#include <iostream>
#include <cmath>
#include <string>

using namespace std;

/**
* Gives the greatest common divisor of two integers or returns 0 if the
* gcd is undefined. Uses the Euclidean GCD algorithm
* @param a an integer
* @param b an integer
* @return the gcd of the specified parameter or 0 if both a and b are 0
*/

/**
* Computes the sum of two fractions
* @param n1 the numerator of the first fraction
* @param d1 the denominator of the first fraction
* @param n2 the numerator of the second fraction
* @param d2 the denominator of the second fraction
* @param num the numerator of the sum
* @param den the denominator of the sum
*/

void add(int n1, int d1, int n2, int d2, int& num, int& den)
{
	num = (n1 * d2 + n2 * d1) / gCD(n1 * d2 + n2 * d1, d1 * d2);
	den = (d1 * d2) / gCD(n1 * d2 + n2 * d1, d1 * d2);
}

/**
* Computes the difference of two fractions
* @param n1 the numerator of the minuend
* @param d1 the denominator of the minuend
* @param n2 the numerator of the subtrahend
* @param d2 the denominator of the subtrahend
* @param num the numerator of the dufferebce
* @param den the denominator of the difference
*/
void sub(int n1, int d1, int n2, int d2, int& num, int& den)
{
	num = (n1 * d2 - n2 * d1) / gCD(n1 * d2 - n2 * d1, d1 * d2);
	den = (d1 * d2) / gCD(n1 * d2 + n2 * d1, d1 * d2);
}

/**
* Computes the product of two fractions
* @param n1 the numerator of the multiplier
* @param d1 the denominator of the multiplier
* @param n2 the numerator of the multiplicand
* @param d2 the denominator of the multiplicand
* @param num the numerator of the product
* @param den the denominator of the product
*/
void mult(int n1, int d1, int n2, int d2, int& num, int& den)
{
	num = (n1 * n2 / gCD(n1 * n2, d2 * d1));
	den = (d1 * d2 / gCD(n1 * n2, d1 * d2));
}

/**
* Computes the quotient of two fractions, if defined
* @param n1 the numerator of the dividend
* @param d1 the denominator of the dividend
* @param n2 the numerator of the divisor
* @param d2 the denominator of the divisor
* @param num the numerator of the quotient
* @param den the numerator of the quotient
* or 0 if the quotient is undefinded
*/
void divd(int n1, int d1, int n2, int d2, int& num, int& den)
{
		num = (n1 * d2) / gCD(n1 * d2, n2 * d1);
		den = (n2 * d1) / gCD(n1 * d2, n2 * d1);
}

/**
* Gives the string representation of a fraction
* @param n the numerator of the fraction
* @param d the denominator of the fraction
* @param normalize gives a string represnetation
* of a fraction in normalized form where the
* numerator and denominator are relatively prime
* and n/d when normalized is false.
* @return n/d when normalized is false; otherwise,
* 1. d = 0 -> nan
* 2. n = 0 -> 0
* 3. d = 1 -> n
* 4. d = -1 -> -n
* 5. n and d have the same sign -> |n|/|d|
* 6. n and d have different signs -> -|n|/|d|
*/
string str(int n, int d, bool normalize)
{
	if (normalize == false)
		return to_string(n) + "/" + to_string(d);
	else if (d == 0)
		return "nan";
	else if (n == 0)
		return "0";
	else if (d == 1)
		return to_string(n);
	else if (d == -1)
		return "-" + to_string(n);
	else if ((d < 0 && n < 0) || (d > 0 && n > 0))
		return to_string(abs(n)) + "/" + to_string(abs(d));
	else if ((d < 0 && n > 0) || (d > 0 && n < 0))
		return "-" + to_string(abs(n)) + "/" + to_string(abs(d));
}

int gCD(int a, int b)
{
	a = abs(a);
	b = abs(b);
	if (a == 0 && b == 0)
		return 0;
	else if (a == 0 || b == 0)
		return abs(a + b);
	else
	{
		int r = a % b;
		while (r != 0)
		{
			a = b;
			b = r;
			r = a % b;
		}
		return b;
	}
}

int main()
{
	int f1n, f1d, f2n, f2d, f3n, f3d, numerator, denominator, addCacheNum, addCacheDen, multiplyCacheNum, multiplyCacheDen, divideCacheNum, divideCacheDen;
	cout << "Enter the numerator and denominator of fraction 1 -> ";
	cin >> f1n >> f1d;
	cout << "Enter the numerator and denominator of fraction 2 -> ";
	cin >> f2n >> f2d;
	cout << "Enter the numerator and denominator of fractoin 3 -> ";
	cin >> f3n >> f3d;
	if (f1d == 0 || f2d == 0 || f3d == 0)
		cout << endl << "ERROR: The denominator of a fraction cannot be equal to 0." << endl;
	else
	{
		cout << endl << "F1 = " << str(f1n, f1d, false) << endl;
		cout << "F2 = " << str(f2n, f2d, false) << endl;
		cout << "F3 = " << str(f3n, f3d, false) << endl << endl;

		add(f1n, f1d, f2n, f2d, numerator, denominator);
		cout << "F1 + F2 = " << str(numerator, denominator, true) << endl;

		sub(f1n, f1d, f2n, f2d, numerator, denominator);
		cout << "F1 - F2 = " << str(numerator, denominator, true) << endl;

		mult(f1n, f1d, f2n, f2d, numerator, denominator);
		cout << "F1 x F2 = " << str(numerator, denominator, true) << endl;

		if (gCD(f1n * f2d, f1d * f2n) == 0)
			cout << "F1 / F2 = nan" << endl;
		else
		{
			divd(f1n, f1d, f2n, f2d, numerator, denominator);
			cout << "F1 / F2 = " << str(numerator, denominator, true) << endl;
		}

		if (gCD(f1n * f2d, f1d * f2n) == 0)
			cout << "F1 x (F2 + F3) / (F1 + F3) = nan";
		else
		{
			add(f2n, f2d, f3n, f3d, addCacheNum, addCacheDen);

			mult(f1n, f1d, addCacheNum, addCacheDen, multiplyCacheNum, multiplyCacheDen);

			add(f1n, f1d, f3n, f3d, addCacheNum, addCacheDen);

			divd(multiplyCacheNum, multiplyCacheDen, addCacheNum, addCacheDen, divideCacheNum, divideCacheDen);

			cout << "F1 x (F2 + F3) / (F1 + F3) = " << str(divideCacheNum, divideCacheDen, true) << endl;
		}
	}
	return 0;
}