;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-advanced-reader.ss" "lang")((modname testfile1) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t quasiquote repeating-decimal #t #t none #t ())))
(define (ggT a b)
  (if (= b 0) a
      (ggT b(remainder a b))
      ))

(define (kgV a b)
  (/ (* a b) (ggT a b)))

(define (zaehler bruch)
  (car bruch))

(define (nenner bruch)
  (cadr bruch))


(define (erweitern bruch zahl)
  (list (* (zaehler bruch)
           zahl)
        (* (nenner bruch)
           zahl)))



(define (kuerzen bruch)
  (let ((teiler (ggT (zaehler bruch) (nenner bruch))))
    (list (/ (zaehler bruch)
             teiler)
          (/ (nenner bruch)
             teiler))))

(define (b-plus b1 b2)
  (kuerzen
   (list
    (+ (* (zaehler b1)
          (nenner b1))
       (* (zaehler b2)
          (nenner b2)))
    (* (nenner b1)
       (nenner b2)))))

(define (b-minus b1 b2)
  (kuerzen
   (list
    (- (* (zaehler b1)
          (nenner b1))
       (* (zaehler b2)
          (nenner b2)))
    (* (nenner b1)
       (nenner b2)))))

(define (b-mal b1 b2)
  (kuerzen
   (list
    (* (zaehler b1) (zaehler b2))
    (* (nenner b1) (nenner b2)))))

(b-minus '(4 6) '(8 3))