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

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

(defun mul-rat (x y)
  (make-rat (* (numer x) (numer y))
	    (* (denom x) (denom y))))

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

(defun equal-ratp (x y)
  (= (* (numer x) (denom y))
     (* (numer y) (denom x))))

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

(defun numer (x) (car x))
(defun denom (x) (cdr x))

(defun print-rat (x)
  (format t "~a/" (numer x))
  (format t "~a~%" (denom x)))

;; Exercise 2.2
(defun make-segment (start end)
  (cons
   (make-point (x-point start) (y-point start))
   (make-point (x-point end) (y-point end))))

(defun start-segment (segment) (car segment))
(defun end-segment (segment) (cdr segment))

(defun average (x y)
  (/ (+ x y) 2))
(defun midpoint-segment (segment)
  (make-point (average (x-point (start-segment segment))
		       (x-point (end-segment segment)))
	      (average (y-point (start-segment segment))
		       (y-point (end-segment segment)))))

(defun make-point (x y)
  (cons x y))

(defun x-point (point) (car point))
(defun y-point (point) (cdr point))

(defun print-point (p)
  (format t "(~a,~a)~%" (x-point p) (y-point p)))