class Fraction:
    """
    A basic mathematical fraction

    Instance variables:
        numerator
        denominator
    """
    
    def __init__(self,top,bottom):
        self._numerator = top
        self._denominator = bottom
        self.simplify()

    def __str__(self):
        return str(self._numerator)+"/"+str(self._denominator)

    def __repr__(self):
        return "<Fraction of value: "+self.__str__()+">"

    def __add__(self,otherFraction):
        if self._denominator==otherFraction._denominator:
            newNumerator = self._numerator + otherFraction._numerator
            newDenominator = self._denominator
        else:
            newNumerator = self._numerator * otherFraction._denominator + \
                           otherFraction._numerator * self._denominator
            newDenominator = self._denominator*otherFraction._denominator
        return Fraction(newNumerator,newDenominator)

    
    def simplify(self):
        #Find the Greatest Common Divisor of the two numbers
        v1 = self._numerator
        v2 = self._denominator

        while v1%v2!=0:
            temp1 = v1
            temp2 = v2
            v1 = temp2
            v2 = temp1%temp2
        gcd = v2

        #Now simply the two terms
        self._numerator = int(self._numerator/gcd)
        self._denominator = int(self._denominator/gcd)
    
    
    def __lt__(self,otherFraction):
        t1 = self._numerator*otherFraction._denominator
        t2 = otherFraction._numerator*self._denominator
        return t1<t2

    def __gt__(self,otherFraction):
        t1 = self._numerator*otherFraction._denominator
        t2 = otherFraction._numerator*self._denominator
        return t1>t2

    def __eq__(self,otherFraction):
        t1 = self._numerator*otherFraction._denominator
        t2 = otherFraction._numerator*self._denominator
        return t1==t2

    def __le__(self,otherFraction):
        return not self>otherFraction

    def __ge__(self,otherFraction):
        return not self<otherFraction
    
    def __ne__(self,otherFraction):
        return not self==otherFraction