Rate (mathematics)

A rate is a special kind of ratio, indicating a relationship between two measurements with the same units.

Example
When dealing with rates, the division operator is sometimes expressed as per. If the units are expressed without abbreviation, the bottom unit is singular. If one travels 5 meters in 2 seconds, the following rate is:


 * $$\frac{5\ \mathrm{meters}}{2\ \mathrm{seconds}} = \frac{5}{2}\ \mathrm{meters\ per\ second} = 2.5\ \mathrm{meters\ per\ second}$$

Often rate is a synonym of rhythm or frequency, a count per second. Examples are heart rate or sample rate.

Unit rate
A unit rate is a rate that is simplified so it has a denominator of 1. This type of rate is frequently used when referring to statistics.

The civics membership in the U.S. House of Representatives is based on a population in the preceding census. In 1990, the population of the United States was about 248,000,000. There are 435 members in the house. On average, how many people are represented by each member of the house?

Write the rate that compares the population size to the number of members of the house. Then divide both the numerator and the denominator by 435.


 * $$\frac{248,000,000\ \mathrm{people}}{435\ \mathrm{members}} = \frac{57,089,000\ \mathrm{people}}{1\ \mathrm{member}}$$

This rate says that each representative represents about 570,000 people.