Adding together fractions of different denominators through a bit of operating overloading and cross multiplication.

fractions.cpp

#include <sstream>
#include <iostream>
using namespace std;

int getGCD(int a, int b)
{
    if(a % b == 0)
    {
        return b;
    }
    
    return getGCD(b, a % b);
}

class Fraction
{
private:
    int nu, de;
public:
    Fraction(int, int);
  	string toString();
	Fraction & operator+=(const Fraction &other);
	const Fraction & operator+(const Fraction &other) const;
};

Fraction::Fraction(int nu, int de)
{
	this->nu = nu; this->de = de;
}

string Fraction::toString()
{
	stringstream sout;
	sout << nu << "/" << de;
	return sout.str();
}

Fraction & Fraction::operator+=(const Fraction &other)
{
	this->nu = this->nu * other.de + this->de * other.nu;
    this->de = this->de * other.de;
    
    int gcd = getGCD(this->nu, this->de);
    this->nu = this->nu / gcd;
    this->de = this->de / gcd;
    
	return *this;
}

const Fraction & Fraction::operator+(const Fraction &other) const
{
	return Fraction(*this) += other;
}

int main()
{
	Fraction fraction(1,4);
	cout << fraction.toString() << endl;
	fraction += Fraction(2,3);
	cout << fraction.toString() << endl;
	return 0;
}