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/

/ Function

Syntax:

/ number → reciprocal

/ numerator &rest denominators+ → quotient

Arguments and Values:

number, denominator—a non-zero number .

numerator, quotient, reciprocal—a number .

Description:

The function / performs division or reciprocation.

If no denominators are supplied, the function / returns the reciprocal of number.

If at least one denominator is supplied, the function / divides the numerator by all of the denominators and returns the resulting quotient.

If each argument is either an integer or a ratio, and the result is not an integer , then it is a ratio.

The function / performs necessary type conversions.

If any argument is a float then the rules of floating-point contagion apply; see Section 12.1.4 (Floating-point Computations).

Examples:


(/ 12 4) → 3 
(/ 13 4) → 13/4 
(/ -8) → -1/8 
(/ 3 4 5) → 3/20 
(/ 0.5) → 2.0 
(/ 20 5) → 4 
(/ 5 20) → 1/4 
(/ 60 -2 3 5.0) → -2.0 
(/ 2 #c(2 2)) → #C(1/2 -1/2)

Exceptional Situations:

The consequences are unspecified if any argument other than the first is zero. If there is only one argument, the consequences are unspecified if it is zero.

Might signal type-error if some argument is not a number . Might signal division-by-zero if division by zero is attempted. Might signal arithmetic-error.

See Also:

floor, ceiling, truncate, round

Expanded Reference: /​

Reciprocal with a single argument​

With one argument, / returns the reciprocal of the number.

(/ 2)
=> 1/2
(/ -8)
=> -1/8
(/ 0.5)
=> 2.0

Basic division​

With two or more arguments, / divides the first argument by all subsequent arguments.

(/ 12 4)
=> 3
(/ 20 5)
=> 4
(/ 3 4 5)
=> 3/20
(/ 60 -2 3 5.0)
=> -2.0

Rational division​

When dividing integers that do not divide evenly, the result is a ratio, not a truncated integer.

(/ 13 4)
=> 13/4
(/ 5 20)
=> 1/4
(/ 1 3)
=> 1/3

Floating-point division​

When any argument is a float, the result is a float.

(/ 10.0 3)
=> 3.3333333
(/ 1 3.0)
=> 0.33333334
(/ 7.0d0 2)
=> 3.5d0

Complex division​

/ handles complex numbers as well.

(/ #c(10 0) 2)
=> 5
(/ 2 #c(2 2))
=> #C(1/2 -1/2)
(/ #c(4.0 2.0) #c(1.0 1.0))
=> #C(3.0 -1.0)