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Quotient


The term "quotient" is most commonly used to refer to the ratio q=r/s of two quantities r and s, where s!=0.

Less commonly, the term quotient is also used to mean the integer part of such a ratio. In the Wolfram Language, the command Quotient[r, s] is defined in this latter sense, returning

 r\s=|_r/s_|,

where |_x_| is the floor function. This is sometimes called integer division.

Since usage concerning fractional part/value and integer part/value can be confusing, the following table gives a summary of names and notations used. Here, S&O indicates Spanier and Oldham (1987).

notationnameS&OGraham et al. Wolfram Language
[x]ceiling function--ceiling, least integerCeiling[x]
mod(m,n)congruence----Mod[m, n]
|_x_|floor functionInt(x)floor, greatest integer, integer partFloor[x]
x-|_x_|fractional valuefrac(x)fractional part or {x}SawtoothWave[x]
sgn(x)(|x|-|_|x|_|)fractional partFp(x)no nameFractionalPart[x]
sgn(x)|_|x|_|integer partIp(x)no nameIntegerPart[x]
nint(x)nearest integer function----Round[x]
m\nquotient----Quotient[m, n]

See also

Ceiling Function, Division, Floor Function, Fraction, Integer Division, Integer Part, Nearest Integer Function, Polynomial Quotient, Quotient Group, Quotient Ring, Quotient Space, Ratio, Rational Number, Remainder Explore this topic in the MathWorld classroom

Related Wolfram sites

http://functions.wolfram.com/IntegerFunctions/Quotient/

Explore with Wolfram|Alpha

References

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.Spanier, J. and Oldham, K. B. An Atlas of Functions. Washington, DC: Hemisphere, p. 74, 1987.

Referenced on Wolfram|Alpha

Quotient

Cite this as:

Weisstein, Eric W. "Quotient." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Quotient.html

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