How do you simplify ratios?

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Answer 1 · 2016-04-12T06:22:36

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.

Example problem: Simplify $70 : 56$ $70:56$

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

$35 : 28$ $35:28$

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

$5 : 4$ $5:4$

$5$ $5$ and $4$ $4$ 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:

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

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

So the GCF is $14$ $14$

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

$5 : 4$ $5:4$