When we multiply two whole numbers together, we know that we are going to end up with more than we started with. When we multiply proper fractions together, we are going to end up with less than we started with. It's a good idea to understand visually what it means, then you can use the rules for multiplying fractions together. Let's see what it really means to multiply fractions together, in this video.

Remember!

When we multiply something, anything, by a proper fraction, we end up with less than we started with.

A fraction of a fraction

We've seen how we can multiply unit fractions by whole numbers, and other fractions by whole numbers, so we're ready to see how we can multiply one fraction by another. In this video, we're going to use a nifty array system to work out our answer, and then see the shortcut we can use going forward.

Your turn

In this applet, you can change the numerator and denominator for each fraction, and then see what happens when you multiply them. You can click the box to show the answer and check if you were correct.

Okay, let's stop and think about this. What if we need to solve $\frac{2}{3}$23x$\frac{9}{4}$94?

$\frac{2}{3}$23 is less than $1$1, so our answer will be less than $\frac{9}{4}$94 . If we turn it around and consider $\frac{9}{4}$94x$\frac{2}{3}$23, we are multiplying $\frac{2}{3}$23by a number greater than $1$1, so we'll end up with more than $\frac{2}{3}$23. Either way, the answer will be the same! Let's see what we end up with:

$\frac{2}{3}$23x$\frac{9}{4}$94 =$\frac{18}{12}$1812= $\frac{6}{4}$64 = $\frac{3}{2}$32 which is less than $\frac{9}{4}$94

$\frac{9}{4}$94x$\frac{2}{3}$23 is also equal to $\frac{3}{2}$32, or $1$1$\frac{1}{2}$12, so that's bigger than $\frac{2}{3}$23.

Did you know?

A proper fraction is a fraction whose numerator (top number) is smaller than the denominator (bottom number). Think of it as a real, or proper fraction, because it's a fraction of $1$1. An improper fraction has a numerator larger than its denominator, so its value is more than $1$1.