How to Simplify a Ratio A : B when A and B are both whole numbers
List the factors of A
List the factors of B
Find the greatest common factor of A and B, GCF(A, B)
Divide A and B each by the GCF
Use the whole number results to rewrite the ratio in simplest form
If the GCF = 1 then the ratio is already in simplest form.
How to Simplify a Ratio A : B when A and B are not whole numbers, in this order
If A or B are mixed numbers convert mixed numbers to improper fractions
If A or B are decimal numbers multiply both values by the same factor of 10 that will eliminate all decimal places
If one value is a fraction and the other a whole number, reduce the fraction to a whole number if you can or turn the whole number into a fraction by giving it a denominator of 1.
If both A and B are fractions and have like denominators, multiply both fractions by the denominator to eliminate it and you are left with two whole numbers
If both A and B are fractions and have unlike denominators, find the LCD(A, B) and rewrite the fractions with the LCD as the denominator. Multiply both fractions by the denominator to eliminate it and you are left with two whole numbers
If both A and B are whole numbers, Find the greatest common factor of A and B, GCF(A, B), and divide A and B each by the GCF
Example: Simplify the ratio 6 : 10
The factors of 6 are: 1, 2, 3, 6
The factors of 10 are: 1, 2, 5, 10
Then the greatest common factor of 6 and 10 is 2
Divide both terms by 2
6 ÷ 2 = 3
10 ÷ 2 = 5
Rewrite the ratio using the results. The simplified ratio is 3 : 5.
6 : 10 = 3 : 5 in simplest form