Ratio 87837 226073988 2008-07-16T18:37:47Z 99.228.121.58 {{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 &mdash; 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 &mdash; 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]] {{algebra-stub}}