#include <string>

class Fraction
{
public:
	Fraction(int N=0, int D=1); 
	Fraction(const Fraction&);
	Fraction& operator=(const Fraction&);
	operator double();
	int numerator() const;
	int denominator() const;
	Fraction reciprocal() const;

	std::string toString();

	Fraction& operator+= (const Fraction&);
	Fraction& operator+= (int);
	Fraction& operator-=(const Fraction&);
	Fraction& operator-=(int);
	Fraction& operator*=(const Fraction&);
	Fraction& operator*=(int);
	Fraction& operator/=(const Fraction&);
	Fraction& operator/=(int);
	~Fraction();
private:
	void simplify();
	int N;
	int D;

};

int gcd(int, int);
Fraction operator+ (const Fraction& left, const Fraction& right);
Fraction operator+ (const Fraction&, int);
Fraction operator+ (int, const Fraction& left);

Fraction operator- (const Fraction& left, const Fraction& right);
Fraction operator- (const Fraction&, int);
Fraction operator- (int, const Fraction& left);

Fraction operator* (int left, const Fraction& right);
Fraction operator* (const Fraction& left, int right);
Fraction operator* (const Fraction& left, const Fraction& right);
Fraction operator/ (const Fraction& left, const Fraction& right);