Simplify the first fraction by finding the factors of its numerator and denominator and canceling out the largest factor that both share. For this example, in the fraction 2/4, the numerator 2 has 1 and 2 as factors and the denominator 4 has 1, 2 and 4 as factors. Canceling out 2 from the numerator and denominator reduces the fraction to 1/2.
Simplify the second fraction through the process in the prior step. For this example, in the fraction 8/12, the numerator has 1, 2, 4 and 8 as factors and the denominator has 1, 2, 3, 4, 6 and 12 as factors. Canceling 4 from the numerator and denominator reduces the fraction to 2/3.
Write down the reduced fractions as an expression of multiplication. In this example, the expression is 1/2 * 2/3.
Compare each fraction's numerator with the other's denominator for common factors greater than 1 that can be canceled out. In this example, the numerator 1 and the denominator 3 have no common factors greater than 1, but the denominator 2 and the numerator 2 both have 2 as a factor, which when canceled out reduces both numbers to 1.
Rewrite the expression from Step 3 with the reduced values from the last step. In this example, 1/2 * 2/3 becomes 1/1 * 1/3 after canceling out the 2 from the first fraction's denominator and the second fraction's numerator.
Multiply the first fraction's numerator by the second's numerator, then multiply the first's denominator by the second's denominator. In this example, multiplying 1 by 1 results in 1, and multiplying 1 by 3 results in 3.
Write down a fraction with the numerators' product as its numerator and the denominators' product as its denominator for the answer. Concluding this example, the answer to 2/4* 8/12 is 1/3.