// Program that includes a defintion for a class that stores rational numbers
// along with some client code.

#include <iostream>
#include <string>

using namespace std;

class rational {
public:
    rational(int numer = 0, int denom = 1) {
        numerator = numer;
        denominator = denom;
        fix_signs();
        reduce();
    }

    int get_numerator() const{
        return numerator;
    }

    int get_denominator() const {
        return denominator;
    }

    // n1/d1 - n2/d2 = (n1 * d2 - n2 * d1) / (d1 * d2)
    rational & operator-=(const rational & rhs) {
        numerator = numerator * rhs.denominator - rhs.numerator * denominator;
        denominator *= rhs.denominator;
        reduce();
    }

private:
    int numerator;
    int denominator;

    void fix_signs() {
        if (denominator < 0) {
            numerator = -numerator;
            denominator = -denominator;
        }
    }
    int gcd(int x, int y) {
        if (x < 0 || y < 0) {
            return gcd(abs(x), abs(y));
        } else if (y == 0) {
            return x;
        } else {
            return gcd(y, x % y);
        }
    }

    void reduce() {
        int common = gcd(numerator, denominator);
        numerator /= common;
        denominator /= common;
    }
};

ostream & operator<<(ostream & out, const rational & value) {
    out << value.get_numerator();
    if (value.get_denominator() != 1) {
        out << "/" << value.get_denominator();
    }
    return out;
}

int main() {
    rational r1(3, 4), r2(5), r3;
    cout << "r1 = " << r1 << ", r2 = " << r2 << ", r3 = " << r3 << endl;
    cout << endl;

    rational r4(6, -16);
    cout << "r4 = " << r4 << endl;
    cout << endl;

    r1 -= r4;
    r2 -= r4;
    r3 -= r4;
    cout << "r1 = " << r1 << ", r2 = " << r2 << ", r3 = " << r3 << endl;
    cout << endl;

    return 0;
}