# How To Divide Ratios

Ratios cannot be expressed as whole-number integers. These numbers are known as rational numbers and are a superset above integers, whole numbers and natural numbers. The mathematical manipulation of ratios is commonly first presented in pre-algebra studies. The division of one ratio by another creates what is known as a complex fraction. Complex fractions are evaluated using standard rules of algebra. In this manipulation, the division operation is changed, and the complex fraction broken into two smaller fractions.

### Step 1

Create a fraction that has a numerator equal to the ratio being divided and the denominator equal to the ratio it is being divided by. For example, (3/5) / (1/3) represents 3/5 divided by 1/3.

### Step 2

Invert the denominator and change the division symbol to a multiplication symbol. Continuing the example, (3/5) / (1/3) = (3/5) * (3/1).

### Step 3

Multiply the numerators and denominators. For example, (3/5) * (3/1) = 9/5.

### Step 4

Simplify the fraction as much as possible.

### Cite This Article

#### MLA

Dockery, Gabriel. "How To Divide Ratios" *sciencing.com*, https://www.sciencing.com/divide-ratios-8475115/. 24 April 2017.

#### APA

Dockery, Gabriel. (2017, April 24). How To Divide Ratios. *sciencing.com*. Retrieved from https://www.sciencing.com/divide-ratios-8475115/

#### Chicago

Dockery, Gabriel. How To Divide Ratios last modified March 24, 2022. https://www.sciencing.com/divide-ratios-8475115/