class Fraction:
    """
    代表分数的类，包含分子和分母
    提供加减乘除运算
    """
    def __init__(self, top, bottom):
        self.num = top
        self.den = bottom

    def __str__(self):
        return str(self.num) + "/" + str(self.den)

    def __add__(self, otherfraction):
        newnum = self.num * otherfraction.den + self.den * otherfraction.num
        newden = self.den * otherfraction.den
        return Fraction(newnum, newden)

    def __sub__(self, otherfraction):
        newnum = self.num * otherfraction.den - self.den * otherfraction.num
        newden = self.den * otherfraction.den
        return Fraction(newnum, newden)

    def __mul__(self, otherfraction):
        newnum = self.num * otherfraction.num
        newden = self.den * otherfraction.den
        return Fraction(newnum, newden)

    def __truediv__(self, otherfraction):
        newnum = self.num * otherfraction.den
        newden = self.den * otherfraction.num
        return Fraction(newnum, newden)

    def __eq__(self, otherfraction):
        firstnum = self.num * otherfraction.den
        secondnum = otherfraction.num * self.den
        return firstnum == secondnum

    def __gt__(self, otherfraction):
        firstnum = self.num * otherfraction.den
        secondnum = otherfraction.num * self.den
        return firstnum > secondnum

    def __lt__(self, otherfraction):
        firstnum = self.num * otherfraction.den
        secondnum = otherfraction.num * self.den
        return firstnum < secondnum

    def __ge__(self, otherfraction):
        firstnum = self.num * otherfraction.den
        secondnum = otherfraction.num * self.den
        return firstnum >= secondnum

    def __le__(self, otherfraction):
        firstnum = self.num * otherfraction.den
        secondnum = otherfraction.num * self.den
        return firstnum <= secondnum

    def __ne__(self, otherfraction):
        firstnum = self.num * otherfraction.den
        secondnum = otherfraction.num * self.den
        return firstnum != secondnum

    def get_num(self):
        return self.num

    def get_den(self):
        return self.den

    def __radd__(self, otherfraction):
        return self


# 约分函数：将分数约分为最简分数
def reduce_fraction(fraction):
    """
    将分数约分为最简分数

    :param fraction: 分数，Fraction 类型
    :return: 约分后的分数，Fraction 类型
    """
    # 求最大公约数
    def gcd(a, b):
        if b == 0:
            return a
        else:
            return gcd(b, a % b)

    g = gcd(fraction.get_num(), fraction.get_den())
    return Fraction(fraction.get_num() // g, fraction.get_den() // g)


# 通分函数：将多个分数通分
def common_denominator(fractions):
    """
    将多个分数通分

    :param fractions: 分数列表，Fraction 类型
    :return: 通分后的分数列表，Fraction 类型
    """
    # 求最大公约数
    def gcd(a, b):
        if b == 0:
            return a
        else:
            return gcd(b, a % b)

    # 求最小公倍数
    def lcm(a, b):
        return a * b // gcd(a, b)

    # 通分
    denominator = 1
    for fraction in fractions:
        denominator = lcm(denominator, fraction.get_den())
    for i in range(len(fractions)):
        fractions[i] = Fraction(fractions[i].get_num() * denominator // fractions[i].get_den(), denominator)
    return fractions