In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced /ˈkwoʊʃənt/) is a quantity produced by the division of two numbers.[1] The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division)[2] or a fraction or ratio (in the case of a general division). For example, when dividing 20 (the dividend) by 3 (the divisor), the quotient is 6 (with a remainder of 2) in the first sense and (a repeating decimal) in the second sense.
In metrology (International System of Quantities and the International System of Units), "quotient" refers to the general case with respect to the units of measurement of physical quantities.[3][4][5]Ratios is the special case for dimensionless quotients of two quantities of the same kind.[3][6]
Quotients with a non-trivial dimension and compound units, especially when the divisor is a duration (e.g., "per second"), are known as rates.[7]
For example, density (mass divided by volume, in units of kg/m3) is said to be a "quotient", whereas mass fraction (mass divided by mass, in kg/kg or in percent) is a "ratio".[8]Specific quantities are intensive quantities resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size".[3]
^"Quotient". Dictionary.com.
^Weisstein, Eric W. "Integer Division". mathworld.wolfram.com. Retrieved 2020-08-27.
^ abc"ISO 80000-1:2022(en) Quantities and units — Part 1: General". iso.org. Retrieved 2023-07-23.
^James, R. C. (1992-07-31). Mathematics Dictionary. Springer Science & Business Media. ISBN 978-0-412-99041-0.
^"IEC 60050 - Details for IEV number 102-01-22: "quotient"". International Electrotechnical Vocabulary (in Japanese). Retrieved 2023-09-13.
^"IEC 60050 - Details for IEV number 102-01-23: "ratio"". International Electrotechnical Vocabulary (in Japanese). Retrieved 2023-09-13.
^"IEC 60050 - Details for IEV number 112-03-18: "rate"". International Electrotechnical Vocabulary (in Japanese). Retrieved 2023-09-13.
^Thompson, A.; Taylor, B. N. (March 4, 2020). "NIST Guide to the SI, Chapter 7: Rules and Style Conventions for Expressing Values of Quantities". Special Publication 811 | The NIST Guide for the use of the International System of Units. National Institute of Standards and Technology. Retrieved October 25, 2021.
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Global Information
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