#include <stdio.h>
#include <math.h>
#include <string>

int lcm(int a, int b) {
    int na = 1, nb = 1;
    while (a * na != b * nb) {
        if (a * na < b * nb) ++na; else ++nb;
    }
    return a * na;
}

int gcm(int a, int b) {
    int i = a < b ? a : b;
    for (; i > 1; --i) {
        if (a % i == 0 && b % i == 0) break;
    }
    return i;
}

class Frac {
private:
    int a, b;

public:
    Frac(int num) {
        a = num;
        b = 1;
    }

    Frac(int num, int den) {
        a = num;
        b = den;
    }

    Frac(const Frac &f) {
        *this = f;
    }

    Frac &operator=(const Frac &f) {
        a = f.a;
        b = f.b;
        return *this;
    }

    Frac &operator+=(const Frac &f) {
        Frac tmp = *this;
        b = lcm(tmp.b, f.b);
        a = tmp.a * b / tmp.b + f.a * b / f.b;
        return *this;
    }

    Frac &operator*=(const Frac &f) {
        a *= f.a;
        b *= f.b;
        return *this;
    }

    Frac reduce() const {
        Frac ret = *this;
        int g = gcm(a, b);
        ret.a /= g;
        ret.b /= g;
        return ret;
    }

    std::string str() const {
        char buf[32];
        if (b == 1) {
            snprintf(buf, sizeof(buf), "%d", a);
        } else {
            snprintf(buf, sizeof(buf), "%d/%d", a, b);
        }
        return buf;
    }
};

Frac operator+(const Frac &f1, const Frac &f2) {
    Frac ret = f1;
    ret += f2;
    return ret;
}

Frac operator*(const Frac &f1, const Frac &f2) {
    Frac ret = f1;
    ret *= f2;
    return ret;
}

int main() {
    Frac a(1, 2);
    Frac b(1, 3);
    Frac c = a + b;
    Frac d = a * b;
    Frac e = d * 15;
    Frac f = e.reduce();
    Frac g = f * 2;
    Frac h = g.reduce();
    printf("a = %s\n", a.str().c_str());
    printf("b = %s\n", b.str().c_str());
    printf("c = %s\n", c.str().c_str());
    printf("d = %s\n", d.str().c_str());
    printf("e = %s\n", e.str().c_str());
    printf("f = %s\n", f.str().c_str());
    printf("g = %s\n", g.str().c_str());
    printf("h = %s\n", h.str().c_str());
}