Online Calculator Resource

Ratio Simplifier

Ratio Simplifier
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Calculator Use

A ratio is a comparison of the value of two numbers. The ratio A : B is read as "A to B" and can also be expressed as a fraction, A/B.

Use this calculator to simplify ratios by reducing to lowest terms. Find the greatest common factor (GCF) and see the work to get a ratio into simplest form.

How to Simplify a Ratio A : B

• List the factors of A
• List the factors of B
• Find the greatest common factor (GCF) of A and B
• Divide A and B each by the GCF
• Use the results to rewrite the ratio in simplest form

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

Example: Simplify the ratio 8 : 36

• The factors of 8 are: 1, 2, 4, 8
• The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
• The greatest common factor of 8 and 36 is 4
• Divide both terms by 4
• 8 ÷ 4 = 2
• 36 ÷ 4 = 9
• Rewrite the ratio using the results. The simplified ratio is 2 : 9.
• 8 : 36 = 2 : 9 in simplest form

Example: Simplify the ratio 3 : 8

• The factors of 3 are 1, 3
• The factors of 8 are: 1, 2, 4, 8
• The greatest common factor of 3 and 8 is 1
• Divide both terms by 1
• 3 ÷ 1 = 3
• 8 ÷ 1 = 8
• Rewrite the ratio using the results. The ratio 3 : 8 is already simplified.

You can conclude that if the greatest common factor is 1 then the ratio is already in simplest form.

Related Calculators

To compare multiple ratios see our Ratio Calculator.

To simplify a fraction into a reduced fraction or mixed number use our Simplifying Fractions Calculator.

Cite this content, page or calculator as:

Furey, Edward "Ratio Simplifier"; from http://www.calculatorsoup.com - Online Calculator Resource.