Fraction Simplifier Calculator

How to Simplify Fractions

Simplifying fractions is an essential skill in mathematics. It involves reducing a fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).

Formula for Simplifying Fractions

The formula to simplify a fraction is:

$$\frac{a}{b} = \frac{a \div GCD(a,b)}{b \div GCD(a,b)}$$

Where:

• \(\frac{a}{b}\) is the original fraction
• \(GCD(a,b)\) is the greatest common divisor of a and b

Calculation Steps

1. Identify the numerator (a) and denominator (b) of the fraction.
2. Find the greatest common divisor (GCD) of a and b.
3. Divide both the numerator and denominator by the GCD.
4. The resulting fraction is in its simplest form.

Example Calculation

Let's simplify the fraction $\frac{24}{36}$:

1. Identify: numerator = 24, denominator = 36
2. Find GCD(24, 36):
   • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
   • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
   • The greatest common factor is 12
3. Divide both numerator and denominator by 12: $$\frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$$
4. The simplified fraction is $\frac{2}{3}$

Visual Representation

These visualizations show how the fraction 24/36 simplifies to 2/3 by dividing both the numerator and denominator by their greatest common divisor (12). Both fractions represent the same value (approximately 0.667), demonstrating their equivalence.