#include <iostream>
#include <string>

using namespace std;

struct reader
{ string input;
  int pos, len;

  reader(string s)
  { input = s;
    pos = 0;
    len = s.length(); }

  void skip_spaces()
  { while (pos < len && input[pos] == ' ')
      pos += 1; }

  char take_char()
  { if (pos >= len)
      return '\n';
    char c = input[pos];
    pos += 1;
    return c; }

  char see_char()
  { if (pos >= len)
      return '\n';
    return input[pos]; }

  string whats_next()
  { skip_spaces();
    if (pos >= len)
      return "end";
    char c = see_char();
    if (c == '+' || c == '-' || c == '/')
      return string(1, c);
    if (c >= '0' && c <= '9')
      return "digit";
    if (c >= 'a' && c <= 'z' || c >= 'A' && c <= 'Z')
      return "letter";
    if (c <= ' ')
      return "space";
    return "other"; }

  int take_int()
  { skip_spaces();
    string n = whats_next();
    if (n != "digit")
    { cerr << "\ntake_int called when int not present\n";
      return -1; }
    int value = 0;
    while (true)
    { string n = whats_next();
      if (n != "digit")
        break;
      char c = take_char();
      value = value * 10 + c - '0'; }
    return value; } };

int gcd(int a, int b)
{ for (int pd = min(a, b); pd > 1; pd -= 1)
    if (a % pd == 0 && b % pd == 0)
      return pd;
  return 1; }

struct rational
{ int top, bot;

  void simplify()
  { if (top == 0)
    { bot = 1;
      return; }
    int d = gcd(top, bot);
    if (d != 1)
    { top /= d;
      bot /= d; }
    if (bot < 0)
    { bot = - bot;
      top = - top; } }

  rational(int t, int b)
  { top = t;
    bot = b;
    simplify(); }

  rational(string s)
  { reader r(s);
    bool neg = false, error = false;
    int wholepart = 0;
    string n = r.whats_next();
    if (n == "-")
    { neg = true;
      r.take_char(); }
    else if (n == "+")
      r.take_char();
    else if (n != "digit")
      error = true;
    int x = r.take_int();
    n = r.whats_next();
    if (n == "end")          // whole thing is just a single int
    { top = x;
      bot = 1; }
    else if (n == "+")
    { wholepart = x;         // must now see top / bot
      r.take_char();
      n = r.whats_next();
      if (n != "digit")
        error = true;
      top = r.take_int();
      n = r.whats_next();       // still need / bot
      if (n != "/")
        error = true;
      r.take_char();
      bot = r.take_int(); }
    else if (n == "/")       // whole thing is top / bot
    { top = x;
      r.take_char();
      bot = r.take_int(); }
    else
      error = true;
    if (error)
    { cerr << "\nimproper number " << r.input << "\n";
      top = 0;
      bot = 0; }
    if (wholepart != 0)
      top += wholepart * bot;
    if (neg)
      top = - top;
    simplify(); }

  void print(ostream & out)
  { if (top < 0)
    { out << "-";
      top = - top; }
    if (bot == 1)
      out << top;
    else if (top > bot)
    { int whole = top / bot;
      int newtop = top - whole * bot;
      out << whole << "+" << newtop << "/" << bot; }
    else
      out << top << "/" << bot; }

  rational operator*(rational b)
  { return rational(top * b.top, bot * b.bot); }

  rational operator/(rational b)
  { return rational(top * b.bot, bot * b.top); }

  rational operator+(rational b)
  { return rational(top * b.bot + b.top * bot, bot * b.bot); }

  rational operator-(rational b)
  { return rational(top * b.bot - b.top * bot, bot * b.bot); }

  rational & operator*=(rational b)
  { top *= b.top;
    bot *= b.bot;
    simplify();
    return * this; }

  rational & operator/=(rational b)
  { top *= b.bot;
    bot *= b.top;
    simplify();
    return * this; }

  rational & operator+=(rational b)
  { int newbot = bot * b.bot;
    top = top * b.bot + b.top * bot;
    bot = newbot;
    simplify();
    return * this; }

  rational & operator-=(rational b)
  { int newbot = bot * b.bot;
    top = top * b.bot - b.top * bot;
    bot = newbot;
    simplify();
    return * this; }
    
  bool operator<(rational b)
  { return top * b.bot < b.top * bot; }
    
  bool operator>(rational b)
  { return top * b.bot > b.top * bot; }
    
  bool operator<=(rational b)
  { return top * b.bot <= b.top * bot; }
    
  bool operator>=(rational b)
  { return top * b.bot >= b.top * bot; }
    
  bool operator==(rational b)
  { return top == b.top && bot == b.bot; }
    
  bool operator!=(rational b)
  { return top != b.top || bot != b.bot; } };

ostream & operator<<(ostream & out, rational a)
{ a.print(out);
  return out; }

void one_test(string s, rational a, rational b, rational c)
{ cout << a << " " << s << " " << b << " is " << c << "\n"; }

void test(rational a, rational b)
{ one_test("plus", a, b, a + b);
  one_test("minus", a, b, a - b);
  one_test("times", a, b, a * b);
  one_test("divided by", a, b, a / b);
  one_test("complicated thing", a, b, (a + b) * (a - b)); }

rational ask(string prompt)
{ int t, b;
  cout << prompt << ", top then bottom: ";
  cin >> t >> b;
  return rational(t, b); }

int mainx()
{ rational w(3, 4);
  rational x(7, 8);
  rational y(1, 10);
  rational z(3, 2);
  w += x;
  w -= y;
  w *= z;
  cout << "(3/4 + 7/8 - 1/10) * 3/2 = " << w << "\n";
  cout << "is 7/8 > 1/10? ";
  if (x < y)
    cout << "yes\n";
  else
    cout << "no\n";

  while (true)
  { rational a = ask("A");
    rational b = ask("B");
    test(a, b); } }

int main()
{ cout << "1/2: " << rational("1/2") << "\n";
  cout << "123/124: " << rational("123/124") << "\n";
  cout << "1+2/3: " << rational("1+2/3") << "\n";
  cout << "123+17/101: " << rational("123+17/101") << "\n";
  cout << "-12+1/4: " << rational("-12+1/4") << "\n";
  cout << "-1/3: " << rational("-1/3") << "\n";
  cout << "-1/371: " << rational("-1/371") << "\n"; }