# What is the difference between ratios and rates?

##### 1 Answer

Both rates and ratios are a comparison of two numbers.

A rate is simply a specific type of ratio.

The difference is that a rate is a comparison of two numbers with *different* units, whereas a ratio compares two numbers with the *same* unit.

For example, in a room full of students, there are 10 boys and 5 girls. This means the **ratio** of boys to girls is 10:5.

If we simplify the ratio, we see that the ratio of boys to girls is 2:1, since

Let's say we'd like to buy a soda for each student in the classroom. The local pizza place offers a group discount on soda purchases: $10 for 20 sodas.

Since we only need 15 sodas, we're wondering how much each soda costs at the discounted **rate.** To find out, we'll set up two rates, because we have 2 different units, dollars and number of sodas:

If

We cross multiply for

#20x = $10#

#x= 10-:20#

#x = 1/2#

Since our unit is $, we'll convert

Thus, the discounted **rate** for the sodas is $.50/1 soda.

Here is a helpful video on simplifying rates and ratios: