How do you simplify ratios?

1 Answer
Apr 12, 2016

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 #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#