TOPICS
Quotient
The term "quotient" is most commonly used to refer to the ratio 
of two quantities 
and 
,
where 
.
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
 |
where 
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).
| notation | name | S&O | Graham et al. | Wolfram Language |
![[x]](https://mathworld.wolfram.com/images/equations/Quotient/Inline6.svg) | ceiling function | -- | ceiling, least integer | Ceiling[x] |
 | congruence | -- | -- | Mod[m, n] |
 | floor function |  | floor, greatest integer, integer part | Floor[x] |
 | fractional value |  | fractional part or  | SawtoothWave[x] |
 | fractional part |  | no name | FractionalPart[x] |
 | integer part |  | no name | IntegerPart[x] |
 | nearest integer function | -- | -- | Round[x] |
 | quotient | -- | -- | 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 classroomRelated Wolfram sites
https://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
QuotientCite this as:
Weisstein, Eric W. "Quotient." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Quotient.html