class rational {
public:
	// constructors
	rational	(); 			// default constructor
	rational	(int i); 		// constructs the rational i/1
	rational	(int i, int j);		// constructs the rational i/j
	rational	(const rational &);	// copy constructor

	// accessor functions
	int 	numerator	() const;
	int 	denominator	() const;

	// assignments
	void 	operator =  	(const rational &);
	void 	operator += 	(const rational &);
	void 	operator -= 	(const rational &);
	void 	operator *= 	(const rational &);
	void 	operator /= 	(const rational &);

	// comparison
	// when called as p.compare(q), this function returns 1 if p > q, 0 if p = q, and -1 if p < q
	int 	compare		(const rational &) const;
	
private:
	// data areas
	int 	top;
	int 	bottom;

	// This operation is used internally.
	// normalize() reduces the numerator and the denominator of the rational to smallest
	// possible values. For example, normalize() will reduce 200/450 to 4/9. To do this
	// normalize() will have to compute the greatest common divisor (gcd) of the numerator
	// and the denominator and then divide.
	// normalize() is used after every arithmetic operation involving rationals to ensure
	// that the numerator and the denminator do not become too large.
	void 	normalize	();
};