Ratio
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{{otheruses4|the mathematical concept|the Swedish institute|Ratio Institute|the academic journal|Ratio (journal)}}
{{expert|date=October 2007}}<!-- see talk page -->
[[Image:Aspect-ratio-4x3.svg|thumb|The ratio of width to height of typical [[computer displays]]]]
A '''ratio''' is a [[quantity]] that denotes the [[proportional (mathematics)|proportional]]{{fact|date=October 2007}}<!-- a circular definition, what is "proportion" then? --> amount or magnitude of one quantity relative to another.
Ratios are [[unitless]] when they relate quantities of the same [[dimension]]. When the two quantities being compared are of different types, the units are the first quantity "per" unit of the second — for example, a speed or [[velocity]] can be expressed in "miles per hour". If the second unit is a measure of time, we call this type of ratio a [[rate]].
''[[Fraction (mathematics)|Fraction]]s'' and ''[[percentage]]s'' are both specific applications of ratios. Fractions relate the part (the numerator) to the whole (the denominator) while percentages indicate parts per 100.
A ratio of 2:3 ("two to three") means that the whole is made up of 2 parts of one thing and 3 parts of another — thus, the whole contains five parts in all. To be specific, if a basket contains 2 apples and 3 oranges, then the ''ratio of apples to oranges'' is 2:3. If another 2 apples and 3 oranges are added to the basket, then it will contain 4 apples and 6 oranges, resulting in a ratio of 4:6, which is equivalent to a ratio of 2:3 (thus ratios [[Reduction (mathematics)|reduce]] like regular fractions). In this case, 2/5 or 40% of the fruit are apples and 3/5 or 60% are oranges in the basket.
Note that in the previous example the proportion of apples in the basket is 2/5 ("two of five" fruits, "two out of five" fruits, "two fifths" of the fruits, or 40% of the fruits). Thus a proportion compares part to whole instead of part to part.
Throughout the [[physical science]]s, ratios of physical quantities are treated as [[real number]]s. For example, the ratio of <math>2 \pi</math> [[metre]]s to 1 metre (say, the ratio of the circumference of a certain [[circle]] to its radius) is the real number <math>2 \pi</math>. That is, <math>2 \pi</math>m/1m = <math>2 \pi</math>. Accordingly, the classical definition of [[measurement]] is the estimation of a ratio between a quantity and a unit of the same kind of quantity. (See also the article on [[Commensurability (mathematics)|commensurability in mathematics]].)
In [[algebra]], two quantities having a ''[[constant]] ratio'' are in a special kind of [[linear]] relationship called [[Proportionality (mathematics)|proportionality]].
[[Category:Elementary mathematics]]
[[Category:Algebra]]
[[ar:نسبة (رياضيات)]]
[[ca:Raó aritmètica]]
[[da:Forhold]]
[[et:Jagatis]]
[[el:Αριθμοδείκτης]]
[[es:Razón aritmética]]
[[eo:Rilatumo]]
[[fr:Ratio]]
[[ko:비 (수학)]]
[[it:Rapporto]]
[[he:יחס (בין מספרים)]]
[[lt:Santykis]]
[[nl:Verhouding (wiskunde)]]
[[ja:比]]
[[pl:Stosunek (matematyka)]]
[[pt:Taxa (razão)]]
[[simple:Ratio]]
[[sr:Рацио]]
[[te:నిష్పత్తి]]
[[th:อัตราส่วน]]
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