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In mathematics and in the natural sciences , the quotient describes a ratio of two quantities to one another, i.e. the result of a division . The quotient of two whole numbers ( dividend and divisor ) is always a rational number and can be written as a fraction (e.g. for two thirds).

A quotient is often used to classify a value in an overall scale, e.g. B. the intelligence quotient , which relates the number determined by an intelligence test for a person to the “average intelligence ” of their age group . The intelligence quotient 100 stands for the average . Other examples are the proportions of the national flag or aspect ratios .

Ratios of similar sizes are often given in percent , whereby the value of the ratio does not change, e.g. B. . To get the percentage, multiply the ratio fraction by one, where . In the example: .

Special quotients in this sense are e.g. B .:

  • The slope as the ratio of the increase in value on the vertical coordinate axis to the increase in value on the horizontal axis.
  • The scale as the ratio of two lengths .

Many physical quantities are also defined as quotients, e.g. B.


Ratio equations or proportions are equations that equate two ratios:

and are also called forelimbs , and hind limbs of proportion. In addition, and are called outer links and and inner links . The proportion can be transformed into an equation of the form by cross multiplication . By swapping the inner links or the outer links of a proportion, new proportions are created: and . In addition, the laws of corresponding addition and subtraction apply :

Laws of corresponding addition and subtraction

Let the proportion be given. Then the proportions also apply

and and and and .

Continuous proportions

Occasionally there is also the spelling


as " , , how behave to be pronounced." These continuous proportions , also called chain proportions or ratio chains, are not to be understood as a single equation, but rather are a short form for the two equations

  • and

or equivalent

  • and
  • .


Web links

Wiktionary: quotient  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. ^ Walter Gellert, Herbert Kästner , Siegfried Neuber (eds.): Lexikon der Mathematik , VEB Bibliographisches Institut Leipzig, 1979. S 447, Proportion .