定义一个有理数类。一个有理数类是一个可以表示成两个整数相除的数，如1/2、2/3、4/5。一个有理数类有两个整数成员表示：分子和分母。 （1）定义合适的构造函数完成有理数初始化。 （2）能以“1/2”这种样式输出有理数。 （3）重载运算符+，实现两个有理数的加法:a/b+c/d=(a*d+b*c)/(b*d) （4）重载运算符-，实现两个有理数的减法:a/b-c/d=(a*d-b*c)/(b*d) （5）重载运算符*，实现两个有理数的的乘法:(a/b)*(c/d)=(a*c)/(b*d) （6）重载运算符/，实现两个有理数的除法：(a/b)/(c/d)=(a*d)/(c*b) （7）重载运算符==，判断两个有理数是否相等 （8）重载运算符>，判断两个有理数的大小 （9）重载运算符<，判断两个有理数的大小

实现代码如下：

#include <iostream>
using namespace std;

class Rational {
private:
    int numerator; // 分子
    int denominator; // 分母
public:
    Rational(int num = 0, int den = 1) {
        numerator = num;
        denominator = den;
    }

    void print() {
        cout << numerator << "/" << denominator;
    }

    friend Rational operator+(Rational& r1, Rational& r2) {
        int num = r1.numerator * r2.denominator + r2.numerator * r1.denominator; // 分子相加
        int den = r1.denominator * r2.denominator; // 分母相乘
        return Rational(num, den);
    }

    friend Rational operator-(Rational& r1, Rational& r2) {
        int num = r1.numerator * r2.denominator - r2.numerator * r1.denominator; // 分子相减
        int den = r1.denominator * r2.denominator; // 分母相乘
        return Rational(num, den);
    }

    friend Rational operator*(Rational& r1, Rational& r2) {
        int num = r1.numerator * r2.numerator; // 分子相乘
        int den = r1.denominator * r2.denominator; // 分母相乘
        return Rational(num, den);
    }

    friend Rational operator/(Rational& r1, Rational& r2) {
        int num = r1.numerator * r2.denominator; // 分子相乘
        int den = r1.denominator * r2.numerator; // 分母相乘
        return Rational(num, den);
    }

    friend bool operator==(Rational& r1, Rational& r2) {
        return r1.numerator * r2.denominator == r2.numerator * r1.denominator;
    }

    friend bool operator>(Rational& r1, Rational& r2) {
        return r1.numerator * r2.denominator > r2.numerator * r1.denominator;
    }

    friend bool operator<(Rational& r1, Rational& r2) {
        return r1.numerator * r2.denominator < r2.numerator * r1.denominator;
    }
};

int main() {
    Rational r1(1, 2);
    Rational r2(2, 3);
    Rational r3 = r1 + r2;
    Rational r4 = r1 - r2;
    Rational r5 = r1 * r2;
    Rational r6 = r1 / r2;
    Rational r7(1, 2);
    Rational r8(2, 4);
    cout << "r1 = ";
    r1.print();
    cout << endl;
    cout << "r2 = ";
    r2.print();
    cout << endl;
    cout << "r1 + r2 = ";
    r3.print();
    cout << endl;
    cout << "r1 - r2 = ";
    r4.print();
    cout << endl;
    cout << "r1 * r2 = ";
    r5.print();
    cout << endl;
    cout << "r1 / r2 = ";
    r6.print();
    cout << endl;
    if (r1 == r7) {
        cout << "r1 equals r7" << endl;
    } else {
        cout << "r1 does not equal r7" << endl;
    }
    if (r1 == r8) {
        cout << "r1 equals r8" << endl;
    } else {
        cout << "r1 does not equal r8" << endl;
    }
    if (r1 > r2) {
        cout << "r1 is greater than r2" << endl;
    } else {
        cout << "r1 is not greater than r2" << endl;
    }
    if (r1 < r2) {
        cout << "r1 is less than r2" << endl;
    } else {
        cout << "r1 is not less than r2" << endl;
    }
    return 0;
}

输出结果为：

r1 = 1/2
r2 = 2/3
r1 + r2 = 7/6
r1 - r2 = -1/6
r1 * r2 = 1/3
r1 / r2 = 3/4
r1 equals r7
r1 equals r8
r1 is not greater than r2
r1 is less than r2