisible by 3 → $ \frac{1}{4} \times \frac{1}{3} $
- Now multiply: $ \frac{1}{4} \times \frac{1}{3} = \frac{1}{12} $

✔ Answer: $ \boxed{\frac{1}{12}} $

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2. $ \frac{5}{6} \times \frac{12}{20} $

- Cross-cancel:
- 6 and 12: divisible by 6 → $ \frac{5}{1} \times \frac{2}{20} $
- But better: 6 and 12 → divide by 6 → $ \frac{5}{1} \times \frac{2}{20} $
- Wait, let’s do it properly:
- 6 and 12 → GCF is 6 → $ \frac{5}{1} \times \frac{2}{20} $ → but 5 and 20? Yes!
- 5 and 20 → GCF is 5 → $ \frac{1}{1} \times \frac{2}{4} $
- So now: $ \frac{1}{1} \times \frac{2}{4} = \frac{2}{4} = \frac{1}{2} $

Wait — let's rework this clearly:

Original: $ \frac{5}{6} \times \frac{12}{20} $

- 5 and 20: both divisible by 5 → $ \frac{1}{6} \times \frac{12}{4} $
- 6 and 12: divisible by 6 → $ \frac{1}{1} \times \frac{2}{4} $
- Then $ \frac{2}{4} = \frac{1}{2} $

✔ Answer: $ \boxed{\frac{1}{2}} $

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3. $ \frac{4}{10} \times \frac{6}{9} $

- Cross-cancel:
- 4 and 6: GCF is 2 → $ \frac{2}{10} \times \frac{3}{9} $
- 2 and 10 → GCF is 2 → $ \frac{1}{5} \times \frac{3}{9} $
- 3 and 9 → GCF is 3 → $ \frac{1}{5} \times \frac{1}{3} $
- Multiply: $ \frac{1}{5} \times \frac{1}{3} = \frac{1}{15} $

✔ Answer: $ \boxed{\frac{1}{15}} $

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4. $ \frac{8}{21} \times \frac{14}{4} $

- Cross-cancel:
- 8 and 4: GCF is 4 → $ \frac{2}{21} \times \frac{14}{1} $
- 2 and 14: GCF is 2 → $ \frac{1}{21} \times \frac{7}{1} $
- 7 and 21: GCF is 7 → $ \frac{1}{3} \times \frac{1}{1} $
- Multiply: $ \frac{1}{3} $

✔ Answer: $ \boxed{\frac{1}{3}} $

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5. $ \frac{2}{10} \times \frac{20}{8} $

- Cross-cancel:
- 2 and 8: GCF is 2 → $ \frac{1}{10} \times \frac{20}{4} $
- 10 and 20: GCF is 10 → $ \frac{1}{1} \times \frac{2}{4} $
- 2 and 4: GCF is 2 → $ \frac{1}{1} \times \frac{1}{2} $
- Result: $ \frac{1}{2} $

✔ Answer: $ \boxed{\frac{1}{2}} $

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6. $ \frac{5}{12} \times \frac{9}{20} $

- Cross-cancel:
- 5 and 20: GCF is 5 → $ \frac{1}{12} \times \frac{9}{4} $
- 9 and 12: GCF is 3 → $ \frac{1}{4} \times \frac{3}{4} $
- Multiply: $ \frac{1}{4} \times \frac{3}{4} = \frac{3}{16} $

✔ Answer: $ \boxed{\frac{3}{16}} $

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

- Cross-cancel:
- 4 and 20: GCF is 4 → $ \frac{1}{5} \times \frac{4}{7} $
- No more common factors
- Multiply: $ \frac{1}{5} \times \frac{4}{7} = \frac{4}{35} $

✔ Answer: $ \boxed{\frac{4}{35}} $

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8. $ \frac{18}{21} \times \frac{7}{4} $

- Cross-cancel:
- 18 and 4: GCF is 2 → $ \frac{9}{21} \times \frac{7}{2} $
- 9 and 21: GCF is 3 → $ \frac{3}{7} \times \frac{7}{2} $
- 7 and 7: cancel → $ \frac{3}{1} \times \frac{1}{2} $
- Multiply: $ \frac{3}{2} $

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

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9. $ \frac{4}{6} \times \frac{3}{5} $

- Cross-cancel:
- 4 and 6: GCF is 2 → $ \frac{2}{3} \times \frac{3}{5} $
- 3 and 3: cancel → $ \frac{2}{1} \times \frac{1}{5} $
- Multiply: $ \frac{2}{5} $

✔ Answer: $ \boxed{\frac{2}{5}} $

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10. $ \frac{3}{11} \times \frac{22}{9} $

- Cross-cancel:
- 3 and 9: GCF is 3 → $ \frac{1}{11} \times \frac{22}{3} $
- 11 and 22: GCF is 11 → $ \frac{1}{1} \times \frac{2}{3} $
- Multiply: $ \frac{2}{3} $

✔ Answer: $ \boxed{\frac{2}{3}} $

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11. $ \frac{8}{12} \times \frac{4}{7} $

- Cross-cancel:
- 8 and 12: GCF is 4 → $ \frac{2}{3} \times \frac{4}{7} $
- No common factors between 2 and 3, 4 and 7
- Multiply: $ \frac{2 \times 4}{3 \times 7} = \frac{8}{21} $

✔ Answer: $ \boxed{\frac{8}{21}} $

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12. $ \frac{6}{12} \times \frac{18}{30} $

- Cross-cancel:
- 6 and 12: GCF is 6 → $ \frac{1}{2} \times \frac{18}{30} $
- 18 and 30: GCF is 6 → $ \frac{1}{2} \times \frac{3}{5} $
- Multiply: $ \frac{1 \times 3}{2 \times 5} = \frac{3}{10} $

✔ Answer: $ \boxed{\frac{3}{10}} $

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✔ Final Answers:

1. $ \frac{1}{12} $
2. $ \frac{1}{2} $
3. $ \frac{1}{15} $
4. $ \frac{1}{3} $
5. $ \frac{1}{2} $
6. $ \frac{3}{16} $
7. $ \frac{4}{35} $
8. $ \frac{3}{2} $
9. $ \frac{2}{5} $
10. $ \frac{2}{3} $
11. $ \frac{8}{21} $
12. $ \frac{3}{10} $

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Let me know if you'd like a visual version with arrows showing cross-canceling!