1. (30)  Implement the following fraction class (make sure you test!!):

class Fraction {
    private:
      int num;
      int den;
    public:
      Fraction(int numerator, int denominator);
      Fraction(const Fraction& f);
      Fraction& operator =(const Fraction& f);
      const Fraction operator -() const;
      friend const Fraction operator +(const Fraction& f1, const Fraction& f2);
      friend const Fraction operator -(const Fraction& f1, const Fraction& f2);
      friend const Fraction operator *(const Fraction& f1, const Fraction& f2);
      friend const Fraction operator /(const Fraction& f1, const Fraction& f2);
      friend bool operator ==(const Fraction& f1, const Fraction& f2);
      friend bool operator !=(const Fraction& f1, const Fraction& f2);
      friend bool operator <(const Fraction& f1, const Fraction& f2);
      friend bool operator <=(const Fraction& f1, const Fraction& f2);
      friend bool operator >(const Fraction& f1, const Fraction& f2);
      friend bool operator >=(const Fraction& f1, const Fraction& f2);
      // Should print out as simplest fraction.  Use gcd.
      friend ostream& operator <<(ostream& os, const Fraction& f);
};