Simplifying Fractions Using GCF worksheet - Free Printable

Absolutely! Let’s solve this worksheet step by step. The goal is to simplify each fraction by finding the GCF (Greatest Common Factor) of the numerator and denominator, then dividing both by that GCF to get the simplest form.

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✔ Key Concept:

To simplify a fraction:
1. Find the GCF of the numerator and denominator.
2. Divide both the numerator and denominator by the GCF.
3. Write the resulting fraction — that’s the simplest form.

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Let’s go problem by problem:

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1. $\frac{4}{10}$

- Factors of 4: 1, 2, 4
- Factors of 10: 1, 2, 5, 10
- GCF = 2
- Simplify: $\frac{4 ÷ 2}{10 ÷ 2} = \frac{2}{5}$

✔ Answer: GCF = 2, Simplest form = $\frac{2}{5}$

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2. $\frac{2}{6}$

- Factors of 2: 1, 2
- Factors of 6: 1, 2, 3, 6
- GCF = 2
- Simplify: $\frac{2 ÷ 2}{6 ÷ 2} = \frac{1}{3}$

✔ Answer: GCF = 2, Simplest form = $\frac{1}{3}$

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3. $\frac{9}{36}$

- Factors of 9: 1, 3, 9
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- GCF = 9
- Simplify: $\frac{9 ÷ 9}{36 ÷ 9} = \frac{1}{4}$

✔ Answer: GCF = 9, Simplest form = $\frac{1}{4}$

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4. $\frac{5}{15}$

- Factors of 5: 1, 5
- Factors of 15: 1, 3, 5, 15
- GCF = 5
- Simplify: $\frac{5 ÷ 5}{15 ÷ 5} = \frac{1}{3}$

✔ Answer: GCF = 5, Simplest form = $\frac{1}{3}$

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5. $\frac{3}{12}$

- Factors of 3: 1, 3
- Factors of 12: 1, 2, 3, 4, 6, 12
- GCF = 3
- Simplify: $\frac{3 ÷ 3}{12 ÷ 3} = \frac{1}{4}$

✔ Answer: GCF = 3, Simplest form = $\frac{1}{4}$

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6. $\frac{6}{18}$

- Factors of 6: 1, 2, 3, 6
- Factors of 18: 1, 2, 3, 6, 9, 18
- GCF = 6
- Simplify: $\frac{6 ÷ 6}{18 ÷ 6} = \frac{1}{3}$

✔ Answer: GCF = 6, Simplest form = $\frac{1}{3}$

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7. $\frac{10}{35}$

- Factors of 10: 1, 2, 5, 10
- Factors of 35: 1, 5, 7, 35
- GCF = 5
- Simplify: $\frac{10 ÷ 5}{35 ÷ 5} = \frac{2}{7}$

✔ Answer: GCF = 5, Simplest form = $\frac{2}{7}$

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8. $\frac{12}{48}$

- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- GCF = 12
- Simplify: $\frac{12 ÷ 12}{48 ÷ 12} = \frac{1}{4}$

✔ Answer: GCF = 12, Simplest form = $\frac{1}{4}$

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9. $\frac{14}{21}$

- Factors of 14: 1, 2, 7, 14
- Factors of 21: 1, 3, 7, 21
- GCF = 7
- Simplify: $\frac{14 ÷ 7}{21 ÷ 7} = \frac{2}{3}$

✔ Answer: GCF = 7, Simplest form = $\frac{2}{3}$

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10. $\frac{18}{24}$

- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- GCF = 6
- Simplify: $\frac{18 ÷ 6}{24 ÷ 6} = \frac{3}{4}$

✔ Answer: GCF = 6, Simplest form = $\frac{3}{4}$

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11. $\frac{20}{80}$

- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- GCF = 20
- Simplify: $\frac{20 ÷ 20}{80 ÷ 20} = \frac{1}{4}$

✔ Answer: GCF = 20, Simplest form = $\frac{1}{4}$

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12. $\frac{8}{16}$

- Factors of 8: 1, 2, 4, 8
- Factors of 16: 1, 2, 4, 8, 16
- GCF = 8
- Simplify: $\frac{8 ÷ 8}{16 ÷ 8} = \frac{1}{2}$

✔ Answer: GCF = 8, Simplest form = $\frac{1}{2}$

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13. $\frac{45}{100}$

- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- GCF = 5
- Simplify: $\frac{45 ÷ 5}{100 ÷ 5} = \frac{9}{20}$

✔ Answer: GCF = 5, Simplest form = $\frac{9}{20}$

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14. $\frac{42}{49}$

- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 49: 1, 7, 49
- GCF = 7
- Simplify: $\frac{42 ÷ 7}{49 ÷ 7} = \frac{6}{7}$

✔ Answer: GCF = 7, Simplest form = $\frac{6}{7}$

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15. $\frac{9}{90}$

- Factors of 9: 1, 3, 9
- Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- GCF = 9
- Simplify: $\frac{9 ÷ 9}{90 ÷ 9} = \frac{1}{10}$

✔ Answer: GCF = 9, Simplest form = $\frac{1}{10}$

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16. $\frac{27}{63}$

- Factors of 27: 1, 3, 9, 27
- Factors of 63: 1, 3, 7, 9, 21, 63
- GCF = 9
- Simplify: $\frac{27 ÷ 9}{63 ÷ 9} = \frac{3}{7}$

✔ Answer: GCF = 9, Simplest form = $\frac{3}{7}$

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## 📝 Final Answer Summary:

| Problem | GCF | Simplest Form |
|---------|-----|----------------|
| 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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You can now fill in the worksheet with these answers! 😊
Let me know if you’d like a printable version or explanation for any specific problem!