# Using Rectangles to Represent Numbers

I like to visualize numbers as rectangles. And why not?

You can find percentages as well as work with fractions this way.

Say we want to find what percent 288/360 is. We can draw two rectangles like so. Here I constructed rectangles of 36×8 and a 36×10. It just so happens that I could fit 36 as my largest width because of the paper size. If you examine the diagram closely you will notice that the smaller rectangle (288 units square) is nested inside the larger one (360 units square). The widths are 8 and 10, respectively, so that tells us that 288 is 80% of 360.

What if the numbers are different? Let’s find what 15/40 is as a percentage.  Here’s a diagram.   Knowing how to represent our numbers is also very useful.  A 4×10 rectangle can clearly show what 10% is and subsequently, what each square represents.

Now all we have to do is shade 15 squares and that looks like 37.5%!

Let’s do another one. 12/25.   Here, each square represents 4% as 25 of those make 100%. Therefore 12/25 is 48%. And it makes sense because 12 is not quite half of 25.

I hope you start to see numbers as shapes too. You should check out my other post called Numbers as Shapes.