Fraction simplifier
Type a numerator and a denominator to get the simplest form of the fraction. The greatest common divisor is found by Euclid's algorithm, and every division is listed so you can check it by hand.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the numerator and the denominator as whole numbers (negative numbers are fine).
- Read the simplified fraction at the top, then the GCD and the division steps below.
How it works
The GCD of a and b is found with Euclid’s algorithm: a = q × b + r, then repeat with (b, r) until r is 0. Dividing the numerator and denominator by the GCD gives the lowest terms. Numbers up to 30 digits are handled exactly with big integers, so there is no rounding.
Worked example
Simplify 252/198.
- 252 = 1 × 198 + 54
- 198 = 3 × 54 + 36
- 54 = 1 × 36 + 18
- 36 = 2 × 18 + 0
The last non-zero remainder is 18, so 252/198 = (252 ÷ 18)/(198 ÷ 18) = 14/11, which is 1 3/11 or 1.272727… as a decimal.
Tips
- A fraction with an even top and bottom can always be halved first.
- If the top is a multiple of the bottom, the result is a whole number.
- A numerator of 0 gives 0, whatever the denominator.
Frequently asked questions
How do you simplify a fraction?
Find the greatest common divisor of the numerator and denominator, then divide both by it. For 252/198 the GCD is 18, so the fraction becomes 14/11. Dividing by a smaller common factor works too, but you may need to repeat it.
What is Euclid's algorithm?
It finds the GCD by repeated division. Divide the larger number by the smaller, replace the larger with the smaller and the smaller with the remainder, and stop when the remainder is 0. The last non-zero remainder is the GCD.
What if the fraction cannot be simplified?
When the GCD is 1 the numerator and denominator share no factor and the fraction is already in lowest terms, like 7/12. The tool says so and shows the steps that proved it.
What happens to negative fractions?
The sign is moved to the numerator, so 6/-8 becomes -3/4. The denominator of the result is always positive.
Can I use decimals or mixed numbers here?
No, this tool takes whole numbers for the top and bottom. For mixed numbers and arithmetic between fractions, use the fraction calculator.