此处摘录做得较好同学的答案
@林泽鑫

//林泽鑫201930381454
#include<iostream>
using namespace std;

//RationalNumber.h
#ifndef RATIONALNUMBER_H
#define RATIONALNUMBER_H
class RationalNumber {
    friend istream& operator>>(istream&, RationalNumber&);
    friend ostream& operator<<(ostream&, const RationalNumber&);
    friend int gcd(int, int);
public:
    RationalNumber(int, int);
    
    RationalNumber operator+(RationalNumber&);
    RationalNumber operator-(RationalNumber&);
    RationalNumber operator*(RationalNumber&);
    RationalNumber operator/(RationalNumber&);

    bool operator>(RationalNumber&);
    bool operator>=(RationalNumber&);
    bool operator<(RationalNumber&);
    bool operator<=(RationalNumber&);
    bool operator==(RationalNumber&);
    bool operator!=(RationalNumber&);

    bool check();
private:
    int numerator;
    int denominator;

    bool isError;
};
#endif // !RATIONALNUMBER_H

//RationalNumber.cpp
int gcd(int num1, int num2) {
    if (num2 == 0)return num1;
    return gcd(num2, num1 % num2);
}

RationalNumber::RationalNumber(int a = 0, int b = 1) {
    if (b == 0) {
        cout << "ERROR\n";
        isError = true;
    }
    else if (a == 0) {
        denominator = 1;
        numerator = 0;
        isError = false;
    }
    else {
        numerator = a / gcd(a, b);
        denominator = b / gcd(a, b);
        isError = false;
    }
}

ostream& operator<<(ostream& output, const RationalNumber& a) {
    if (a.denominator == 1)output << a.numerator;
    else
        output << a.numerator << "/" << a.denominator;
    return output;
}

istream& operator>>(istream& input, RationalNumber& b) {
    int temp1, temp2;
    input >> temp1 >> temp2;
    RationalNumber temp(temp1,temp2);
    b = temp;
    return input;
} 

RationalNumber RationalNumber::operator+(RationalNumber& operand) {
    RationalNumber ret(numerator*operand.denominator+denominator*operand.numerator
    ,denominator*operand.denominator);
    return ret;
}

RationalNumber RationalNumber::operator-(RationalNumber& operand) {
    RationalNumber ret(numerator * operand.denominator - denominator * operand.numerator
        , denominator * operand.denominator);
    return ret;
}

RationalNumber RationalNumber::operator*(RationalNumber& operand) {
    RationalNumber ret(numerator * operand.numerator, denominator * operand.denominator);
    return ret;
}

RationalNumber RationalNumber::operator/(RationalNumber& operand) {
    RationalNumber ret(numerator * operand.denominator, denominator * operand.numerator);
    return ret;
}

bool RationalNumber::operator<(RationalNumber& operand) {
    return numerator * operand.denominator < denominator * operand.numerator;
}

bool RationalNumber::operator<=(RationalNumber& operand) {
    return numerator * operand.denominator <= denominator * operand.numerator;
}

bool RationalNumber::operator>(RationalNumber& operand) {
    return numerator * operand.denominator > denominator * operand.numerator;
}

bool RationalNumber::operator>=(RationalNumber& operand) {
    return numerator * operand.denominator >= denominator * operand.numerator;
}

bool RationalNumber::operator==(RationalNumber& operand) {
    return numerator * operand.denominator == denominator * operand.numerator;
}

bool RationalNumber::operator!=(RationalNumber& operand) {
    return numerator * operand.denominator != denominator * operand.numerator;
}

bool RationalNumber::check() {
    return isError;
}
//test.cpp
int main() {
    RationalNumber a, b;
    cin >> a >> b;
    if (!a.check() && !b.check()) {
        cout << a + b << endl;
        cout << a - b << endl;
        cout << a * b << endl;
    }
}