The term "quotient" is most commonly used to refer to the ratio 
of two quantities r and s, where 
.
Less commonly, the term quotient is also used to mean the integer part of such a ratio. In Mathematica, 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 (D. W. Cantrell, pers. comm.). Here, S&O indicates Spanier and Oldham (1987).
| notation | name | S&O | Graham et al. | Mathematica |
 |
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  |
no name |
 |
fractional part |  |
no name | FractionalPart[ x] |
 |
integer part |  |
no name | IntegerPart[ x] |
 |
nearest integer function | -- | -- | Round[ x] |
 |
quotient | -- | -- | Quotient[ m, n] |
Ceiling Function, Division, Floor Function, Fraction, Integer Division, Integer Part, Nearest Integer, Polynomial Quotient, Quotient Group, Quotient Ring, Quotient Space, Ratio, Rational Number, Remainder
