How do you simplify ratios?
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
In this method, we will divide both sides of the ratio by each factor we find in turn.
Trying each prime number in turn, the next number which both sides are divisible by is
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