# Ratio Simplifier

## Calculator Use

Use this calculator to simplify ratios of the form A : B. A or B can be whole numbers, integers, decimal numbers, fractions or mixed numbers. They can be different types, for example, one fraction and one decimal. The ratio values can be positive or negative.

This calculator simplifies ratios by converting all values to whole numbers then reducing the whole numbers to lowest terms using the greatest common factor (GCF). The full solution shows all work and the steps to get a ratio into simplest form.

### What is a Ratio?

A ratio is a comparison of the value of two numbers. The ratio A : B is read as "A to B" and describes the relative proportion of two amounts.

## 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

### 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.