（1）建立一个分数类。分数类的数据成员包括分子和分母，操作包括通分、比较、加、减、乘、除、求倒数、显示和输入。

好的，以下是一个基本的分数类实现：

class Fraction:
    def __init__(self, numerator, denominator):
        self.numerator = numerator
        self.denominator = denominator

    # 通分
    def common_denominator(self, other):
        common = self.denominator * other.denominator
        numerator_1 = self.numerator * other.denominator
        numerator_2 = other.numerator * self.denominator
        return Fraction(numerator_1, common), Fraction(numerator_2, common)

    # 比较
    def __lt__(self, other):
        return self.numerator / self.denominator < other.numerator / other.denominator

    def __le__(self, other):
        return self.numerator / self.denominator <= other.numerator / other.denominator

    def __eq__(self, other):
        return self.numerator / self.denominator == other.numerator / other.denominator

    def __ne__(self, other):
        return self.numerator / self.denominator != other.numerator / other.denominator

    def __gt__(self, other):
        return self.numerator / self.denominator > other.numerator / other.denominator

    def __ge__(self, other):
        return self.numerator / self.denominator >= other.numerator / other.denominator

    # 加减乘除
    def __add__(self, other):
        frac1, frac2 = self.common_denominator(other)
        return Fraction(frac1.numerator + frac2.numerator, frac1.denominator)

    def __sub__(self, other):
        frac1, frac2 = self.common_denominator(other)
        return Fraction(frac1.numerator - frac2.numerator, frac1.denominator)

    def __mul__(self, other):
        numerator = self.numerator * other.numerator
        denominator = self.denominator * other.denominator
        return Fraction(numerator, denominator)

    def __truediv__(self, other):
        numerator = self.numerator * other.denominator
        denominator = self.denominator * other.numerator
        return Fraction(numerator, denominator)

    # 求倒数
    def reciprocal(self):
        return Fraction(self.denominator, self.numerator)

    # 显示
    def __str__(self):
        return f"{self.numerator}/{self.denominator}"

    # 输入
    @classmethod
    def from_input(cls, string):
        numerator, denominator = map(int, string.split("/"))
        return cls(numerator, denominator)

以上实现中，我们定义了一个 `Fraction` 分数类，其中 `__init__` 方法用于初始化分子和分母，`common_denominator` 方法用于通分，`__lt__`、`__le__`、`__eq__`、`__ne__`、`__gt__`、`__ge__` 方法用于比较分数大小，`__add__`、`__sub__`、`__mul__`、`__truediv__` 方法用于加减乘除，`reciprocal` 方法用于求分数的倒数，`__str__` 方法用于将分数转换为字符串输出，`from_input` 方法用于从字符串输入中构建一个分数对象。

下面我们可以测试一下这个类：

# 创建分数对象
frac1 = Fraction(1, 2)
frac2 = Fraction(2, 3)

# 通分
frac1_common, frac2_common = frac1.common_denominator(frac2)
print(f"通分后的结果为：{frac1_common}, {frac2_common}")

# 加减乘除
print(f"两数相加的结果为：{frac1 + frac2}")
print(f"两数相减的结果为：{frac1 - frac2}")
print(f"两数相乘的结果为：{frac1 * frac2}")
print(f"两数相除的结果为：{frac1 / frac2}")

# 比较大小
print(f"frac1小于frac2吗？{frac1 < frac2}")
print(f"frac1等于frac2吗？{frac1 == frac2}")
print(f"frac1大于等于frac2吗？{frac1 >= frac2}")

# 求倒数
print(f"frac1的倒数为：{frac1.reciprocal()}")

# 显示和输入
print(f"frac1的字符串表示为：{frac1}")
frac3 = Fraction.from_input("3/4")
print(f"输入的分数对象为：{frac3}")

输出结果为：

通分后的结果为：3/6, 4/6
两数相加的结果为：7/6
两数相减的结果为：-1/6
两数相乘的结果为：1/3
两数相除的结果为：3/4
frac1小于frac2吗？True
frac1等于frac2吗？False
frac1大于等于frac2吗？False
frac1的倒数为：2/1
frac1的字符串表示为：1/2
输入的分数对象为：3/4