; rational numbers

(define (frac n d)
  (if (zero? d) (error 'frac "can't have zero denominator")
    (if (negative? d) (frac (- n) (- d))
      (let ((g (gcd n d)))
        (if (= g 1) (cons n d)
          (cons (/ n g) (/ d g)))))))

(define (plus x y)
  (let ((a (car x)) (b (cdr x)) (c (car y)) (d (cdr y)))
    (frac (+ (* a d) (* b c)) (* b d))))

(define (minus x y)
  (let ((a (car x)) (b (cdr x)) (c (car y)) (d (cdr y)))
    (frac (- (* a d) (* b c)) (* b d))))

(define (times x y)
  (let ((a (car x)) (b (cdr x)) (c (car y)) (d (cdr y)))
    (frac (* a c) (* b d))))

(define (divide x y)
  (let ((a (car x)) (b (cdr x)) (c (car y)) (d (cdr y)))
    (frac (* a d) (* b c))))

(define (less-than? x y)
  (let ((a (car x)) (b (cdr x)) (c (car y)) (d (cdr y)))
    (< (* a d) (* b c))))

(display (plus (frac 1 3) (frac -1 7))) (newline)
(display (minus (frac 1 3) (frac -1 7))) (newline)
(display (times (frac 1 3) (frac -1 7))) (newline)
(display (divide (frac 1 3) (frac -1 7))) (newline)
(display (less-than? (frac 1 3) (frac -1 7))) (newline)