#include <iostream>

using namespace std;

struct fraction
{ int top, bot; };

fraction makefr(const int t, const int b)
{ fraction r;
  r.top = t;
  r.bot = b;
  return r; }

void print(const fraction f)
{ cout << f.top << "/" << f.bot; }

fraction multiply(const fraction f, const fraction g)
{ return makefr(f.top * g.top, f.bot * g.bot); }

fraction divide(const fraction f, const fraction g)
{ return makefr(f.top * g.bot, f.bot * g.top); }         // beware of zeros

fraction add(const fraction f, const fraction g)
{ return makefr(f.top * g.bot + f.bot * g.top, f.bot * g.bot); }

fraction subtract(const fraction f, const fraction g)
{ return makefr(f.top * g.bot - f.bot * g.top, f.bot * g.bot); }

bool lessthan(const fraction f, const fraction g)        // "less" is already defined in a library
{ return f.top * g.bot < f.bot * g.top; }                // beware of negatives

int main()
{ fraction half = makefr(1, 2);
  fraction quarter = makefr(1, 4);
  fraction seven_eighths = makefr(7, 8);

  fraction x = add(half, quarter);

  print(half);
  cout << " * ";
  print(quarter);
  cout << " = ";
  print(x);
  cout << "\n";

  print(x);
  cout << " < ";
  print(seven_eighths);
  cout << " = ";
  bool y = lessthan(x, seven_eighths);
  cout << (y ? "true" : "false") << "\n"; }