Ratio

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This article is about the mathematical concept. For the Swedish institute, see Ratio Institute. For the academic journal, see Ratio (journal).

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A ratio is a quantity that denotes the proportional^{[citation needed]} 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 is written as two whole numbers (the terms) separated by a colon (:) which is read as the word "to". For example, 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.

Ratios can be converted from centimeters to meters by simply adding two zeros to the number representing the ratio. For example; 1:10 means that 1 centimeter represents 10 centimeters in real life, but to convert that to 10 meters, add to zeros on to the ratio, therefore giving you a ratio of 1:1000. This means that one centimeter represents 1000 centimeters in real life, or 10 meters. This works for converting meters to kilometers too. Conversions in ratio representation is useful for simplifying map scales to easier to read terms. (Article by jcebrammall)

Throughout the physical sciences, ratios of physical quantities are treated as real numbers. For example, the ratio of Failed to parse (Missing texvc executable; please see math/README to configure.): 2 \pi

metres to 1 metre (say, the ratio of the circumference of a certain circle to its radius) is the real number Failed to parse (Missing texvc executable; please see math/README to configure.): 2 \pi

. That is, Failed to parse (Missing texvc executable; please see math/README to configure.): 2 \pi m/1m = Failed to parse (Missing texvc executable; please see math/README to configure.): 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.

More examples

The ratio of heights of the Eiffel Tower (300 m) and the Great Pyramid of Giza (139 m) is 300:139, so one structure is more than twice the height of the other (more precisely, 2.16 times).
The ratio of the mass of Jupiter to the mass of the Earth is approximately 318:1, meaning that Jupiter's mass is 318 times that of the earth.
If two axles are connected by gear wheels, the number of times one axle turns for each turn of the other is known as the gear ratio, one familiar example of which is the number of turns of the pedals of a bicycle compared with number of turns of the rear wheel.
The ratio of hydrogen atoms to oxygen in water (H₂O) is 2:1, which means for every one oxygen atom, there would be two hydrogen atoms as well.
In statistics, the ratio of the probability of something happening to the probability of it not happening is called the odds of the event happening.
In music, the interval of a perfect fifth is formed by two pitches, or frequencies, at a ratio of 3:2, with the higher note being 1.5 times the frequency of the lower.