This reducing fractions worksheet helps students master the skill of simplifying proper fractions through guided examples and practice problems.

Let's solve the "Reducing Fractions Worksheet" step by step.

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Goal:

Simplify each fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

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Example Given:

Simplify $ \frac{18}{27} $

- GCF of 18 and 27 is 9
- $ \frac{18 ÷ 9}{27 ÷ 9} = \frac{2}{3} $

So, $ \frac{18}{27} = \frac{2}{3} $

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Now let’s simplify each fraction:

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#### a. $ \frac{4}{20} $
- GCF of 4 and 20 is 4
- $ \frac{4 ÷ 4}{20 ÷ 4} = \frac{1}{5} $
✔ Answer: $ \frac{1}{5} $

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#### b. $ \frac{5}{10} $
- GCF of 5 and 10 is 5
- $ \frac{5 ÷ 5}{10 ÷ 5} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $

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#### c. $ \frac{14}{21} $
- GCF of 14 and 21 is 7
- $ \frac{14 ÷ 7}{21 ÷ 7} = \frac{2}{3} $
✔ Answer: $ \frac{2}{3} $

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#### d. $ \frac{9}{15} $
- GCF of 9 and 15 is 3
- $ \frac{9 ÷ 3}{15 ÷ 3} = \frac{3}{5} $
✔ Answer: $ \frac{3}{5} $

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#### e. $ \frac{16}{24} $
- GCF of 16 and 24 is 8
- $ \frac{16 ÷ 8}{24 ÷ 8} = \frac{2}{3} $
✔ Answer: $ \frac{2}{3} $

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#### f. $ \frac{18}{48} $
- GCF of 18 and 48 is 6
- $ \frac{18 ÷ 6}{48 ÷ 6} = \frac{3}{8} $
✔ Answer: $ \frac{3}{8} $

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#### g. $ \frac{16}{44} $
- GCF of 16 and 44 is 4
- $ \frac{16 ÷ 4}{44 ÷ 4} = \frac{4}{11} $
✔ Answer: $ \frac{4}{11} $

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#### h. $ \frac{9}{21} $
- GCF of 9 and 21 is 3
- $ \frac{9 ÷ 3}{21 ÷ 3} = \frac{3}{7} $
✔ Answer: $ \frac{3}{7} $

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#### i. $ \frac{25}{30} $
- GCF of 25 and 30 is 5
- $ \frac{25 ÷ 5}{30 ÷ 5} = \frac{5}{6} $
✔ Answer: $ \frac{5}{6} $

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#### j. $ \frac{8}{22} $
- GCF of 8 and 22 is 2
- $ \frac{8 ÷ 2}{22 ÷ 2} = \frac{4}{11} $
✔ Answer: $ \frac{4}{11} $

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#### k. $ \frac{12}{30} $
- GCF of 12 and 30 is 6
- $ \frac{12 ÷ 6}{30 ÷ 6} = \frac{2}{5} $
✔ Answer: $ \frac{2}{5} $

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#### l. $ \frac{3}{20} $
- GCF of 3 and 20 is 1 → already in simplest form
✔ Answer: $ \frac{3}{20} $

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#### m. There are 36 students in Frank's class. 27 of them are buying lunch today. Write and simplify the fraction of students that are buying lunch.

- Fraction: $ \frac{27}{36} $
- GCF of 27 and 36 is 9
- $ \frac{27 ÷ 9}{36 ÷ 9} = \frac{3}{4} $
✔ Answer: $ \frac{3}{4} $

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✔ Final Answers:

| Problem | Simplified Fraction |
|--------|---------------------|
| a | $ \frac{1}{5} $ |
| b | $ \frac{1}{2} $ |
| c | $ \frac{2}{3} $ |
| d | $ \frac{3}{5} $ |
| e | $ \frac{2}{3} $ |
| f | $ \frac{3}{8} $ |
| g | $ \frac{4}{11} $ |
| h | $ \frac{3}{7} $ |
| i | $ \frac{5}{6} $ |
| j | $ \frac{4}{11} $ |
| k | $ \frac{2}{5} $ |
| l | $ \frac{3}{20} $ |
| m | $ \frac{3}{4} $ |

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📌 Summary:

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

This method ensures the fraction is in its lowest terms.

Let me know if you'd like this as a printable answer key! 😊