Question

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

Answer 1

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)

Answer 2

In order to add and subtract fractions, we must be able to find a common denominator.
The LCD, or least common denominator, is the LCM of the denominators. Once we've added, subtracted or multiplied fractions, we often have to simplify the fraction.
In order to do this, we divide the numerator and denominator by their GCF. This means we must be able to find the LCM and GCF in order to work with fractions.