- Plural of ratio
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.
ratios in Catalan: Raó aritmètica
ratios in Danish: Forhold
ratios in Estonian: Jagatis
ratios in Modern Greek (1453-): Αριθμοδείκτης
ratios in Spanish: Razón aritmética
ratios in Esperanto: Rilatumo
ratios in Korean: 비 (수학)
ratios in Italian: Rapporto
ratios in Hebrew: יחס (בין מספרים)
ratios in Lithuanian: Santykis
ratios in Dutch: Verhouding (wiskunde)
ratios in Japanese: 比
ratios in Polish: Stosunek (matematyka)
ratios in Portuguese: Taxa (razão)
ratios in Simple English: Ratio
ratios in Serbian: Рацио
ratios in Telugu: నిష్పత్తి
ratios in Thai: อัตราส่วน