def greatest_common_factor(a,b):
    """Returns: Greatest common factor of a and b.
    
    Precondition: a and b are integers."""
    while a != b:
        if a > b:
            a -= b
        else:
            b -= a
    return a

def lowest_common_multiple(a, b):
    """Compute the lowest common multiple of a and b"""
    
    "Precondition: a and b are integers."""
    return a * b / greatest_common_factor(a, b)

class Fraction(object):
    """ Class to hold a fraction.
    
    numerator [int]
    denominator [int > 0]
    """
    
    def __init__(self, numerator, denominator):
        """ Initialize fraction
        Precondition: numerator [int] denominator [int > 0]
        
        """  
        self.numerator = numerator
        self.denominator = denominator
        
        
    def __add__(self, other):
        """ slightly less lazy way to add fractions """
        
        lcm = lowest_common_multiple(self.denominator, other.denominator)       
        bottom = lcm
        top = (lcm / self.denominator) * self.numerator + (lcm / other.denominator) * other.numerator 
        
        return Fraction(top, bottom)
    
    def __str__(self):
        return str(self.numerator) + "/" + str(self.denominator)
    
    def __eq__(self, other):
        self.reduce()
        other.reduce()
        return self.numerator == other.numerator and self.denominator == other.denominator
    
    def reduce(self):
        if self.numerator == 0: return
        gcf = greatest_common_factor(self.numerator, self.denominator)
        self.numerator /= gcf
        self.denominator /= gcf
        
    
class MixedNumber(Fraction):
    """ Class to hold a fraction.
    
    whole_number [int]
    numerator [int]
    denominator [int > 0]
    """
    
    def __init__(self, whole_number, numerator, denominator):
        """ Initialize mixed number
        Precondition: whole_number [int] numerator [int] denominator [int > 0]
        
        """  
        Fraction.__init__(self, numerator, denominator)
        self.whole_number = whole_number
        
    def __str__(self):
        return str(self.whole_number) + " " + Fraction.__str__(self)
    
    def __add__(self, other):
        """ add mixed numbers
        
        precondition: fractions are proper
        """
        
        assert isinstance(other, Fraction)
        
        new_fraction = Fraction.__add__(self, other)
        
        new_whole_number = self.whole_number
        
        if isinstance(other,MixedNumber):
        
            new_whole_number = new_whole_number + other.whole_number
        
        if new_fraction.numerator >= new_fraction.denominator:
            new_fraction.numerator = new_fraction.numerator - new_fraction.denominator
            new_whole_number = new_whole_number + 1
            
        return MixedNumber(new_whole_number, new_fraction.numerator, new_fraction.denominator)