Fraction Simplifier & Engine

Reduce fractions instantly and view the step-by-step mathematical logic.

Enter Fraction

Calculations execute instantly in your browser.

Simplified Form

4 / 3

Mixed Number

1 1/3

Greatest Common Divisor

256

Decimal

1.3333

Percentage

133.33%

Euclidean Algorithm Engine

To reduce this fraction, the engine calculates the Greatest Common Divisor (GCD) using the Euclidean algorithm, dividing the larger number by the smaller number until the remainder is zero.

How The Math Actually Works

Simplifying a fraction means finding the smallest possible whole numbers for the numerator and denominator while keeping the exact same proportional value.

The Euclidean Algorithm:

Discovered by the ancient Greek mathematician Euclid, this algorithm is the most efficient way for a computer (or human) to find the Greatest Common Divisor (GCD) of two numbers. It works on the principle that the GCD of two numbers also divides their difference.

Divide the larger number by the smaller number.
Look at the remainder.
If the remainder is 0, the smaller number is your GCD.
If the remainder is not 0, replace the larger number with the smaller number, and the smaller number with the remainder. Repeat step 1.

Mixed Numbers: If the numerator is larger than the denominator, it is called an "improper fraction." The tool automatically divides the numerator by the denominator to extract the whole numbers, leaving the remaining fraction alongside it.