#include <iostream>

using namespace std;

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(); }

  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; } };

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 main()
{ 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";

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