numerator, denominator

numerator, denominator Function

Syntax:

numerator rational → numerator

denominator rational → denominator

Arguments and Values:

rational—a rational.

numerator—an integer .

denominator—a positive integer .

Description:

numerator and denominator reduce rational to canonical form and compute the numerator or denominator of that number.

numerator and denominator return the numerator or denominator of the canonical form of rational.

If rational is an integer , numerator returns rational and denominator returns 1.

Examples:

(numerator 1/2) → 1 
(denominator 12/36) → 3 
(numerator -1) → -1 
(denominator (/ -33)) → 33 
(numerator (/ 8 -6)) → -4 
(denominator (/ 8 -6)) → 3 

See Also:

Notes:

(gcd (numerator x) (denominator x)) → 1

Expanded Reference: numerator, denominator

numerator and denominator return the numerator and denominator of a rational number in its canonical (reduced) form.

(numerator 1/2)
=> 1
(denominator 1/2)
=> 2
(numerator 3/4)
=> 3
(denominator 3/4)
=> 4

The values returned are always in reduced form, even if the original ratio was not.

(numerator 6/8)
=> 3
(denominator 6/8)
=> 4
(denominator 12/36)
=> 3
(numerator 12/36)
=> 1

For integer arguments, numerator returns the integer itself and denominator returns 1.

(numerator 5)
=> 5
(denominator 5)
=> 1
(numerator -1)
=> -1
(denominator -1)
=> 1

The sign is carried by the numerator. The denominator is always positive.

(numerator -3/4)
=> -3
(denominator -3/4)
=> 4
(numerator (/ 8 -6))
=> -4
(denominator (/ 8 -6))
=> 3

The numerator and denominator are always coprime (their GCD is 1).

(let ((r 12/18))
  (gcd (numerator r) (denominator r)))
=> 1

(let ((r 100/75))
  (values (numerator r) (denominator r)))
=> 4
=> 3