Sort Rational Numbers

1. Suppose you have the definition of class Rational:

   
   #include <iostream>
   #include <stdexcept>
   #include <iterator>
   #include <algorithm>
   #include <vector>
   using std::vector;
   using std::invalid_argument;
   using std::ostream_iterator;
   using std::ostream;
   using std::cout;
   
   class Rational
   {
   friend ostream& operator<<(ostream& output, const Rational& b) {
       output << b.numerator;
       if (b.denominator > 1)
           output << '/' << b.denominator;
       return output;
       }
   
   public:
       Rational(int n=0, int d=1): numerator(n), denominator(d) {
           if (d==0)
               throw( invalid_argument("Divide by Zero") );
       }
       int getNumerator() { return numerator; }
       int getDenominator() { return denominator; }
   protected:
       int numerator;
       int denominator;
   
   };
   
   int main()
   {
       ostream_iterator<Rational> output( cout, " " );
       vector<Rational> a;
       for (int i=1; i<6; ++i)
           for (int j=1; j<4; ++j)
               a.push_back(Rational(i, j));
       copy(a.begin(), a.end(), output);
       cout << '\n';
   }  

2. Now at the end of the program, we want to add three lines to sort these rational numbers:

       sort(a.begin(), a.end(), f);
       copy(a.begin(), a.end(), output);
       cout << '\n';
   
   

3. How should you define the function f() so that the sort algorithm knows how to compare two Rational correctly?