This calculator reduces any fraction to its lowest terms by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. A fraction is in its simplest or lowest form when the numerator and denominator share no common factors other than one, meaning no further reduction is possible. Simplifying fractions makes them easier to compare, add, subtract and understand, and it is a foundational skill in school mathematics and any field that involves ratios, proportions or probability. The GCD is found using the Euclidean algorithm, one of the oldest algorithms in mathematics, which works by repeatedly replacing the pair (a, b) with (b, a mod b) until the remainder is zero, at which point the last non-zero value is the GCD. Dividing both the numerator and denominator by the GCD produces an equivalent fraction in lowest terms because you are multiplying both parts of the fraction by the same value (the reciprocal of the GCD), which leaves the ratio unchanged. To use the calculator, enter the numerator and denominator of your fraction. You can include a negative numerator to represent a negative fraction. The calculator returns the simplified fraction, the GCD it used, and the decimal equivalent. If the fraction is already in its simplest form, the GCD will be 1 and the fraction will display unchanged. This tool suits students, teachers, and anyone working with ratios or probability values. The denominator cannot be zero.
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2/3
simplified fraction
GCD used12
Decimal0.6667
Original24/36
How it works
The Euclidean algorithm finds the GCD by repeatedly applying: GCD(a, b) = GCD(b, a mod b) until the remainder is zero. The last non-zero remainder is the GCD. Both the numerator and denominator are then divided by the GCD. If the denominator of the result is negative, the signs are flipped so the negative sign is always expressed in the numerator. A GCD of 1 means the fraction was already in its lowest terms.
Worked example
To simplify 24/36: apply the Euclidean algorithm: GCD(36, 24) = GCD(24, 12) = GCD(12, 0) = 12. Divide both by 12: numerator 24 ÷ 12 = 2, denominator 36 ÷ 12 = 3. The simplified fraction is 2/3. As a decimal: 2 ÷ 3 = 0.6667. The fraction cannot be reduced further because GCD(2, 3) = 1.
