Simplifying Fractions: Reducing to Lowest Terms

Why Simplify Fractions?

A simplified fraction:

  • Is easier to compare (e.g., 2/3 vs. 4/6)
  • Reduces complexity in calculations
  • Makes results clearer in real-world contexts, like recipes or measurements

A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

How to Simplify Fractions

1. Find the Greatest Common Divisor (GCD)

Identify the largest number that divides both the numerator and denominator.

Example: For 12/18, the factors are:

  • 12: 1, 2, 3, 4, 6, 12
  • 18: 1, 2, 3, 6, 9, 18
  • GCD: 6

2. Divide Both Numbers

Divide the numerator and denominator by the GCD.

Example: 12/18 ÷ 6/6 = 2/3

3. Check: Ensure no further common factors exist.

Alternative Method: Step-by-Step Division

If finding the GCD feels tricky, divide by smaller common factors repeatedly:

Example: 36/48

  • Divide by 2: 36/48 ÷ 2/2 = 18/24
  • Divide by 2 again: 18/24 ÷ 2/2 = 9/12
  • Divide by 3: 9/12 ÷ 3/3 = 3/4

Result: 36/48 = 3/4

Simplifying in Calculations

Simplify before or during operations to keep numbers manageable:

Multiplying

4/6 × 3/8

  • Simplify 4/6 = 2/3
  • Then 2/3 × 3/8 = 6/24 = 1/4

Adding

2/10 + 3/15

  • Simplify 2/10 = 1/5
  • Simplify 3/15 = 1/5
  • Then 1/5 + 1/5 = 2/5

Practice Problem

Simplify these fractions:

  1. 15/25
  2. 24/36
  3. 9/27

Answers:

  1. 3/5
  2. 2/3
  3. 1/3

Common Mistakes to Avoid

  • Stopping Early: Ensure the fraction is fully reduced (e.g., 6/12 = 1/2, not 3/6)
  • Changing the Value: Always divide numerator and denominator by the same number to preserve the fraction's value

What's Next?

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