Unit Rate Calculator with Fractions

Unit Rate Calculator with Fractions

This calculator helps you determine the unit rate when dealing with quantities expressed as fractions. A unit rate is the ratio of two different quantities where one of the quantities is 1. For example, miles per hour, dollars per pound, or tasks per day. When working with fractions, we often need to find out "how much of something per one unit of something else."

How to Calculate Unit Rate with Fractions

To find the unit rate when dealing with fractional quantities, you essentially divide the first quantity by the second quantity. Let's say your first quantity is represented by the fraction $\frac{a}{b}$ and your second quantity is represented by the fraction $\frac{c}{d}$.

The unit rate is calculated as:

Unit Rate = $\frac{\text{Quantity 1}}{\text{Quantity 2}}$ = $\frac{\frac{a}{b}}{\frac{c}{d}}$

To divide fractions, you invert the second fraction and multiply:

Unit Rate = $\frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$

The result gives you the rate per single unit of the second quantity.

Example:

Suppose you can paint $\frac{3}{4}$ of a wall in $\frac{5}{6}$ of an hour. What is the unit rate of painting in walls per hour?

• Quantity 1: $\frac{3}{4}$ walls
• Quantity 2: $\frac{5}{6}$ hours

Using the formula:

Unit Rate = $\frac{\frac{3}{4}}{\frac{5}{6}} = \frac{3}{4} \times \frac{6}{5} = \frac{18}{20}$

Simplifying the fraction:

Unit Rate = $\frac{18}{20} = \frac{9}{10}$ walls per hour.

This means you can paint $\frac{9}{10}$ of a wall in one hour.