# 有理数

class Rational():

    @staticmethod
    def __gcd(m, n):
        if n == 0:
            m, n = n, m

        while m != 0:
            m, n = n % m, m

        return n


    def __init__(self, num, den = 1):

        if not isinstance(num, int) or not isinstance(den, int):
            raise TypeError

        if den == 0:
            raise ZeroDivisionError

        sign = 1
        if num < 0:
            num, sign = -num, -sign

        if den < 0:
            den, sign = -num, -sign

        g = Rational.__gcd(num, den)
        self.__num = sign * (num // g)
        self.__den = den // g

    def den(self):
        return self.__den

    def num(self):
        return self.__num


    def __add__(self, another):
        den = self.__den * another.den()
        num = (self.__num * another.den() + self.__den * another.num())

        return (Rational(num, den))

    def __mul__(self, another):
        return Rational(self.__num * another.num(), self.__den * another.den())

    def __sub__(self, another):
        den = self.__den * another.den()
        num = (self.__num * another.den() - self.__den * another.num())

        return Rational(num, den)

    def __floordiv__(self, another):
        if another.num() == 0:
            raise ZeroDivisionError

        return Rational(self.__num * another.den(), self.__den * another.num())

    def __eq__(self, another):
        return self.__num * another.den() == self.__den * another.num()


    def __lt__(self, another):
        return self.__num * another.den() < self.__den * another.num()

    def __gt__(self, another):
        return self.__num * another.den() > self.__den * another.num()

    def __ne__(self, another):
        return self.__num * another.den() != self.__den * another.num()

    def __le__(self, another):
        return self.__num * another.den() <= self.__den * another.num()

    def __ge__(self, another):
        return self.__num * another.den() >= self.__den * another.num()

    def __str__(self):

        return str(self.__num) + '/' + str(self.__den)




r1 = Rational(3, 15)
r2= Rational(5, 15)
print(r1, r2)
print(r1 + r2)
print(r1 - r2)
print(r1 >= r2)
print(r1 <= r2)