Hi there,

A ratio is a way of comparing two numbers and showing the relationship between them, and it can be expressed in several different ways. I'll use the variables "a" and "b" to express ratios below:

a:b
a/b
a to b

In the Resources section below, I'm including a study guide on proportions and ratios. It should give you additional helpful insight!

Hope this helps!

Alex

To elaborate on The previous answer, here are a couple of examples of very interesting universal ratios.

For every planar circle in the universe - that is, every ordinary circle drawn flat - the ratio of its circumference to its diameter is the same, not matter how big or how small the circle is.  Divide those two numbers and you always get the same value.  Do it for really big circles and do it for microscopic circles and you end up with the same value every time.  We call this number "pi"

Here's another one: find two numbers - let's just call them x and y with x being the name of the larger of the two - such that the ratio of x/y is exactly the same as (x+y)/y.  That seems tricky, but we're just talking about two numbers.  Any two numbers such that
 x/y = (x+y)/x
This is really interesting because there are an infinite number of values for x and y that satisfy this equation (just as there are an infinite number of circles whose circumference to diameter ratio is pi).  But there is only one value of that ratio that works!  Play with some examples, see if you can narrow in on that ratio.  There are values for x and y, both whole numbers less than 10, that are close, where the two ratios are within 0.25 of each other.  Can you find them?

This ratio is called the "golden ratio" and it comes up in all kinds of places - art, architecture, biology, just to name three.  Do a Bing search on "golden ratio" and you'll see what I mean.