Q:

Overloading the Multiplication Operator

I have looked at many of the other posts dealing with overloading the * operator and I still am unable to see the issue.
    #include <iostream>
#include <string>
#include <cmath>

using namespace std;

class Fraction{
    private:
        int num, den;
    public:
        void set(int n, int d);
        void setNum(int newNum);
        void setDen(int newDen);
        Fraction add(Fraction other);
        Fraction simplify();
        Fraction(int new_Num = 0, int new_Den = 0){
            num = new_Num;
            den = new_Den;
        };
        void output(Fraction& f);
        void cleanerFunction(Fraction& f);
        int gcd();
        Fraction reduce();
        friend ostream& operator <<(ostream& os, Fraction& f);
        friend istream& operator >>(istream& in, Fraction& f);
        friend Fraction operator + ( const Fraction&, const Fraction& );
        friend inline Fraction operator - ( const Fraction&, const Fraction& );
        friend Fraction operator * ( const Fraction&, const Fraction& );
        friend Fraction operator / ( const Fraction&, const Fraction& );
        friend bool operator < ( const Fraction&, const Fraction& );
        friend bool operator <= ( const Fraction&, const Fraction& );
        friend bool operator > ( const Fraction&, const Fraction& );
        friend bool operator >= ( const Fraction&, const Fraction& );
        friend bool operator == ( const Fraction&, const Fraction& );

};
int gcd(int x, int y);
Fraction reduce(Fraction f);
void reduce(Fraction& f);

Fraction operator + ( const Fraction& f, const Fraction& r){
    int temp_Num, temp_Den;
    temp_Num = (f.num * r.den) + (f.den * r.num);
    temp_Den = (f.den * r.den);
    Fraction temp_Frac(temp_Num, temp_Den);
    temp_Frac.cleanerFunction(temp_Frac);
    return temp_Frac;

};
Fraction operator - ( const Fraction& f, const Fraction& r){
    int temp_Num, temp_Den;
    temp_Num = (f.num * r.den) - (f.den * r.num);
    temp_Den = (f.den * r.den);
    Fraction temp_Frac(temp_Num, temp_Den);
    temp_Frac.cleanerFunction(temp_Frac);
    return temp_Frac;

};
Fraction operator * ( const Fraction& f, const Fraction& r){
    int temp_Num, temp_Den;
    temp_Num = (f.num * r.num);
    temp_Den = (f.den * r.den);
    Fraction temp_Frac(temp_Num, temp_Den);
    temp_Frac.cleanerFunction(temp_Frac);
    return temp_Frac;
};
Fraction operator / ( const Fraction& f, const Fraction& r){
    int temp_Num, temp_Den;
    temp_Num = (f.num * r.den);
    temp_Den = (f.den * r.num);
    Fraction temp_Frac(temp_Num, temp_Den);
    return temp_Frac;

};

bool operator < ( const Fraction& f, const Fraction& r){
    return (f.num * r.den) < (r.num * f.den);
};
bool operator <= ( const Fraction& f, const Fraction& r){
    return (f.num * r.den) <= (r.num * f.den);
};
bool operator > ( const Fraction& f, const Fraction& r){
    return (f.num * r.den) > (r.num * f.den);
};
bool operator >= ( const Fraction& f, const Fraction& r){
    return (f.num * r.den) >= (r.num * f.den);
};
bool operator == ( const Fraction& f, const Fraction& r ){
    return (f.num * r.den) == (r.num * f.den);
};

ostream& operator <<(ostream& os, Fraction& f)
{
    f.output(f);
    return os;
}

istream& operator >>(istream& in, Fraction& f)
{
    char ch;
    int temp_Num, temp_Den;
    in >> temp_Num >> ch >> temp_Den;
    f.set(temp_Num, temp_Den);
    f.cleanerFunction(f);
    return in;
}

 int main()
{
     cout <<"HELLO\n";
     cout << "Testing declarations " << endl;
     cout << "Fraction x, y(2), z(-5,-6), w(1,-3);" << endl;
     Fraction x, y(2), z(-5,-6), w(1,-3);
     cout << "z = " << z << ", y = " << y << ",  z = " << z << ", w = " << w << endl;
     cout << "Testing >> overloading: \nEnter a fraction in the format " << "integer _numerator/integer _denominator" << endl;
     cin >> x;
     cout << "You entered the equivalent of: " << x << endl;
     //cout << z << " -  (" << w << ") = " << z - w << endl;
     cout << "Testing the constructor  and normalization routines: " << endl;
     y =Fraction(-128, -48);
     cout << "y =Fraction(-128, -48) outputs  as " << y << endl;
     y =Fraction(-128, 48);
     cout << "y =Fraction(-128, 48 ) outputs  as " << y << endl;
     y = Fraction(128,-48);
     cout << "y = Fraction(128, -48) outputs  as " << y << endl;
     Fraction a(1,1);
     cout << "Fraction a(1,1); a outputs  as: " << a << endl;
     Fraction ww = y*a;
     cout <<  y << " * " << a << " = " << ww << endl;
     w = Fraction(25,9);
     z = Fraction(3,5);
     cout << "Testing arithmetic and relational operator  overloading" << endl;
     //cout << w << " * " << z << " = " << w * z << endl;
     //cout << w << " + " << z << " = " << w + z << endl;
     //cout << w << " - " << z << " = " << w - z << endl;
     //cout << w << " / " << z << " = " << w / z << endl;
     cout << w << " <  " << z << " = " << (w < z) << endl;
     cout << w << " < " << w << " = " << (w < w) << endl;
     cout << w << " <= " << z << " = " << (w <= z) << endl;
     cout << w << " <= " << w << " = " << (w <= w) << endl;
     cout << w << " >  " << z << " = " << (w > z) << endl;
     cout << w << " > " << w << " = " << (w > w) << endl;
     cout << w << " >= " << z << " = " << (w >= z) << endl;
     cout << w << " >= " << w << " = " << (w >= w) << endl;
     w = Fraction(-21,9);
     z = Fraction(3,5);
     //cout << w << " * " << z << " = " << w * z << endl;
     //cout << w << " + " << z << " = " << w + z << endl;
     //cout << w << " - " << z << " = " << w - z << endl;
     //cout << w << " / " << z << " = " << w / z << endl;
     cout << w << " <  " << z << " = " << (w < z) << endl;
     cout << w << " < " << w << " = " << (w < w) << endl;
     cout << w << " <= " << z << " = " << (w <= z) << endl;
     cout << w << " <= " << w << " = " << (w <= w) << endl;
     cout << w << " >  " << z << " = " << (w > z) << endl;
     cout << w << " > " << w << " = " << (w > w) << endl;
     cout << w << " >= " << z << " = " << (w >= z) << endl;
     cout << w << " >= " << w << " = " << (w >= w) << endl;
     return 0;
   return 0;
}

Fraction Fraction::add(Fraction other){
    Fraction result;
    result.num = num*other.den + other.num *den;
    result.den = den*other.den;
    return result;

}

Fraction Fraction::simplify(){
    Fraction f1;
    f1.num = 4; f1.den=5;
    return f1;

}

int gcd(int x, int y){
    if( y<0)
        y =-y;

    if(x % y == 0)
        return y;
    else
        return gcd(y, x%y);
}

int Fraction::gcd(){
    Fraction temp;
    if( den<0)
            den =-den;

        if(num % den == 0)
            return den;
        else{
            temp.num =den;
            temp.den= num%den;
            return temp.gcd();
        }
}

void Fraction::set(int n, int d){
    num = n;
    den = d;

}

void Fraction::setNum(int newNum){
    num = newNum;
}
void Fraction::setDen(int newDen){
    den = newDen;
}
Fraction Fraction::reduce(){
    Fraction temp;
    temp.set(num,den);
    int m = temp.gcd();
    num /= m;
    den /= m;
}
Fraction reduce(Fraction f){
    int m = f.gcd();

}
void reduce(Fraction& f){

}

void Fraction::output(Fraction& f){

    f.cleanerFunction(f);
    cout << num << "/"<< den;
}

void Fraction::cleanerFunction(Fraction& f){
    int temp_Num = num;
    int temp_Den = den;

    if ((temp_Num != 0) && (temp_Den == 0))
        temp_Den = 1;
    if ((temp_Num > 0) && (temp_Den < 0 )){
        temp_Den = abs(temp_Den);
        temp_Num = -temp_Num;
    };
    if (( temp_Num < 0) && (temp_Den < 0)){
        temp_Den = abs(temp_Den);
        temp_Num = abs(temp_Num);
    };

    num = temp_Num;
    den = temp_Den;
}

There is the relevant code, if you need more I can post. The code *cout << w * z << endl; * and everything in Main() cannot be modified, everything else can.
Error I get is 
error: cannot bind 'std::ostream {aka std::basic_ostream}' lvalue to 'std::basic_ostream&&'
The commented out lines in Main() are the lines where I get error messages. So I get problems with the (+,-,*,/) operators. I wanted to just look at the * so I could then go back and apply the same fix to the rest of those.

A:

You get error message at cout << w * z << endl; because there is no overload of operator<< which takes class Fraction as an argument. Try defining this overload:
std::ostream& operator<<(std::ostream& os, const Fraction& f)
{
    return os << f.den << "/" << f.num;
}

And add the following line to the definition of class Fraction in order to make den and num available to this function:
friend std::ostream& operator<<(std::ostream& os, const Fraction& f);

