Simplifying Fractions Worksheets - Math Monks - Free Printable

Let's solve each of the fractions on the Reducing Fractions Worksheet by simplifying them to their lowest terms. We'll do this by finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by that number.

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🔹 Problem 1:

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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🔹 Problem 2:

2. $ \frac{24}{6} $
- This is an improper fraction. Divide: $ 24 \div 6 = 4 $
- So, $ \frac{24}{6} = 4 $

✔ Answer: $ 4 $

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🔹 Problem 3:

3. $ \frac{2}{12} $
- GCD of 2 and 12 is 2
- $ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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🔹 Problem 4:

4. $ \frac{5}{50} $
- GCD of 5 and 50 is 5
- $ \frac{5 \div 5}{50 \div 5} = \frac{1}{10} $

✔ Answer: $ \frac{1}{10} $

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🔹 Problem 5:

5. $ \frac{2}{8} $
- GCD of 2 and 8 is 2
- $ \frac{2 \div 2}{8 \div 2} = \frac{1}{4} $

✔ Answer: $ \frac{1}{4} $

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🔹 Problem 6:

6. $ \frac{4}{12} $
- GCD of 4 and 12 is 4
- $ \frac{4 \div 4}{12 \div 4} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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🔹 Problem 7:

7. $ \frac{6}{14} $
- GCD of 6 and 14 is 2
- $ \frac{6 \div 2}{14 \div 2} = \frac{3}{7} $

✔ Answer: $ \frac{3}{7} $

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🔹 Problem 8:

8. $ \frac{8}{64} $
- GCD of 8 and 64 is 8
- $ \frac{8 \div 8}{64 \div 8} = \frac{1}{8} $

✔ Answer: $ \frac{1}{8} $

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🔹 Problem 9:

9. $ \frac{40}{10} $
- $ 40 \div 10 = 4 $
- So, $ \frac{40}{10} = 4 $

✔ Answer: $ 4 $

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🔹 Problem 10:

10. $ \frac{11}{22} $
- GCD of 11 and 22 is 11
- $ \frac{11 \div 11}{22 \div 11} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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🔹 Problem 11:

11. $ \frac{10}{25} $
- GCD of 10 and 25 is 5
- $ \frac{10 \div 5}{25 \div 5} = \frac{2}{5} $

✔ Answer: $ \frac{2}{5} $

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🔹 Problem 12:

12. $ \frac{7}{28} $
- GCD of 7 and 28 is 7
- $ \frac{7 \div 7}{28 \div 7} = \frac{1}{4} $

✔ Answer: $ \frac{1}{4} $

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🔹 Problem 13:

13. $ \frac{22}{10} $
- Simplify: GCD of 22 and 10 is 2
- $ \frac{22 \div 2}{10 \div 2} = \frac{11}{5} $
- $ \frac{11}{5} $ is an improper fraction; can be written as $ 2\frac{1}{5} $, but since it says "reducing", we leave it as $ \frac{11}{5} $

✔ Answer: $ \frac{11}{5} $ or $ 2\frac{1}{5} $

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🔹 Problem 14:

14. $ \frac{25}{35} $
- GCD of 25 and 35 is 5
- $ \frac{25 \div 5}{35 \div 5} = \frac{5}{7} $

✔ Answer: $ \frac{5}{7} $

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🔹 Problem 15:

15. $ \frac{6}{4} $
- GCD of 6 and 4 is 2
- $ \frac{6 \div 2}{4 \div 2} = \frac{3}{2} $
- $ \frac{3}{2} = 1\frac{1}{2} $, but simplest form is $ \frac{3}{2} $

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

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✔ Final Answers:

| # | Reduced Fraction |
|---|------------------|
| 1 | $ \frac{1}{2} $ |
| 2 | $ 4 $ |
| 3 | $ \frac{1}{6} $ |
| 4 | $ \frac{1}{10} $ |
| 5 | $ \frac{1}{4} $ |
| 6 | $ \frac{1}{3} $ |
| 7 | $ \frac{3}{7} $ |
| 8 | $ \frac{1}{8} $ |
| 9 | $ 4 $ |
|10 | $ \frac{1}{2} $ |
|11 | $ \frac{2}{5} $ |
|12 | $ \frac{1}{4} $ |
|13 | $ \frac{11}{5} $ |
|14 | $ \frac{5}{7} $ |
|15 | $ \frac{3}{2} $ |

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📝 Summary:

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

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