Multiplying Fractions with Cross Cancelling Worksheet | Free ... - Free Printable

Let's solve each of these fraction multiplication problems using cross cancelling (also known as simplifying before multiplying). Cross cancelling helps reduce fractions before you multiply, making the computation easier.

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1) $ \frac{3}{8} \times \frac{7}{6} $

- No common factors between numerator and denominator across the fractions.
- Multiply directly:
$$
\frac{3 \times 7}{8 \times 6} = \frac{21}{48}
$$
- Simplify: Divide numerator and denominator by 3 → $ \frac{7}{16} $

✔ Answer: $ \boxed{\frac{7}{16}} $

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2) $ \frac{2}{5} \times \frac{5}{7} $

- Cancel 5 in numerator of second fraction with 5 in denominator of first:
$$
\frac{2}{\cancel{5}} \times \frac{\cancel{5}}{7} = \frac{2}{1} \times \frac{1}{7} = \frac{2}{7}
$$

✔ Answer: $ \boxed{\frac{2}{7}} $

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3) $ \frac{3}{5} \times \frac{1}{3} $

- Cancel 3 in numerator and denominator:
$$
\frac{\cancel{3}}{5} \times \frac{1}{\cancel{3}} = \frac{1}{5} \times \frac{1}{1} = \frac{1}{5}
$$

✔ Answer: $ \boxed{\frac{1}{5}} $

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4) $ \frac{3}{4} \times \frac{2}{7} $

- No common factors to cancel.
- Multiply:
$$
\frac{3 \times 2}{4 \times 7} = \frac{6}{28}
$$
- Simplify: divide by 2 → $ \frac{3}{14} $

✔ Answer: $ \boxed{\frac{3}{14}} $

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5) $ \frac{2}{3} \times \frac{1}{2} $

- Cancel 2 in numerator and denominator:
$$
\frac{\cancel{2}}{3} \times \frac{1}{\cancel{2}} = \frac{1}{3} \times \frac{1}{1} = \frac{1}{3}
$$

✔ Answer: $ \boxed{\frac{1}{3}} $

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6) $ \frac{7}{8} \times \frac{2}{5} $

- No common factors.
- Multiply:
$$
\frac{7 \times 2}{8 \times 5} = \frac{14}{40}
$$
- Simplify: divide by 2 → $ \frac{7}{20} $

✔ Answer: $ \boxed{\frac{7}{20}} $

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7) $ \frac{6}{7} \times \frac{7}{10} $

- Cancel 7 in numerator and denominator:
$$
\frac{6}{\cancel{7}} \times \frac{\cancel{7}}{10} = \frac{6}{1} \times \frac{1}{10} = \frac{6}{10} = \frac{3}{5}
$$

✔ Answer: $ \boxed{\frac{3}{5}} $

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8) $ \frac{2}{9} \times \frac{3}{8} $

- Cancel 3 and 9: 9 ÷ 3 = 3, so:
$$
\frac{2}{\cancel{9}^3} \times \frac{\cancel{3}}{8} = \frac{2}{3} \times \frac{1}{8} = \frac{2}{24} = \frac{1}{12}
$$

✔ Answer: $ \boxed{\frac{1}{12}} $

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9) $ \frac{3}{4} \times \frac{4}{9} $

- Cancel 4 in numerator and denominator:
$$
\frac{3}{\cancel{4}} \times \frac{\cancel{4}}{9} = \frac{3}{1} \times \frac{1}{9} = \frac{3}{9} = \frac{1}{3}
$$

✔ Answer: $ \boxed{\frac{1}{3}} $

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10) $ \frac{2}{50} \times \frac{5}{18} $

- Simplify $ \frac{2}{50} = \frac{1}{25} $
- Now: $ \frac{1}{25} \times \frac{5}{18} $
- Cancel 5 and 25: 25 ÷ 5 = 5
$$
\frac{1}{\cancel{25}^5} \times \frac{\cancel{5}}{18} = \frac{1}{5} \times \frac{1}{18} = \frac{1}{90}
$$

✔ Answer: $ \boxed{\frac{1}{90}} $

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11) $ \frac{9}{24} \times \frac{6}{90} $

- Simplify both fractions:
- $ \frac{9}{24} = \frac{3}{8} $
- $ \frac{6}{90} = \frac{1}{15} $
- Now: $ \frac{3}{8} \times \frac{1}{15} = \frac{3}{120} = \frac{1}{40} $

Alternatively, cross-cancel:
- 9 and 90: 9/9 = 1, 90/9 = 10
- 6 and 24: 6/6 = 1, 24/6 = 4
- So:
$$
\frac{9}{24} \times \frac{6}{90} = \frac{1}{4} \times \frac{1}{10} = \frac{1}{40}
$$

✔ Answer: $ \boxed{\frac{1}{40}} $

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12) $ \frac{2}{45} \times \frac{9}{20} $

- Cancel 9 and 45: 45 ÷ 9 = 5, so:
$$
\frac{2}{\cancel{45}^5} \times \frac{\cancel{9}}{20} = \frac{2}{5} \times \frac{1}{20} = \frac{2}{100} = \frac{1}{50}
$$

✔ Answer: $ \boxed{\frac{1}{50}} $

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13) $ \frac{5}{6} \times \frac{8}{7} $

- No common factors.
- Multiply:
$$
\frac{5 \times 8}{6 \times 7} = \frac{40}{42}
$$
- Simplify: divide by 2 → $ \frac{20}{21} $

✔ Answer: $ \boxed{\frac{20}{21}} $

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14) $ 2\frac{1}{2} \times \frac{1}{10} $

- Convert mixed number: $ 2\frac{1}{2} = \frac{5}{2} $
- Now: $ \frac{5}{2} \times \frac{1}{10} $
- Cancel 5 and 10: 10 ÷ 5 = 2
$$
\frac{\cancel{5}}{2} \times \frac{1}{\cancel{10}^2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
$$

✔ Answer: $ \boxed{\frac{1}{4}} $

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15) $ \frac{3}{2} \times \frac{5}{6} $

- No common factors.
- Multiply:
$$
\frac{3 \times 5}{2 \times 6} = \frac{15}{12}
$$
- Simplify: divide by 3 → $ \frac{5}{4} $ or $ 1\frac{1}{4} $

But question says "improper fraction if necessary" → keep as improper.

✔ Answer: $ \boxed{\frac{5}{4}} $

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16) $ 2\frac{4}{7} \times \frac{1}{10} $

- Convert: $ 2\frac{4}{7} = \frac{18}{7} $
- Multiply: $ \frac{18}{7} \times \frac{1}{10} = \frac{18}{70} $
- Simplify: divide by 2 → $ \frac{9}{35} $

✔ Answer: $ \boxed{\frac{9}{35}} $

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17) $ \frac{7}{9} \times \frac{15}{4} $

- Cancel 3 from 15 and 9:
- 15 ÷ 3 = 5, 9 ÷ 3 = 3
- So:
$$
\frac{7}{\cancel{9}^3} \times \frac{\cancel{15}^5}{4} = \frac{7}{3} \times \frac{5}{4} = \frac{35}{12}
$$
- This is already simplified. As improper fraction: $ \frac{35}{12} $

✔ Answer: $ \boxed{\frac{35}{12}} $

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18) $ \frac{5}{2} \times 3\frac{3}{5} $

- Convert mixed number: $ 3\frac{3}{5} = \frac{18}{5} $
- Multiply: $ \frac{5}{2} \times \frac{18}{5} $
- Cancel 5 in numerator and denominator:
$$
\frac{\cancel{5}}{2} \times \frac{18}{\cancel{5}} = \frac{1}{2} \times \frac{18}{1} = \frac{18}{2} = 9
$$

✔ Answer: $ \boxed{9} $

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## ✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{7}{16} $ |
| 2 | $ \frac{2}{7} $ |
| 3 | $ \frac{1}{5} $ |
| 4 | $ \frac{3}{14} $ |
| 5 | $ \frac{1}{3} $ |
| 6 | $ \frac{7}{20} $ |
| 7 | $ \frac{3}{5} $ |
| 8 | $ \frac{1}{12} $ |
| 9 | $ \frac{1}{3} $ |
| 10 | $ \frac{1}{90} $ |
| 11 | $ \frac{1}{40} $ |
| 12 | $ \frac{1}{50} $ |
| 13 | $ \frac{20}{21} $ |
| 14 | $ \frac{1}{4} $ |
| 15 | $ \frac{5}{4} $ |
| 16 | $ \frac{9}{35} $ |
| 17 | $ \frac{35}{12} $ |
| 18 | $ 9 $ |

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