Question

How do you simplify ratios?

Answer 1

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:

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

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

So the GCF is `14`

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

`5:4`