Editing Rate (mathematics) (section)

{{Short description|Ratio between two related quantities in different units}}
{{refimprove|date=February 2015}}
{{Other uses|Rate (disambiguation){{!}}Rate}}

In [[mathematics]], a '''rate''' is the [[quotient]] of two [[quantity|quantities]], often represented as a [[fraction]].<ref>See Webster's New International Dictionary of the English Language, 2nd edition, Unabridged.  Merriam Webster Co. 2016. p.2065 definition 3.</ref> If the [[divisor (mathematics)|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 (mathematics)|dividend]] (the fraction numerator) of the rate expresses the corresponding '''rate of change''' in the other ([[dependent variable|dependent]]) variable. In some cases, it may be regarded as a change to a value, which is caused by a change of a value in respect to another value. For example, acceleration is a change in velocity with respect to time  

''Temporal rate'' is a common type of rate ("per unit of time"), such as [[speed]], [[heart rate]], and [[flux]].<ref name="International Electrotechnical Vocabulary x558">{{cite web | title=IEC 60050 - Details for IEV number 112-03-18: "rate" | website=International Electrotechnical Vocabulary | url=https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=112-03-18 | language=ja | access-date=2023-09-13}}</ref> 
In fact, often ''rate'' is a synonym of [[rhythm]] or [[frequency]], a count per second (i.e., [[hertz]]); e.g., [[radio frequencies]] or [[sample rate]]s.
In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate; for example, a [[heart rate]] is expressed as "beats per minute". 

Rates that have a non-time divisor or denominator include [[exchange rate]]s, [[literacy rate]]s, and [[electric field]] (in volts per meter).

A rate defined using two numbers of the same units will result in a [[dimensionless quantity]], also known as ''[[ratio]]'' or simply as a ''rate'' (such as [[tax rate]]s) or counts (such as [[literacy rate]]). Dimensionless rates can be expressed as a [[percentage]] (for example, the global [[literacy rate]] in 1998 was 80%), [[fraction (mathematics)|fraction]], or [[multiple (mathematics)|multiple]].