import eprog.EprogException;
import java.lang.Number;

class Bruch extends Number
{
	public Bruch() throws EprogException
	{
		zaehler = 0;
		nenner = 1;
	}

	public Bruch(int Zaehler) throws EprogException
	{
		zaehler = Zaehler;
		nenner = 1;
	}

	public Bruch(int Zaehler, int Nenner) throws EprogException
	{
		if(Nenner == 0)
			throw new EprogException();
		zaehler = Zaehler;
		nenner = Nenner;
	}  

	public float floatValue() 
	{
		return (float)doubleValue();
	}

	public double doubleValue() 
	{
		return (double)zaehler / (double)nenner;
	}

	public long longValue() 
	{
		return Math.round(doubleValue());
	}

	public int intValue() 
	{
		return (int)longValue();
	}

	public byte byteValue() 
	{
		return (byte)longValue();
	}
	

	public String toString()
	{
		if(nenner == 0)
			return "(infinite)";
		if(zaehler == 0)
			return "0";
		return zaehler + "/" + nenner;	
	}

	public Bruch add(Bruch summand) throws EprogException
	{
		return new Bruch(zaehler * summand.nenner + summand.zaehler * nenner, nenner * summand.nenner).kuerzen();
	}

	public Bruch subtract(Bruch subtraktor) throws EprogException
	{
		return add(new Bruch(-subtraktor.zaehler, subtraktor.nenner));
	}

	public Bruch multiply(Bruch faktor) throws EprogException
	{	
		return new Bruch(zaehler * faktor.zaehler, nenner * faktor.nenner).kuerzen();
	}

	public Bruch divide(Bruch divisor) throws EprogException
	{	
		return multiply(divisor.invert());
	}

	public Bruch invert() throws EprogException
	{
		return new Bruch(nenner, zaehler).kuerzen();
	}
	
	public Bruch negate() throws EprogException
	{
		return new Bruch(-zaehler, nenner);
	}

	public Bruch kuerzen() throws EprogException
	{
		if(nenner == 0)
			throw new EprogException();
		if(zaehler == 0)
		{
			nenner = 1;
			return this;
		}
		
		long ggT = Math.min(Math.abs(zaehler), Math.abs(nenner));
		while (zaehler / ggT != (double)zaehler / ggT || nenner / ggT != (double)nenner / ggT) {
			ggT = ggT - 1;
		}
		if(nenner < 0)
			ggT = -ggT;
		zaehler /= ggT;
		nenner /= ggT;
		return this;
	}

	public boolean equals(int valInt) throws EprogException
	{
		if(nenner * valInt != zaehler)
			return false;
		return true;
	}

	int zaehler;
	int nenner;
}