; rational number package

(define (make-rat n d)
  (let ((g (gcd n d)))
    (cons (/ n g) (/ d g))))

(define (numer x) (car x))

(define (denom x) (cdr x))

(define (add-rat x y)
  (make-rat (+ (* (numer x) (denom y))
               (* (denom x) (numer y)))
            (* (denom x) (denom y))))

(define (sub-rat x y)
  (make-rat (- (* (numer x) (denom y))
               (* (denom x) (numer y)))
            (* (denom x) (denom y))))

(define (mult-rat x y)
  (make-rat (* (numer x) (numer y))
            (* (denom x) (denom y))))

(define (div-rat x y)
  (make-rat (* (numer x) (denom y))
            (* (denom x) (numer y))))