A ratio is a mathematical comparison of two numbers, based on division. For example, suppose you bring 2 scarves and 3 caps with you on a ski vacation. Here are a few ways to express the ratio of scarves to caps:
![image0.jpg](https://www.dummies.com/wp-content/uploads/437095.image0.jpg)
The simplest way to work with a ratio is to turn it into a fraction. Be sure to keep the order the same: The first number goes on top of the fraction, and the second number goes on the bottom.
In practice, a ratio is most useful when used to set up a proportion β that is, an equation involving two ratios. Typically, a proportion looks like a word equation, as follows:
![image1.jpg](https://www.dummies.com/wp-content/uploads/437096.image1.jpg)
For example, suppose you know that both you and your friend Andrew brought the same proportion of scarves to caps. If you also know that Andrew brought 8 scarves, you can use this proportion to find out how many caps he brought. Just increase the terms of the fraction
![image2.jpg](https://www.dummies.com/wp-content/uploads/437097.image2.jpg)
so that the numerator becomes 8. Do this in two steps:
![image3.jpg](https://www.dummies.com/wp-content/uploads/437098.image3.jpg)
As you can see, the ratio 8:12 is equivalent to the ratio 2:3 because the fractions
![image4.jpg](https://www.dummies.com/wp-content/uploads/437099.image4.jpg)
are equal. Therefore, Andrew brought 12 caps.