Simplify Fractions Calculator — reduce to lowest terms

How it works

A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. To get there, per Wolfram MathWorld, a reduced fraction has "common terms canceled out of the numerator and denominator" — which means dividing both by their greatest common divisor (GCD).

For 8/12, the GCD of 8 and 12 is 4. Dividing top and bottom by 4 gives 2/3, and 2 and 3 have no common factor, so the fraction is fully reduced. The value never changes — 8/12 and 2/3 are the same number — only the way it is written becomes simplest.

The calculator also shows the decimal value, which is the numerator divided by the denominator, and it keeps the sign on the numerator (so −8/12 and 8/−12 both read as −2/3).

Worked example

Take 8/12. The greatest common divisor of 8 and 12 is 4, so divide both by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3. The simplified fraction is 2/3, whose decimal value is 0.6667 (rounded). There are no further common factors, so 2/3 is in lowest terms.

Frequently asked questions

How do you simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. The result has no shared factors and is in lowest terms. For 8/12 the GCD is 4, giving 2/3.

What is the greatest common divisor?

It is the largest whole number that divides two numbers evenly. For 8 and 12 the common divisors are 1, 2 and 4, so the greatest is 4. Dividing a fraction's top and bottom by their GCD reduces it in a single step.

Does simplifying change the value of a fraction?

No. A simplified fraction is equal to the original — 8/12 and 2/3 represent exactly the same number. Only the form changes: lowest terms uses the smallest whole numbers possible.

How do I know a fraction is fully reduced?

It is fully reduced when the numerator and denominator share no common factor greater than 1 — equivalently, when their GCD is 1. For example, 3/7 is already in lowest terms.

Can this simplify improper fractions?

Yes. An improper fraction (numerator larger than denominator) reduces the same way: 14/4 becomes 7/2. The calculator leaves it as an improper fraction; convert it to a mixed number separately if you prefer.

How are negative fractions handled?

The sign is placed on the numerator, so both −8/12 and 8/−12 simplify to −2/3. A fraction and its simplified form always have the same sign and value.