2.1.rkt

#lang racket
(define (make-rat n d)
  (let ((g (gcd n d)))
  (sign-clean (/ n g) (/ d g))))

(define (sign-clean n d)
  (cons (if (>= d 0) n (- n))
        (abs d)))

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

(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))
     (* (denom x) (numer y))))

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

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

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