from math import *

def gcd(a,b):
    u, v = a, b

    counter2=0;
    while v != 0:
        r = u % v
        #print "The remainder is", r
        u = v
        v = r
        counter2 +=1

    return u

class Fraction:
    def __init__(self,num=0,denom=1):
        if denom==0: # fraction is undefined
            self._n=0
            self._d=0
        else :
            factor = gcd(abs(num),abs(denom))
            if denom < 0:
                factor=-factor
            self._n=num/factor
            self._d=denom/factor

    def __str__(self):
        if self._d == 0:
            return 'Undefined'
        elif self._d == 1 :
            return str(self._n)
        else:
            return str(self._n) + '/' + str(self._d)

    def __add__(self,other): # Addition of two fractions
        return Fraction(self._n*other._d+other._n*self._d,self._d*other._d)

    def __sub__(self,other): # Subtraction of two fractions
        return Fraction(self._n*other._d-other._n*self._d,self._d*other._d)

    def __mul__(self,other): # Multiplication of two fractions
        return Fraction(self._n*other._n,self._d*other._d)

    def __div__(self,other): # division of two fractions self/other
        return Fraction(self._n*other._d,self._d*other._n)

    def __neg__(self): # negation of a fraction
        return Fraction(-self._n,self._d)

    def n_invert(self): # negative reciprocal of a fraction
        return Fraction(self._d,self._n).__neg__()
        #return -Fraction(self._d,self._n)

      # conversion of a fraction to a mixed number
      # so far if a user tries to convert a proper fraction to a mixed number,
      # the warning is displayed, but the mixed number is still created,
      # with 0 as the whole part (quotient)
    def fraction2mixed(self):
        if self._n < self._d:
            print "Warning: you tried to convert a proper fraction to a mixed number!"
            print "The mixed number was created, but its whole part (quotient) is 0"
            return MixedNumber(0,self._n,self._d)
        else:
            return MixedNumber(self._n//self._d,self._n%self._d,self._d)

class MixedNumber(Fraction):
    def __init__(self,quotient=0,num=0,denom=1): # initially, by default, we have 0 0/1 
        self._q=quotient

        if num < denom: # fractional part if a proper fraction
            Fraction.__init__(self,num,denom)
        else: # takes care of improper fraction as a fractional part
              # of the mixed number
            self._q += num // denom
            r=num%denom
            Fraction.__init__(self,r,denom)

    def __str__(self):
        if self._d == 0: # if denominator is 0, the mixed number is undefined
            return 'Undefined'
        elif self._n == 0: # if the numerator is 0
            if self._q == 0: # and the whole part(quotient) is 0
                return str(0)
            else: # and the whole part (quotient) is not 0
                return str(self._q)
        else:
            str1='   ' + str(self._n) + '\n'
            str2=str(self._q)+'  -\n'
            str3='   ' + str(self._d)
            return str1+str2+str3+'\n'
            #return str(self._q) + '  ' + str(self._n) + ' ' + str(self._d)

      # conversion of a mixed number to improper fraction
    def mixed2fraction(self): 
        return Fraction(self._q*self._d+self._n,self._d)

    def __add__(self,other): # Addition of two mixed numbers or
                             #a mixed number and a fraction
        a=self.mixed2fraction()
        print self, '    is ', a
        if isinstance(other,MixedNumber):
            b=other.mixed2fraction()
            print other, '    is ', b
            c=a+b
        elif isinstance(other,Fraction):
            c=a+other
        elif isinstance(other,int):
            b=Fraction(other,1)
            c=a+b
        else:
            print 'Tried to perform the following operation:',self,' + ',other
            raiseTypeError('These items cannot be added')

        return c.fraction2mixed()

    def __sub__(self,other): # Subtraction of two fractions
        pass

    def __mul__(self,other): # Multiplication of two fractions
        pass

    def __div__(self,other): # division of two mixed numbers
        a=self.mixed2fraction()
        print self, '    is ', a
        if isinstance(other,MixedNumber):
            b=other.mixed2fraction()
            print other, '    is ', b
            c=a/b
        elif isinstance(other,Fraction):
            c=a/other
        elif isinstance(other,int):
            b=Fraction(other,1)
            c=a/b
        else:
            print 'Tried to perform the following operation:',self,' / ',other
            raiseTypeError('These items cannot be added')

        return c.fraction2mixed()

    def __neg__(self): # negation of a fraction
        pass

    def n_invert(self): # negative reciprocal of a fraction
        pass

def main():
    print "Converting mixed numbers to improper fractions"
    # m1 = 2 5/4
    m1=MixedNumber(2,5,4)
    m2=MixedNumber(1,2,3)
    # m2 = 1 2/3
    print m1
    print m2
    f1=m1.mixed2fraction()
    print m1, "  is  ",f1
    f2=m2.mixed2fraction()
    print m2, "  is  ",f2

    tt=raw_input('Press Enter to continue')

    print "Converting fraction to a mixed number"

    f3=Fraction(4,12)
    print f3
    m3=f3.fraction2mixed()
    print f3, "  is\n", m3

    tt=raw_input('Press Enter to continue')

    print "Adding two mixed numbers"

    m4=m1+m2
    print m1, "  +\n", m2, "   is\n",m4

    tt=raw_input('Press Enter to continue')

    print "Adding a mixed number and a fraction"

    m5 = m1 + f3
    print m1,"  +  ", f3, " is\n", m5

    tt=raw_input('Press Enter to continue')

    print "Adding a mixed number and an integer"

    m6 = m1+2
    print m1,"  +  ", 2, "  is\n",m6

    tt=raw_input('Press Enter to continue')

    print "Dividing a mixed number by a mixed number"

    m7=m1/m2
    print m7

    tt=raw_input('Press Enter to continue')

    print "Dividing a mixed number by 2"

    m8=m1/2
    print m8

    tt=raw_input('Press Enter to continue')

    print "Multiplication"

    m9=m1*m2
    print m9

main()