# Ratio Simplifier

## Calculator Use

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.

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.