Simplifying Ratios

Why do we simplify ratios?

We simplify ratios to make the relation or comparison of quantities easier to understand.

Example:
There are 21 horses and 231 chickens on a farm.

The ratio of the number of horses to the number of chickens on the farm can be written as 21 : 231.

This tells us that for the 21 horses on the farm, there are 231 chickens.

However, to better understand the relation between the number of horses and the number of chickens, we should simplify this ratio as below.

      

This simplified ratio, 1 : 11 tells us that for every horse on the farm, there are 11 chickens.

How do we simplify ratios?

To simplify a given ratio, divide all the terms of the ratio by the same number until you cannot divide them any further (as shown above).

Or you may divide the terms by their greatest common factor (GCF) to get the simplest form of the ratio (as below).


Example:

Simplify 144 : 252 using GCF.



So, 144 : 252 = 4 : 7 in its simplest form.