Ratio

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The ratio of width to height of typical computer displays

A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared. Mathematically they are represented by separating each quantity with a colon, for example the ratio 2:3, which is read as the ratio "two to three".

The quantities being compared in a ratio might be physical quantities such as speed or temperature, or may simply refer to amounts of particular objects. A common example of the latter case is the ratio of water to cement used in concrete, which is commonly stated as 1:4. This means that the amount of cement used is four times greater than the amount of water used. It does not say anything about the total amounts of cement and water used, nor the amount of concrete being made, because the ratio is only a relative comparison of the two quantities

In general, a ratio of 2:3 means that the amount of the first quantity is (two thirds) of the amount of the second quantity - this pattern works with ratios with more than two terms. This does not mean that a ratio can be converted to a single fraction. A single fraction only represents one part of the ratio. If the ratio deals with objects or amounts of objects, this is often expressed as "for every two parts of the first quantity there are three parts of the second quantity". If these two quantities are the only quantities in a particular situation, for example apples and oranges in a fruit basket containing no other types of fruit, it is sometimes said that "the whole" contains five parts, made up of two parts apples and three parts oranges. In this case, , or 40% of the whole are apples and , or 60% of the whole are oranges. This comparison of a specific quantity to "the whole" is sometimes called a proportion. Proportions are sometimes expressed as percentages as demonstrated above.

Note that ratios can be reduced like fractions, so that the ratio 4:6 is identical in meaning to the ratio 2:3.

Ratios are unitless when they relate quantities of the same units. 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.

Ratios are used frequently throughout the physical sciences, and in many cases a ratio is thought of as a single value. For example, the ratio 60 metres to 1 second, or 60:1 is written as 60ms^/1, "60 metres per second" and is thought of as a measurement of velocity. In this case, the measurement is actually a ratio between two quantities with different units.

In algebra, two variable quantities having a constant ratio are in a special kind of relationship called proportionality.