Simplify Fractions Calculator

Reduce Fraction to Lowest Terms

What Does It Mean to Simplify a Fraction?

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1. A simplified fraction represents the same value as the original but uses the smallest possible numbers.

For example, 8/12 can be simplified to 2/3 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4. Both fractions represent the same value, but 2/3 is in its simplest form.

How to Simplify Fractions

Follow these steps to simplify any fraction:

  1. Find the GCD: Calculate the greatest common divisor of the numerator and denominator
  2. Divide both numbers: Divide both numerator and denominator by the GCD
  3. Check the result: The result is in lowest terms if numerator and denominator have no common factors

Formula

Simplified Fraction = (Numerator รท GCD) / (Denominator รท GCD)

Where GCD is the Greatest Common Divisor of the numerator and denominator. This ensures the fraction is reduced to its lowest terms.

Example

Simplification Example

Problem: Simplify 24/36

Solution:

  1. Find GCD of 24 and 36: GCD(24, 36) = 12
  2. Divide numerator: 24 รท 12 = 2
  3. Divide denominator: 36 รท 12 = 3
  4. Simplified fraction: 2/3

Frequently Asked Questions

How do I find the GCD?

The greatest common divisor can be found using the Euclidean algorithm or by listing all factors of both numbers and finding the largest one they share.

What if the numerator is larger than the denominator?

The fraction is called an "improper fraction" but can still be simplified the same way. For example, 15/10 simplifies to 3/2.

Can all fractions be simplified?

No. Fractions where the numerator and denominator are coprime (GCD = 1) are already in simplest form. For example, 3/7 cannot be simplified further.