In mathematics, a rate is the quotient of two quantities, often represented as a fraction.
[1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change in the other (dependent) variable.
Rates and ratios often vary with time, location, particular element (or subset) of a set of objects, etc.
For example, miles per hour in transportation is the output (or benefit) in terms of miles of travel, which one gets from spending an hour (a cost in time) of traveling (at this velocity).
For example, in finance, one could define I by assigning consecutive integers to companies, to political subdivisions (such as states), to different investments, etc.
For example, 5 miles (mi) per kilowatt-hour (kWh) corresponds to 1/5 kWh/mi (or 200 Wh/mi).
Rates are relevant to many aspects of everyday life.
The speed of the car (often expressed in miles per hour) is a rate.
The amount of interest paid per year is a rate.
) can be formally defined in two ways:[3] where f(x) is the function with respect to x over the interval from a to a+h.
An instantaneous rate of change is equivalent to a derivative.
In contrast, the instantaneous velocity can be determined by viewing a speedometer.