Math worksheet for simplifying fractions using the GCF, designed for grades 6-9.

Let's solve each problem step by step using the Greatest Common Factor (GCF) to simplify the fractions.

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🔷 How to Simplify a Fraction Using GCF:

1. Find the GCF of the numerator and denominator.
2. Divide both the numerator and denominator by the GCF.
3. Write the simplified fraction.

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✔ Solutions:

#### 1.
- Fraction: $ \frac{4}{10} $
- Factors of 4: 1, 2, 4
- Factors of 10: 1, 2, 5, 10
- GCF = 2
- $ \frac{4 ÷ 2}{10 ÷ 2} = \frac{2}{5} $
- Answer: GCF = 2, $ \frac{2}{5} $

#### 2.
- $ \frac{2}{6} $
- Factors: 2 → 1, 2; 6 → 1, 2, 3, 6
- GCF = 2
- $ \frac{2 ÷ 2}{6 ÷ 2} = \frac{1}{3} $
- Answer: GCF = 2, $ \frac{1}{3} $

#### 3.
- $ \frac{9}{36} $
- Factors: 9 → 1, 3, 9; 36 → 1, 2, 3, 4, 6, 9, 12, 18, 36
- GCF = 9
- $ \frac{9 ÷ 9}{36 ÷ 9} = \frac{1}{4} $
- Answer: GCF = 9, $ \frac{1}{4} $

#### 4.
- $ \frac{5}{15} $
- Factors: 5 → 1, 5; 15 → 1, 3, 5, 15
- GCF = 5
- $ \frac{5 ÷ 5}{15 ÷ 5} = \frac{1}{3} $
- Answer: GCF = 5, $ \frac{1}{3} $

#### 5.
- $ \frac{3}{12} $
- Factors: 3 → 1, 3; 12 → 1, 2, 3, 4, 6, 12
- GCF = 3
- $ \frac{3 ÷ 3}{12 ÷ 3} = \frac{1}{4} $
- Answer: GCF = 3, $ \frac{1}{4} $

#### 6.
- $ \frac{6}{18} $
- Factors: 6 → 1, 2, 3, 6; 18 → 1, 2, 3, 6, 9, 18
- GCF = 6
- $ \frac{6 ÷ 6}{18 ÷ 6} = \frac{1}{3} $
- Answer: GCF = 6, $ \frac{1}{3} $

#### 7.
- $ \frac{10}{35} $
- Factors: 10 → 1, 2, 5, 10; 35 → 1, 5, 7, 35
- GCF = 5
- $ \frac{10 ÷ 5}{35 ÷ 5} = \frac{2}{7} $
- Answer: GCF = 5, $ \frac{2}{7} $

#### 8.
- $ \frac{12}{48} $
- Factors: 12 → 1, 2, 3, 4, 6, 12; 48 → 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- GCF = 12
- $ \frac{12 ÷ 12}{48 ÷ 12} = \frac{1}{4} $
- Answer: GCF = 12, $ \frac{1}{4} $

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#### 9.
- $ \frac{14}{21} $
- Factors: 14 → 1, 2, 7, 14; 21 → 1, 3, 7, 21
- GCF = 7
- $ \frac{14 ÷ 7}{21 ÷ 7} = \frac{2}{3} $
- Answer: GCF = 7, $ \frac{2}{3} $

#### 10.
- $ \frac{18}{24} $
- Factors: 18 → 1, 2, 3, 6, 9, 18; 24 → 1, 2, 3, 4, 6, 8, 12, 24
- GCF = 6
- $ \frac{18 ÷ 6}{24 ÷ 6} = \frac{3}{4} $
- Answer: GCF = 6, $ \frac{3}{4} $

#### 11.
- $ \frac{20}{80} $
- Factors: 20 → 1, 2, 4, 5, 10, 20; 80 → 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- GCF = 20
- $ \frac{20 ÷ 20}{80 ÷ 20} = \frac{1}{4} $
- Answer: GCF = 20, $ \frac{1}{4} $

#### 12.
- $ \frac{8}{16} $
- Factors: 8 → 1, 2, 4, 8; 16 → 1, 2, 4, 8, 16
- GCF = 8
- $ \frac{8 ÷ 8}{16 ÷ 8} = \frac{1}{2} $
- Answer: GCF = 8, $ \frac{1}{2} $

#### 13.
- $ \frac{45}{100} $
- Factors: 45 → 1, 3, 5, 9, 15, 45; 100 → 1, 2, 4, 5, 10, 20, 25, 50, 100
- GCF = 5
- $ \frac{45 ÷ 5}{100 ÷ 5} = \frac{9}{20} $
- Answer: GCF = 5, $ \frac{9}{20} $

#### 14.
- $ \frac{42}{49} $
- Factors: 42 → 1, 2, 3, 6, 7, 14, 21, 42; 49 → 1, 7, 49
- GCF = 7
- $ \frac{42 ÷ 7}{49 ÷ 7} = \frac{6}{7} $
- Answer: GCF = 7, $ \frac{6}{7} $

#### 15.
- $ \frac{9}{90} $
- Factors: 9 → 1, 3, 9; 90 → 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- GCF = 9
- $ \frac{9 ÷ 9}{90 ÷ 9} = \frac{1}{10} $
- Answer: GCF = 9, $ \frac{1}{10} $

#### 16.
- $ \frac{27}{63} $
- Factors: 27 → 1, 3, 9, 27; 63 → 1, 3, 7, 9, 21, 63
- GCF = 9
- $ \frac{27 ÷ 9}{63 ÷ 9} = \frac{3}{7} $
- Answer: GCF = 9, $ \frac{3}{7} $

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✔ Final Answers Summary:

| # | GCF | Simplified Fraction |
|---|-----|----------------------|
| 1 | 2 | $ \frac{2}{5} $ |
| 2 | 2 | $ \frac{1}{3} $ |
| 3 | 9 | $ \frac{1}{4} $ |
| 4 | 5 | $ \frac{1}{3} $ |
| 5 | 3 | $ \frac{1}{4} $ |
| 6 | 6 | $ \frac{1}{3} $ |
| 7 | 5 | $ \frac{2}{7} $ |
| 8 | 12 | $ \frac{1}{4} $ |
| 9 | 7 | $ \frac{2}{3} $ |
|10 | 6 | $ \frac{3}{4} $ |
|11 | 20 | $ \frac{1}{4} $ |
|12 | 8 | $ \frac{1}{2} $ |
|13 | 5 | $ \frac{9}{20} $ |
|14 | 7 | $ \frac{6}{7} $ |
|15 | 9 | $ \frac{1}{10} $ |
|16 | 9 | $ \frac{3}{7} $ |

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✔ All fractions are now in their simplest form using the GCF method.

Let me know if you'd like this as a printable worksheet or with visual steps!