Write two fractions that you want to multiply next to each other with a multiplication sign between them. For example, if you want to multiply 4/6 by 3/8, write "4/6 x 3/8."
Find the greatest common factor of the first fraction's numerator and the second fraction's denominator, which is the largest number that you can divide into both. For example, the largest number that you can divide into the first fraction's numerator of 4 and the second fraction's denominator of 8 is 4, the greatest common factor.
Divide the first fraction's numerator and the second fraction's denominator each by the greatest common factor. Then cross out the original number and replace it with each result. For example, divide 4 by 4, which equals 1, and divide 8 by 4, which equals 2. Then cross out 4 and replace it with a 1, and cross out 8 and replace it with a 2. This leaves 1/6 x 3/2.
Find the greatest common factor of the first fraction's denominator and the second fraction's numerator. In the example, the greatest common factor of 6 and 3 is 3.
Divide the first fraction's denominator and the second fraction's numerator each by their greatest common factor. Then cross out the original number and replace it with each result. For example, divide 6 by 3, which equals 2, and divide 3 by 3, which equals 1. Then cross out 6 and replace it with 2, and cross out 3 and replace it with 1. This leaves 1/2 x 1/2.
Multiply the fractions' numerators. Then multiply the fractions' denominators. For example, multiply 1 by 1, which equals 1. Then multiply 2 by 2, which equals 4. This leaves 1/4 as your answer in its lowest terms.