Simplify Fractions Calculator

What is a simplify fractions calculator?

A simplify fractions calculator reduces a fraction to its lowest terms. A fraction is in lowest terms when the numerator and the denominator share no common factor other than 1. Simplifying does not change the value of the fraction — it only writes the same quantity with the smallest possible whole numbers, which makes results easier to read and compare.

How does the calculator work?

You enter a numerator and a denominator (the denominator must not be zero). The calculator finds the greatest common divisor (GCD) of their absolute values and divides both numbers by it. The sign is normalized so that the denominator stays positive: if the original denominator is negative, the minus sign moves to the numerator. Improper fractions (where the numerator is larger than the denominator) are returned as-is in reduced form.

Formula

To simplify a fraction, divide the numerator and denominator by their greatest common divisor:

The decimal value is simply:

Where $a$ is the numerator and $b$ is the denominator.

Worked examples

1. Simplify $\frac{6}{8}$: $\gcd(6, 8) = 2$, so $\frac{6}{8} = \frac{3}{4} = 0.75$.

2. Simplify $\frac{50}{100}$: $\gcd(50, 100) = 50$, so $\frac{50}{100} = \frac{1}{2} = 0.5$.

3. Simplify the improper fraction $\frac{18}{12}$: $\gcd(18, 12) = 6$, so $\frac{18}{12} = \frac{3}{2} = 1.5$.

4. Simplify a negative fraction $\frac{-4}{8}$: $\gcd(4, 8) = 4$, so $\frac{-4}{8} = \frac{-1}{2} = -0.5$.

Notes

• The denominator can never be zero; division by zero is undefined.
• An already reduced fraction (such as $\frac{3}{4}$) is returned unchanged.
• The sign is always carried by the numerator, so the denominator stays positive.

You can also convert the result with the fraction to decimal converter or find common factors with the greatest common factor calculator.