Fraction Simplifier

Reduce any fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator. This tool helps you quickly express fractions in their lowest terms.

Numerator

Enter the top number of the fraction

Denominator

Enter the bottom number of the fraction (cannot be zero)

How it works

Reduce any fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator. This tool helps you quickly express fractions in their lowest terms.

The Formula

To simplify a fraction a/b:
1. Find the Greatest Common Divisor (GCD) of |a| and |b|.
2. Divide both 'a' and 'b' by the GCD.
Simplified Fraction = (a ÷ GCD) / (b ÷ GCD)

Worked Example

Simplify 12/18
To simplify 12/18, we find the GCD of 12 and 18, which is 6. Dividing both numerator and denominator by 6 gives 12 ÷ 6 = 2 and 18 ÷ 6 = 3. So, 12/18 simplifies to 2/3.

Tips, Assumptions & Limitations

Always ensure your fraction is in its simplest form for final answers.
The GCD is the largest number that divides both the numerator and denominator without a remainder.
This calculator can handle improper fractions and negative numbers.

FAQ

A simplified fraction, or a fraction in its lowest terms, is one where the numerator and denominator have no common factors other than 1. This means you cannot divide both numbers by any integer other than 1 to make them smaller.

To manually simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both the numerator and the denominator by this GCD. The resulting fraction will be in its simplest form.

Yes, this calculator can simplify both proper and improper fractions. An improper fraction is one where the numerator is greater than or equal to the denominator.