以下是一个基本的分数类的示例代码，其中包括一些常见错误的解决方法：

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

    def simplify(self):
        # 寻找最大公约数来简化分数
        common_divisor = self.find_gcd(self.numerator, self.denominator)
        self.numerator = self.numerator // common_divisor
        self.denominator = self.denominator // common_divisor

    def find_gcd(self, a, b):
        # 使用辗转相除法来寻找最大公约数
        while b != 0:
            a, b = b, a % b
        return a

    def add(self, other_fraction):
        # 分数相加
        new_numerator = self.numerator * other_fraction.denominator + other_fraction.numerator * self.denominator
        new_denominator = self.denominator * other_fraction.denominator
        result = Fraction(new_numerator, new_denominator)
        result.simplify()
        return result

    def subtract(self, other_fraction):
        # 分数相减
        new_numerator = self.numerator * other_fraction.denominator - other_fraction.numerator * self.denominator
        new_denominator = self.denominator * other_fraction.denominator
        result = Fraction(new_numerator, new_denominator)
        result.simplify()
        return result

    def multiply(self, other_fraction):
        # 分数相乘
        new_numerator = self.numerator * other_fraction.numerator
        new_denominator = self.denominator * other_fraction.denominator
        result = Fraction(new_numerator, new_denominator)
        result.simplify()
        return result

    def divide(self, other_fraction):
        # 分数相除
        new_numerator = self.numerator * other_fraction.denominator
        new_denominator = self.denominator * other_fraction.numerator
        result = Fraction(new_numerator, new_denominator)
        result.simplify()
        return result


# 示例使用
fraction1 = Fraction(3, 4)
fraction2 = Fraction(1, 2)

add_result = fraction1.add(fraction2)
print(f"Addition result: {add_result.numerator}/{add_result.denominator}")

subtract_result = fraction1.subtract(fraction2)
print(f"Subtraction result: {subtract_result.numerator}/{subtract_result.denominator}")

multiply_result = fraction1.multiply(fraction2)
print(f"Multiplication result: {multiply_result.numerator}/{multiply_result.denominator}")

divide_result = fraction1.divide(fraction2)
print(f"Division result: {divide_result.numerator}/{divide_result.denominator}")

这个示例代码中，我们定义了一个名为Fraction的分数类，其中包含了一些常见的操作方法如simplify，add，subtract，multiply和divide。在方法中，我们首先定义了一个__init__构造函数来初始化分子和分母。然后，我们使用辗转相除法来寻找最大公约数，以简化分数。在加法、减法、乘法和除法方法中，我们执行相应的数学运算，并创建一个新的Fraction对象来保存运算结果，并通过simplify方法简化结果。

注意，这只是一个基本示例，可能还有其他错误和边界情况需要考虑和处理，具体取决于你的需求和使用场景。