Fraction simplifier

What is a fraction simplifier?

A fraction simplifier reduces a fraction to its lowest terms, also called its simplest form. A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. Simplifying makes fractions easier to read, compare, and work with, and it produces the canonical way of writing a given value: 8/12, 4/6, and 2/3 all represent the same number, but 2/3 is the simplest form.

Formula

The key is the greatest common divisor (GCD) of the numerator $n$ and the denominator $d$. Dividing both by their GCD yields the reduced fraction:

The GCD itself is found with the Euclidean algorithm, repeatedly replacing the larger number with the remainder of dividing it by the smaller until the remainder is zero.

How to use

1. Enter the numerator (the top number of the fraction).
2. Enter the denominator (the bottom number).
3. Read off the simplified numerator and simplified denominator, which together form the reduced fraction.

The denominator must be a non-zero value, since division by zero is undefined.

Worked example

Simplify the fraction 8/12. The greatest common divisor of 8 and 12 is 4:

As a second example, simplify 18/24. The GCD of 18 and 24 is 6:

FAQ

What if the numerator and denominator have no common factors? Then the fraction is already in lowest terms and the result equals the input. For example, 3/4 simplifies to 3/4 because the GCD of 3 and 4 is 1.

Can I simplify a fraction with a negative numerator? Yes. The simplifier divides by the GCD of the absolute values, so the sign of the result follows the sign of the original fraction.