How to Multiply Fractions

In a previous article we looked at fractions and how to add them. In this article we'll look at how to multiply fractions, which is much easier than addition. I assume now that you know the basics of fractions, such as expressions like nominator (top) and denominator (bottom).

Multiplication of fractions is as simple as multiplying the nominators and the denominators.

3/4 * 6/7 = (3*6) / (4*7) = 18/28

As always we want this fraction as simple as possible, so find the highest factor in both 18 and 28 and divide both top and bottom by that number. In this case that would be 2, and we end up with 9/14.

18/28 = 9/14

Let's look at a practical example where you would need to know how to multiply fractions.

You are making brownies, and the recipe asks for 1/4 cup of oil. You want to make half of the recipe i.e. 1/2 . Multiply both top and bottom to find how much oil you should use.

1/4 * 1/2 = 1/8 cup oil.

The original recipe also asks for 3 cups of flour, and here you should think of 3 as 3/1. If you have a whole number you can always use 1 as a denominator. Multiply top and bottom as with the oil:

3/1 * 1/2 = 3/2

Now your nominator is greater than your denominator and you will have to break up the fraction. Subtract the bottom from the top, and break the fraction up into two pieces.

3/2 = 2/2 + 1/2

When the nominator is equal to the denominator the fraction is equal to one. You would thus end up with one and a half cup of flour.

Even when you have more fractions you need to multiply the rule this stands. Multiply the nominators, multiply the denominators and simplify it as much you can.

4/5 * 5/7 * 3/1 * 4/10 = (4*5*3*4) / (5*7*1*10) = 240/350 = 24/35

To know fractions is vital for further understanding of mathematics, and if it's been a while since you last looked into to it there's no need to fret. A few exercises and a little effort can get you a long way, and there is no one except yourself who can make you learn how to solve them. Mathematics can be very fun when you feel like you master it, even if it's only baby steps. Take it at your own pace and allow yourself to fail every once in a while. Double check your results with a calculator, and make sure that the results sound logical.