Editing Rate (mathematics) (section)

==Properties and examples==
{{further|Ratio}}

Rates and ratios often vary with time, location, particular element (or subset) of a set of objects, etc. Thus they are often [[Function (mathematics)|mathematical functions]].

A rate (or ratio) may often be thought of as an output-input ratio, [[benefit-cost ratio]], all considered in the broad sense. 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).

A set of sequential indices may be used to enumerate elements (or subsets) of a set of ratios under study. For example, in finance, one could define I by assigning consecutive integers to companies, to political subdivisions (such as states), to different investments, etc. The reason for using indices I is so a set of ratios (i=0, N) can be used in an equation to calculate a function of the rates such as an average of a set of ratios. For example, the average velocity found from the set of v<sub> I </sub>'s mentioned above. Finding averages may involve using weighted averages and possibly using the [[harmonic mean]].

A ratio r=a/b has both a numerator "a" and a denominator "b". The value of a and b may be a [[real number]] or [[integer]]. The [[Multiplicative inverse|inverse]] of a ratio r is 1/r = b/a. A rate may be equivalently expressed as an inverse of its value if the ratio of its units is also inverse. For example, 5 [[mile]]s (mi) per [[kilowatt-hour]] (kWh) corresponds to 1/5 kWh/mi (or 200 [[Watt-hour|Wh]]/mi).

Rates are relevant to many aspects of everyday life. For example:
''How fast are you driving?'' The speed of the car (often expressed in miles per hour) is a rate. ''What interest does your savings account pay you?'' The amount of interest paid per year is a rate.