# How do you simplify ratios?

##### 1 Answer

Method 1: Divide both sides by each common factor you find in turn.

Method 2: Find the greatest common factor of the two numbers and divide both sides by it.

#### Explanation:

Example problem: Simplify

**Method 1**

In this method, we will divide both sides of the ratio by each factor we find in turn.

Given

#35:28#

Trying each prime number in turn, the next number which both sides are divisible by is

#5:4#

**Method 2**

In this method we find the greatest common factor first, then divide both sides by it.

To find the GCF proceed as follows:

Divide the larger number by the smaller to give a quotient and remainder.

If the remainder is zero then the smaller number is the GCF.

Otherwise repeat with the smaller number and the remainder.

So in our example:

#70/56 = 1# with remainder#14#

#56/14 = 4# with remainder#0#

So the GCF is

Divide both sides of our original ratio by

#5:4#