How can knowing the gcf and lcm you when you add subtract and multiply fractions?

If the denominators are different numbers, it is necessary to find a common denominator. Find the Lowest Common Multiple (LCM) of the denominators (also known as the Lowest Common Denominator, or LCD) and convert the fractions to equivalent fractions with the same denominator. Now they have the same denominator, proceed as above.

Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 (here LCM=12)

You don't have to do anything to fractions to multiply them, but you may need to reduce one after multiplying. To do that, find the GCF of the numerator and the denominator and divide both of them by it. If the GCF is 1, the fraction is in its simplest form.

Example: 1/4 · 2/5 = 1·2/4·5=2/20=1/10 (here GCF=2)