# Ratios

Ratios are mathematic comparisons of two numbers and are based on division. Chances are you deal with ratios daily, without even realizing it. However, when you fully understand ratios, you may be able to use them in ways you never imagined.

Are you still confused about what a ratio is? If you are more of a visual learner, consider this example. If you bring two hats and three scarves with you on your ski vacation, there are a few ways you can express the ratio of hats to scarves:

2 : 3 or 2 to 2 to 3 or 2/3

That is a ratio (perhaps oversimplified a bit)!

**Working with Ratios: The Easiest Method**

The easiest way to work with a ratio is to turn it into a faction. Make sure you keep the order the same. The first number listed is your numerator (the top number) and the second number is the denominator (the bottom number).

When working with ratios, they are must useful when setup as a proportion. A proportion is an equation that is made up of two ratios. In most cases, proportions look like word equations, for example:

Hats/scarves = 2/3

A practical example of working with ratios is here: consider if you knew that you and your friend brought the same proportion of hats to scarves as you did. You also know your friend brought along 6 scarves. You can use the proportion word problem to discover how many hats they brought along.

To do this, you must increase the terms of your current faction to make the numerator 6. There are two steps to this process:

**Step 1:** scarves/hats = 2 x 3/3 x 3 (because two times three is six, which is how many scarves your friend brought along)

**Step 2**: scarves/hats = 6/9

The ratio of 2:3 is equivalent to the new ratio of 6:9 because of the fractions 2/3 and 6/9. Also, your answer is that your friend brought along nine hats.

**Using Ratios to Compare Values**

Ratios tell you how much of one thing there is compared to something else. The trick to using ratios to help solve problems is to make sure you always multiply or divide the given numbers by the exact same value.

For example, 5:6 is the same as 5 x 3 : 6 x 3 = 15 : 18.

This can be used for many things, including recipes. If you have a recipe for pancakes that uses four cups of flour and three cups of milk, the ratio used to represent the amount of flour compare to the amount milk is 4 : 3. If you want to make enough pancakes for many people, you may have to double the quantity, so you will multiply both numbers by two.

4 x 2 : 3 x 2 = 8 : 6. In other words, to double the recipe, you need eight cups of flour and two cups of milk. The ratio remains the same so the pancakes will turn out as expected.

**The Bottom Line**

Ratios can be a bit intimidating at first. However, when you take the time to break them down, they are easier to understand. While there are many math concepts you will never use in real life, ratios are not one of these. As a result, learning how to use them can be quite beneficial.