rational.h

int gcd(const int& n, const int& m) {
  int a = n, b = m;
  if (b > a) swap(a, b);
  while (b) {
    a = a % b;
    swap(a, b);
  }
  return a;
}

int lcm(const int& n, const int& m) { return n / gcd(n, m) * m; }

class Rational {
 public:
  Rational(int numer, int denom) : n{numer}, d{denom} {
    if (d == 0) throw ZeroDivError{};
  };
  Rational() : n{1}, d{1} {};
  
  int num() const { return n; }
  int denom() const { return d; }
  float dec() const { return (float)n / d; }
  void simplify();
 private:
  int n;  // numerator
  int d;  // denominator
  class ZeroDivError {};  // for exception generation
};

void Rational::simplify() {
  int gcd_value;
  while (true) {
    gcd_value = gcd(n, d);
    if (gcd_value == 1) break;

    n /= gcd_value;
    d /= gcd_value;
  }
}

ostream& operator<<(ostream& os, Rational& r) {
  os << r.num() << '/' << r.denom();
  return os;
}

Rational operator+(const Rational& a, const Rational& b) {
  int lcm_val = lcm(a.denom(), b.denom());
  int af1 = lcm_val / a.denom();  // additional factor
  int af2 = lcm_val / b.denom();
  Rational res{ (a.num() * af1) + (b.num() * af2), lcm_val};
  res.simplify();
  return res;
}

Rational operator-(const Rational& a, const Rational& b) {
  int lcm_val = lcm(a.denom(), b.denom());
  int af1 = lcm_val / a.denom();  // additional factor
  int af2 = lcm_val / b.denom();
  Rational res{(a.num() * af1) - (b.num() * af2), lcm_val};
  res.simplify();
  return res;
}

Rational operator*(const Rational& a, const Rational& b) {
  Rational res{a.num() * b.num(), a.denom() * b.denom()};
  res.simplify();
  return res;
}

Rational operator/(const Rational& a, const Rational& b) {
  Rational temp{b.denom(), b.num()};
  return a*temp;
}

bool operator==(const Rational& a, const Rational& b) {
  Rational _a = a, _b = b;
  _a.simplify(); _b.simplify();
  return (_a.num() == _b.num()) && (_a.denom() == _b.denom());
}

bool operator!=(const Rational& a, const Rational& b) { 
  return !(a == b); 
}

bool operator>(const Rational& a, const Rational& b) { 
  return a.dec() > b.dec(); 
}

bool operator<(const Rational& a, const Rational& b) { 
  return a.dec() < b.dec(); 
}

bool operator>=(const Rational& a, const Rational& b) {
  return a.dec() >= b.dec();
}

bool operator<=(const Rational& a, const Rational& b) {
  return a.dec() <= b.dec();
}