class Fraction:
    """
    Each Fraction object consists of a numerator and a denominator.
    Fractions are reduced by dividing the numerator and denominator
    by their greatest common divisor (GCD).
    """
    def __init__(self, numerator, denominator = 1):
        """
        Construct a fraction and reduce it.
        @param numerator the fraction's numerator.
        @param denominator the fraction's denominator.
        """
        if denominator == 0:
            raise ZeroDivisionError('Denominator cannot be 0.')
        
        if numerator == 0:
            self._numerator   = 0
            self._denominator = 1
        else:
            # Determine fraction's sign: 
            # 1 if positive, -1 if negative
            if (   ((numerator <  0) and (denominator >= 0))
                or ((numerator >= 0) and (denominator <  0)) ):
                sign = -1
            else:
                sign = 1

            # Greatest common divisor.
            gcd = self._gcd(numerator, denominator)
            
            # Reduce the fraction.
            self._numerator   = sign*abs(numerator)//gcd
            self._denominator = abs(denominator)//gcd
    
    def _gcd(self, a, b):
        """
        Private method!
        Calculate the greatest common divisor of a and b.
        @param a
        @param b
        @return the GCD of a and b.
        """
        while b:
            a, b = b, a%b
            
        return a
    
    def add(self, other):
        """
        Return the Fraction value of self + other.
        """
        num = (self._numerator   * other._denominator +
               self._denominator * other._numerator)
        den =  self._denominator * other._denominator
        
        return Fraction(num, den)
            
    def __add__(self, other):
        """
        Return the Fraction value of self + other.
        """
        return self.add(other)
            
    def __sub__(self, other):
        """
        Return the Fraction value of self - other.
        """
        num = (self._numerator   * other._denominator -
               self._denominator * other._numerator)
        den =  self._denominator * other._denominator
        
        return Fraction(num, den)
            
    def __mul__(self, other):
        """
        Return the Fraction value of self * other.
        """
        num = self._numerator   * other._numerator
        den = self._denominator * other._denominator
        
        return Fraction(num, den)
            
    def __truediv__(self, other):
        """
        Return the Fraction value of self / other.
        """
        num = self._numerator   * other._denominator
        den = self._denominator * other._numerator
        
        return Fraction(num, den)

    def __repr__(self):
        '''
        @return the string representation of a Fraction object.
        '''
        return (f'{self._numerator}/{self._denominator}')