Guide

How to Simplify Fractions

Simplifying a fraction means writing it with the smallest possible numbers while keeping the same value.

A fraction is in lowest terms when its numerator and denominator share no common factor other than 1. To get there, divide both by their greatest common factor (GCF).

Open the Simplify Fractions Calculator →

Step by step

1
Find the greatest common factor (GCF)
The GCF is the largest number that divides both the numerator and denominator. For 12/16, the GCF is 4.
2
Divide both by the GCF
12 ÷ 4 = 3 and 16 ÷ 4 = 4.
3
Write the simplified fraction
The result is 3/4.
4
Check it can't reduce further
3 and 4 share no common factor above 1, so 3/4 is fully simplified.

Worked example

Simplify 12/16. The GCF of 12 and 16 is 4. Divide both by 4: 12 ÷ 4 = 3 and 16 ÷ 4 = 4. The answer is 3/4.

Common mistakes to avoid

Dividing the top and bottom by different numbers.
Stopping before the fraction is fully reduced.
Using a common factor that isn't the greatest, which means more steps.

Practice this skill

Try it yourself on the Simplify Fractions Calculator, generate a printable worksheet, or work through it one step at a time in guided practice.

Frequently asked

What does it mean to simplify a fraction?

It means rewriting it with the smallest whole numbers possible while keeping the same value, by dividing top and bottom by their greatest common factor.

How do you find the greatest common factor?

List the factors of both numbers and pick the largest they share, or use prime factorization. For 12 and 16 the GCF is 4.

Is 3/4 already simplified?

Yes. 3 and 4 have no common factor above 1, so 3/4 is in lowest terms.