List the prime factors of both the numerator and the denominator. Start with the lowest prime numbers, excluding 1. For example, the fraction 12/15 would be expressed as (2 x 2 x 3)/(3 x 5).
Cancel out common factors. In the example from Step 1, you would cancel out the 3 in both the numerator and denominator, leaving you with (2 x 2)/5.
Solve the remaining equation. Because your fraction is still expressed as (2 x 2)/5, solve for 2 x 2. The result is 4/5 -- the lowest possible reduced fraction for 12/15.
Find the largest common factor of both your numerator and denominator. For example, starting with the fraction 12/18, the largest common factor is 6. In this method, the largest common factor does not have to be a prime number.
Divide the numerator and denominator by the largest common factor. Using the example 12/18, this would become (12 ÷ 6)/(18 ÷ 6).
Solve the division and express the newly reduced fraction as 2/3.