Teaching Multiplication of Fractions Visually

This is a very short post outlining how to teach the multiplication of fractions using a geometrical interpretation. I have tested this with kids across a wide range of the ability spectrum, and it has always helped. I hope it works for you too.

While fractions are easy for most kids, multiplication of fractions can sometimes be a little tricky. What I mean is that kids learn how to multiply fractions easily without really learning why it works. I wanted to make sure my daughter understood the concept, so I resorted to a geometrical interpretation.

Here are the basic prerequisites for this approach:

1. Understand what a fraction is
2. Understand how to compute areas. Basically, that A = L x W

Here are a few examples of how to interpret multiplication of fraction geometrically.

This diagram shows a "unit" square. The length of the shaded rectangle is 1/2 and the width 1/2. Simple visual inspection shows that we have divided the unit square into 4 equal pieces. Hence, the product 1/4.

Here is another example. Multiply 2/3 and 3/5.


The length is 2/3. The width is 3/5. The product is 6/15. You kid should figure this out by counting.

Finally, let me show how to illustrate multiplication of fractions involving improper fractions.

Hopefully, it is clear by now that this geometrical interpretation works equally well for heterogeneous fractions.

The point of the geometrical interpretation is that it can be used to teach multiplication right after understanding the concept of a fraction. As always, the key to learning things well is to use lots of examples and to spend enough time thinking about the concepts.