# What is a Ratio?

A ratio is a comparison of two things. We might compare boys to girls, cars to trucks or hours asleep to hours awake.

Whatever we choose to compare can then be written as a ratio. There are three different forms.

A ratio can be written as a to b, a : b or

Here are some examples:

1.) 4 boys and 5 girls would be written as 4 to 5, 4 : 5 or

2.) 3 parts yellow and 4 parts blue would be written as 3 to 4, 3 : 4, or

Ratios can be part-to-part, part-to-whole, or whole-to-part. Let's take a look at what this means.

When we compare boys to girls in a classroom, we are comparing part of the class to another part of the class. This would be a part-to-part comparison.

When we compare boys to the whole class, this is a part-to-whole comparison.

If we were to compare the class to the girls, this would be whole-to-part comparison.

Given an example, we can actually write all the different types of ratios.

Example: A class is made up of 14 girls and 15 boys.

Part-to-Part 14 : 15 shows girls to boys

Part-to-Whole 14: 29 shows girls to the class

Whole-to-Part 29 : 14 shows the class to the girls

OR

Part-to-Part 15:14 shows boys to girls

Part-to-Whole 15 : 29 shows boys to the class

Whole-to-Part 29 : 15 shows the class to the boys

Example: A painter is mixing colors to get the right shade of green. He has used 4 parts blue for every 5 parts yellow.

Part-to-Part 4: 5 shows blue to yellow

Part-to-Whole 4 : 9 shows blue to the entire mixture

Whole-to-Part 9 : 4 shows the entire mixture to blue

OR

Part-to-Part 5 : 4 shows yellow to blue

Part-to-Whole 5 : 9 shows yellow to the entire mixture

Whole-to-Part 9 : 5 shows the entire mixture to yellow

The order that you write the ratio is important! 4 to 5 is not the same as 5 to 4.

Example:

1.) Write a ratio of triangles to squares. 4 : 7

2.) Write a ratio of squares to triangles.7 : 4

Notice that the order of the numbers depends on the order of what you want to compare.

3.) Write a ratio of triangles to total shapes.4 : 11

4.) Write a ratio of total shapes to triangles.11 : 4

Let's Review:

Ratios are used to compare two quantities. You can compare parts with parts or parts with the whole. When you write a ratio you have three choices for the form of your answer. You can write your answer as a : b, a to b or .