How To Multiply Fractions

Since fractions are just another way of representing percentages, it makes sense that each fraction consists of two numbers, a numerator at the top and a denominator at the bottom.  The numerator on top is just a portion of the whole which is the denominator at the bottom.  As an example, if you consider 9/12, you see that this is just 9 out of the total which is 12, or stated in decimal or percent form as 0.75 or 75 %.  So with this being said when you are multiplying fractions you actually just multiplying percentages and decimals that are written in a different form.  In fact even whole numbers are actually fractions just simplified and occurring only when the numerator is equal to or is some multiple of the denominator.  Multiplication of percentages, decimals, and whole numbers is performed in the same way as fractions except that fractions have both a numerator and denominator that are multiplied.

It should also be noted that when multiplying two or more fractions, the denominators of each fraction do not need to be the same as would be the case of adding or subtracting fractions.  In the process of fraction multiplication, in each of the two or more fractions the numerators are multiplied by one another to yield a final resulting numerator, just as are the denominators to yield a final product.  The fractions may be reduced or simplified before multiplication or as a final product.

A couple of fraction multiplication examples will further clarify this process.

Example 1: What is 3/5’s of 6/8?

This question is basically asking what 3/5’s is as a percentage (or in decimal form) of 6/8’s, in other words, 3/5’s times 6/8’s.  We solve this below.

(3/5)(6/8) = (3 x 6)/(5 x 8) = 18/40 = 9/20 = 0.45 = 45 %

It makes sense for us to yield a much smaller number as we are being asked to find 60 % (or 3/5) of 75 % (or 6/8).

Example 2: Find (5/22)(8/16)(2/8).

This question is just asking us to multiply each of the three fractions by one another and since the fractions are relatively small and none above one (or an improper fraction), we expect the final number to be quite small.

(5/22)(8/16)(2/8) = (5 x 8 x 2)/(22 x 16 x 8) = 80/2816 = 10/352 = 5/176

For this example you can see that you can also multiply as many fractions at once you would like to, of course if working with several fractions it does simplify things to perform the multiplication in multiple steps as opposed to just one.