# How do you simplify ratios?

Apr 12, 2016

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 $70 : 56$

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Method 1

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

Given $70 : 56$, first note that both sides are even (since they end with even digits), so divide both sides by $2$ to get:

$35 : 28$

Trying each prime number in turn, the next number which both sides are divisible by is $7$, so divide both sides by $7$ to get:

$5 : 4$

$5$ and $4$ have no common factor, so we can stop.

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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:

$\frac{70}{56} = 1$ with remainder $14$

$\frac{56}{14} = 4$ with remainder $0$

So the GCF is $14$

Divide both sides of our original ratio by $14$ to get:

$5 : 4$