public class Bruch {

	public int zaehler;
	public int nenner;

	public Bruch(int zaehler, int nenner) {
		this.zaehler = zaehler;
		this.nenner = nenner;
	}
	
	public Bruch(int zaehler) {
		this.zaehler = zaehler;
		this.nenner = 1;
	}
	
	public String toString() {
		this.kuerze();
		String s = this.zaehler + " / " + this.nenner;
		return s;
	}
	
	public void addiere(Bruch b) {
		this.zaehler = (this.zaehler * b.nenner) + (b.zaehler * this.nenner);
		this.nenner = this.nenner * b.nenner;
		this.kuerze();
	}
	
	public void subtrahiere(Bruch b) {
		this.zaehler = (this.zaehler * b.nenner) - (b.zaehler * this.nenner);
		this.nenner = this.nenner * b.nenner;
		this.kuerze();
	}
	
	public void multipliziere(Bruch b) {
		this.zaehler = this.zaehler * b.zaehler;
		this.nenner = this.nenner * b.nenner;
		this.kuerze();
	}
	
	public void dividiere(Bruch b) {
		this.zaehler = this.zaehler * b.nenner;
		this.nenner = this.nenner * b.zaehler;
		this.kuerze();
	}
	
	public double wert() {
		double wert = (double) this.zaehler / (double) this.nenner;
		return wert;
	}
	
	public void kuerze() {
		int ggT = ggT(this.zaehler, this.nenner);
		this.nenner = this.nenner / ggT;
		this.zaehler = this.zaehler / ggT;
	}
	
	private static int ggT(int x, int y) {
	    while (y != 0) {
	        int temp = x % y;

	        x = y;

	        y = temp;
	    }
	    return x;
	}
	
	public static Bruch addiere(Bruch a, Bruch b) {
		int zaehler = (a.nenner * b.zaehler) + (b.nenner * a.zaehler);
		int nenner = a.nenner * b.nenner;
		
		Bruch c = new Bruch(zaehler, nenner);
		c.kuerze();
		return c;
	}
	
	public static Bruch subtrahiere(Bruch a, Bruch b) {
		int zaehler = (b.nenner * a.zaehler) - (a.nenner * b.zaehler);
		int nenner = a.nenner * b.nenner;
		
		Bruch c = new Bruch(zaehler, nenner);
		c.kuerze();
		return c;
	}
	
	public static Bruch multipliziere(Bruch a, Bruch b) {
		int zaehler = a.zaehler * b.zaehler;
		int nenner = b.nenner * a.nenner;
		
		Bruch c = new Bruch(zaehler, nenner);
		c.kuerze();
		return c;
	}
	
	public static Bruch dividiere(Bruch a, Bruch b) {
		int zaehler = a.zaehler * b.nenner;
		int nenner = a.nenner * b.zaehler;
		
		Bruch c = new Bruch(zaehler, nenner);
		c.kuerze();
		return c;
	}
	
	//Nur für Jack Static Result
	public static void main(String[] args) {
		
	}
	
}