Simplifying fractions
Simplify a fraction to lowest terms using the greatest common divisor.
Enter a fraction – the lowest terms and visualisation appear instantly.
What simplifying a fraction means
Simplifying means dividing both the numerator and denominator by the same number. The value of the fraction does not change – we just write it with smaller numbers. 8/12 and 2/3 are the same amount, only 8/12 is divided into smaller parts.
(a ÷ k) / (b ÷ k) = a/b (for common divisor k)
Lowest terms and the GCD
A fraction is in lowest terms when the numerator and denominator have no common divisor other than 1. The fastest way there is dividing by the greatest common divisor (GCD) of the numerator and denominator. For 8/12, the GCD is 4, so 8/12 = 2/3.
Simplifying step by step
You don't need to know the GCD right away – you can simplify step by step with smaller numbers too. 8/12 → (÷2) → 4/6 → (÷2) → 2/3. The result is the same. The calculator shows both views: step-by-step simplification and straight via the GCD.
Why the value does not change
Dividing both the numerator and denominator by the same number is like multiplying the whole fraction by 1 written as k/k. And multiplying by 1 changes nothing. In the bars above, both fractions have the same length of coloured part – they only differ in how many pieces the bar is divided into.
Tip: if the numerator is larger than the denominator, the fraction is "improper" and can also be written as a mixed number.