(load "util.scm")

(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? x y)
  (= (* (numer x) (denom y))
     (* (numer y) (denom x))))

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

; Examples
; (define one-half (make-rat 1 2))
; (print-rat one-half)
; (define one-third (make-rat 1 3))
; (print-rat (add-rat one-half one-third))
; (print-rat (mul-rat one-half one-third))
; (print-rat (add-rat one-third one-third))

(display "ex-2.1")

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

(print-rat (make-rat 3 9))
(print-rat (make-rat -3 9))
(print-rat (make-rat 3 -9))
(print-rat (make-rat -3 -9))

(display "\n\nex-2.2")