A fraction is in lowest terms when the numerator and denominator have no common factor other than 1.

Method 1:
To put a fraction in lowest terms, find the largest common factor that divides both the numerator and the denominator. Divide both the numerator and the denominator by that number.

Method 2
To reduce fractions is to break the numerator and denominator down to their prime factors, and remove every prime factor the two have in common. Let's do that example one more time, using this method. Assume you want to simplify fraction 12/16

The prime factors of 12 are 2 x 2 X 3.
The prime factors of 16 are 2 x 2 x 2 x 2.

We remove the 2 x 2 the numerator and denominator have in common:
We get
3/2 x 2 or 3/4