#include<math.h>
#include<iostream.h>
class rational
{
	int numerator,denominator;
	void optimization();
public:
	rational(int x=0,int y=1);  //聲明帶默認值的構造函數
	friend rational operator +(rational &num1,rational &num2);
	//聲明重載運算符"+"
	friend rational operator -(rational &num1,rational &num2);
	friend rational operator *(rational &num1,rational &num2);
	friend rational operator /(rational &num1,rational &num2);
	friend bool operator==(rational &num1,rational &num2);
	//聲明比較運算符"=="重載函數
	friend double real(rational& x);  //聲明將分數轉換為浮點數的函數
	friend ostream &operator<<(ostream&,rational &); //聲明"<<"重載
	friend istream &operator>>(istream&,rational &); //聲明">>"重載
};
void rational::optimization()
{
	int gcd,min,max;
	if(numerator==0)
	{  //如分子為0，則置分母為1后返回
		denominator=1;
		return;
	}
	gcd=(abs(numerator)>abs(denominator)?abs(denominator):abs(numerator));
	if(gcd==0) return;
	/*//也可如此用循環求最大公約數
	for(max=gcd;max>1;max--)
		if((numerator%max==0)&&(denominator%max==0))
			break;
  */
	//以下用輾轉相除法求最大公約數，此方法較好
    if(abs(numerator)>abs(denominator))
	{max=numerator;min=denominator;}
	else
	{min=numerator;max=denominator;}
	do{
		gcd=max%min;
		max=min;
		min=gcd;
	}while(gcd!=0);

	numerator/=max;
	denominator/=max;
	if(numerator<0 && denominator<0)
	{
		numerator=-numerator;
		denominator=-denominator;
	}
	else if(numerator<0 || denominator<0)
	{
		numerator=-abs(numerator);
		denominator=abs(denominator);
	}
}
rational::rational(int x,int y)
{
	numerator=x;
	denominator=y;
	optimization();
}
rational operator +(rational &num1,rational &num2)
{
	rational temp;
	temp.denominator=num1.denominator*num2.denominator;
	temp.numerator=num1.numerator*num2.denominator+
		num1.denominator*num2.numerator;
	temp.optimization();
	return temp;
}
rational operator -(rational &num1,rational &num2)
{
	rational temp;
	temp.denominator=num1.denominator*num2.denominator;
	temp.numerator=num1.numerator*num2.denominator-
		num1.denominator*num2.numerator;
	temp.optimization();
	return temp;
}
rational operator *(rational &num1,rational &num2)
{
	rational temp;
	temp.denominator=num1.denominator*num2.denominator;
	temp.numerator=num1.numerator*num2.numerator;
	temp.optimization();
	return temp;
}	
rational operator /(rational &num1,rational &num2)
{
	rational temp;
	temp.denominator=num1.denominator*num2.numerator;
	temp.numerator=num1.numerator*num2.denominator;
	temp.optimization();
	return temp;
}	
bool operator==(rational &num1,rational &num2)
{
	if(num1.numerator==num2.numerator && 
		num1.denominator==num2.denominator)
		return true;
	else 
		return false;
}
double real(rational& x)
{
	return (double(x.numerator))/(x.denominator);
}
ostream &operator<<(ostream& out,rational &obj)
{
	out<<obj.numerator;
	if(obj.numerator!=0 && obj.denominator!=1 &&obj.denominator!=0)
		cout<<"/"<<obj.denominator<<"\n";
	else if(obj.denominator==0)
		cout<<"ERROR!The denominator is equal to 0.\n";
	else cout<<"\n";
	return out;
}
istream &operator>>(istream& in,rational &obj)
{
	cout<<"Input the numerator ,denominator of the rational:\n";
	in>>obj.numerator;
	in>>obj.denominator;
	obj.optimization();
	return in;
}
void main()
{
	rational r1,r2,r3;
	cin>>r1;
	cin>>r2;
	cout<<"r1="<<r1;
	cout<<"r2="<<r2;
	r3=r1+r2;
	cout<<"r1+r2=";cout<<r3;
	r3=r1-r2;
	cout<<"r1-r2=";cout<<r3;
	r3=r1*r2;
	cout<<"r1*r2=";cout<<r3;
	r3=r1/r2;
	cout<<"r1/r2=";cout<<r3;
	if(r1==r2) 
		cout<<"r2 is equal to r1.\n";
	else
		cout<<"r2 isn't equal to r1.\n";
}