問題 2.1

(define (gcd a b) (if (= b 0) a (gcd b (remainder a b))))


(define (make-rat n d)
  (let ((g (gcd n d)))
    (let ((ng (/ n g)) (dg (/ d g)))
      (if (< ng 0)
          (cons (- ng) (- dg))
          (cons ng dg)))))

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

;(define make-rat cons)

(define (numer x) (car x))
(define (denom x) (cdr x))

(define (print-rat x)
  (display (numer x))
  (display "/")
  (display (denom x))
  (newline))

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

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

(define (mul-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))))

(define (equal-rat?)
  (= (* (numer x) (denom y))
     (* (numer y) (denom x))))

(define one-half (make-rat 1 2))
(define one-third (make-rat 1 3))
(define one-mthird (make-rat 1 -3))
(define two-third (make-rat 2 3))