# 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 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.