AskDefine | Define ratio

Dictionary Definition

ratio n : the relative magnitudes of two quantities (usually expressed as a quotient)

User Contributed Dictionary

English

Etymology

From ratio.

Pronunciation

  • /ɻeɪ.ʃi.oʊ/

Noun

  1. A number representing a comparison between two things.
  2. A judicial decision.

Translations

Latin

Pronunciation

  • /ratjo/

Inflection

Descendants

Extensive Definition

A ratio is a quantity that denotes the proportional 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.
Fractions and percentages 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 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 sciences, ratios of physical quantities are treated as real numbers. For example, the ratio of 2 \pi metres to 1 metre (say, the ratio of the circumference of a certain circle to its radius) is the real number 2 \pi. That is, 2 \pim/1m = 2 \pi. 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 in mathematics.)
In algebra, two quantities having a constant ratio are in a special kind of linear relationship called proportionality.
ratio in Catalan: Raó aritmètica
ratio in Danish: Forhold
ratio in Estonian: Jagatis
ratio in Modern Greek (1453-): Αριθμοδείκτης
ratio in Spanish: Razón aritmética
ratio in Esperanto: Rilatumo
ratio in Korean: 비 (수학)
ratio in Italian: Rapporto
ratio in Hebrew: יחס (בין מספרים)
ratio in Lithuanian: Santykis
ratio in Dutch: Verhouding (wiskunde)
ratio in Japanese: 比
ratio in Polish: Stosunek (matematyka)
ratio in Portuguese: Taxa (razão)
ratio in Simple English: Ratio
ratio in Serbian: Рацио
ratio in Telugu: నిష్పత్తి
ratio in Thai: อัตราส่วน

Synonyms, Antonyms and Related Words

Vernunft, amount, analogousness, arithmetical proportion, balance, brain, brains, caliber, commensurability, comparability, comparableness, comparativeness, compass, conception, continued fraction, correlation, correspondence, cut, degree, discourse of reason, discursive reason, equivalence, esprit, extent, fraction, geometric ratio, grade, gray matter, harmonic proportion, head, headpiece, height, improper fraction, intellect, intellection, intellectual faculty, intelligence, interval, leap, level, mark, measure, mens, mental capacity, mentality, mind, notch, nous, nuance, pas, peg, percent, percentage, period, pitch, plane, plateau, point, power of reason, proportion, proportionability, psyche, quota, quotum, range, rate, rationality, reach, reason, reasoning, reasoning faculty, relationship, remove, round, rule of three, rung, scale, scope, shade, shadow, similarity, smarts, space, stair, standard, step, stint, tread, understanding
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