#include<iostream>
#include<cmath>
using namespace std;


class fraction 
{
     
   public:  
      int numer , denom;
      fraction();//Default Constructor
      fraction(int n, int d);//Alternate Constructor
      int GCF();//Finds The GCF 
      fraction reciprocal();//Displays Reciprocal
      void display();//Displays the Fraction
      void reduce();//Puts Fraction into simplest form
      double convert();//Converts to Decimal
      void assign(int n, int d);//Assigns numerators and denoms
      int getnumer();//gets the numerator
      int getdenom();//gets the denominator
      friend ostream& operator << (ostream& outs, const fraction f1);
      //Display Operator
      fraction operator * (fraction f1); //Multiplication 
      fraction operator / (fraction f1); //Division 
      fraction operator + (fraction f1); //Addition 
      fraction operator - (fraction f1); //Subtraction 

      bool operator ==(fraction f1);//Equals 
      bool operator <(fraction f1);//Less Than 
      bool operator >(fraction f1);//Greater Than
    
};//EndPublic
      
      
ostream& operator << (ostream& outs,const fraction f1)//<< Display Operator
      { 
      outs<<f1.numer<<"/"<<f1.denom;
      return outs;
      }
     
fraction::fraction()//Default Constructor
      {        }
           
fraction::fraction(int n, int d) //Alternate Constructor
      {        
      numer=n;
      denom=d;
      }
            
int fraction :: getnumer()//gets numerator
      { 
      return numer;
      }
       
int fraction :: getdenom()//gets denom
      { 
      return denom;
      }         
                
void fraction::assign(int n, int d)//assigns num and denom to fraction
{      numer = n;
      denom = d;
      }
       
void fraction:: display()//Displays 
      {
      cout<<numer<<"/"<<denom;
      }  
         
int fraction::GCF()//Finds GCF
      {
      bool done= false;
      int gcf=0;
      if (abs(numer)<= abs(denom))
             {
             gcf=abs(numer);
             }//End If
      else
             {
             gcf=abs(denom);
             }//End Else
      while (gcf > 1 &&! done)
             {
             if (numer%gcf== 0 && denom%gcf == 0)
                {
                done= true;
                }//End If     
          else
                {
                gcf --;
                }//End Else
             }//End While
           return gcf;
      }
       
void fraction::reduce()//Changes To Simplest Form
      { 
      int gcf = GCF();
      numer=numer/gcf;
      denom=denom/gcf;
      }
       
fraction fraction::operator * (fraction f1)//Multiplication 
      {
      fraction temp;
      temp.numer= numer*f1.numer;
      temp.denom= denom*f1.denom;
      temp.reduce();
      return temp;
      }
                 
fraction fraction::operator / (fraction f1)//Division 
      {
      fraction temp;
      temp.numer= numer*f1.denom;
      temp.denom= denom*f1.numer;
      temp.reduce();
      return temp;
      }  
       
fraction fraction::operator + (fraction f1)//Addition 
      {
      fraction temp;
      temp.denom=denom*f1.denom;
      temp.numer=(numer*f1.denom) + (denom*f1.numer);
      temp.reduce();
      return temp;
      }
       
fraction fraction::operator - (fraction f1)//Subtraction
      { 
      fraction temp;
      temp.denom=denom*f1.denom;
      temp.numer=(numer*f1.denom)-(denom*f1.numer);
      temp.reduce();
      return temp;
      }
       
double fraction::convert()//Converts to Decimal
      {
      double decimal;
      decimal=static_cast<double>(numer)/static_cast<double>(denom);
      return decimal;
      }
     
fraction fraction::reciprocal() //Recriprocal 
      {
      fraction temp;
      temp.numer=denom;
      temp.denom=numer;
      return temp;
      }     
       
bool fraction::operator ==(fraction f1)//Equals 
      { 
      return convert() == f1.convert();
      }

bool fraction::operator <(fraction f1)//Less Than 
      {
      return convert() < f1.convert();
      }
      
bool fraction::operator >(fraction f1)//Greater Than 
      {
      return convert() > f1.convert();
      }