How to Simplify Fractions

Objective

Class Note: Explaining how to simplify fractions step-by-step, with worked examples.

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Steps to Simplify Fractions

1. Factorize Both Numerator and Denominator

   • Write both numbers as products of their factors.

2. Identify and Cancel Common Factors

   • Cancel out any common factors between numerator and denominator.

3. Write the Simplified Fraction

   • After canceling, write what remains.

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Worked Examples

Example 1

Fraction: 3/6

• 3 = 3 × 1
• 6 = 3 × 2
• Cancel the common factor (3):
• Remaining: 1/2

Example 2

Fraction: 3/9

• 3 = 3 × 1
• 9 = 3 × 3
• Cancel the common factor (3):
• Remaining: 1/3

Example 3

Fraction: 6/8

• 6 = 3 × 2
• 8 = 4 × 2
• Cancel the common factor (2):
• Remaining: 3/4

Example 4

Fraction: 8/12

• 8 = 4 × 2
• 12 = 4 × 3
• Cancel the common factor (4):
• Remaining: 2/3

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Practice Problems

Try to simplify:

1. 9/15
2. 12/30
3. 35/49

Solutions

1. 9/15

• 9 = 3 × 3
• 15 = 3 × 5
• Cancel 3: 3/5

2. 12/30

• 12 = 6 × 2
• 30 = 6 × 5
• Cancel 6: 2/5

3. 35/49

• 35 = 7 × 5
• 49 = 7 × 7
• Cancel 7: 5/7

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Summary

• Find the largest common factor of the numerator and denominator.
• Divide both parts by that factor.
• The result is the fraction in its simplest form.