Reducing Fractions Worksheets - Math Monks - Free Printable

Let's solve each of the fractions by reducing them to their lowest terms. This means we need to divide both the numerator and denominator by their greatest common divisor (GCD).

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🔹 Example:

$$
\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}
$$

We divide both top and bottom by 5, which is the GCD of 10 and 15.

Now let’s go through each problem:

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① $ \frac{5}{10} $

- GCD of 5 and 10 is 5
- $ \frac{5 \div 5}{10 \div 5} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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② $ \frac{8}{10} $

- GCD of 8 and 10 is 2
- $ \frac{8 \div 2}{10 \div 2} = \frac{4}{5} $

✔ Answer: $ \frac{4}{5} $

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③ $ \frac{6}{9} $

- GCD of 6 and 9 is 3
- $ \frac{6 \div 3}{9 \div 3} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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④ $ \frac{8}{12} $

- GCD of 8 and 12 is 4
- $ \frac{8 \div 4}{12 \div 4} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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⑤ $ \frac{12}{15} $

- GCD of 12 and 15 is 3
- $ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} $

✔ Answer: $ \frac{4}{5} $

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⑥ $ \frac{5}{15} $

- GCD of 5 and 15 is 5
- $ \frac{5 \div 5}{15 \div 5} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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⑦ $ \frac{9}{18} $

- GCD of 9 and 18 is 9
- $ \frac{9 \div 9}{18 \div 9} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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⑧ $ \frac{14}{21} $

- GCD of 14 and 21 is 7
- $ \frac{14 \div 7}{21 \div 7} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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⑨ $ \frac{12}{18} $

- GCD of 12 and 18 is 6
- $ \frac{12 \div 6}{18 \div 6} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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✔ Final Answers:

| Problem | Reduced Fraction |
|--------|------------------|
| ① | $ \frac{1}{2} $ |
| ② | $ \frac{4}{5} $ |
| ③ | $ \frac{2}{3} $ |
| ④ | $ \frac{2}{3} $ |
| ⑤ | $ \frac{4}{5} $ |
| ⑥ | $ \frac{1}{3} $ |
| ⑦ | $ \frac{1}{2} $ |
| ⑧ | $ \frac{2}{3} $ |
| ⑨ | $ \frac{2}{3} $ |

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📝 Tip:

To reduce a fraction:
1. Find the greatest common divisor (GCD) of the numerator and denominator.
2. Divide both numerator and denominator by that number.
3. The result is the simplified fraction.

Let me know if you'd like a visual explanation or practice with other fractions!