# Ratios

A ratio is a comparison of two quantities with the same units. The numbers are non negatives. Both numbers can not be zero. For example we might want to compare the number 5 to the number 2

There are three ways to write a ratio (we will use the above example)

5 to 2 (Using the word "to")

5 : 2 (Using a colon :)

5/2 (looking like a fraction - the fraction bar stands for the word "to")

Order matters when writing ratios.  If you want to compare the number 2 to the number 5 the ratio is written as 2 to 5, 2:5 or 2/5.

We simplify ratios when ever possible.  For example, if we are comparing the number 15 to the number 5 we would initially say the ratio is 15 to 5.  In this example each number shares the common factor of 5.  After dividing both numbers by 5 we get a ratio of 3 : 1.

Below are some examples of ratios:

We have 12 apples, 10 oranges, and 6 bananas

Apples to Bananas = 12 to 6 (simplified: 2 to 1)

Oranges to Bananas = 10/6 (simplified: 5/3)

Oranges to Apples = 10 : 12 (simplified 5 : 6)

Bananas to Apples = 6 : 12 (simplified: 1 :2)

Bananas to Oranges = 6 to 10 (simplified: 3 to 5)