# Quotient

## Mathematical result of division / From Wikipedia, the free encyclopedia

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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 $6{\tfrac {2}{3}}=6.66...$ (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/m^{3}) 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]}