chained if-else not working (C++)

I'm a beginner and am having trouble with my chained if-else statement. When I run the program, and I enter which item I select, it always outputs "Invalid entry.". Why isn't it executing the proper function when it is equal to it in the if-statement?

Thank you,

Don

#include <iostream>
using namespace std;

int sum(int int1, int int2 ){

    return int1 + int2;

}

int difference( int int1, int int2 ){

    return int1 - int2;

}

int product( int int1, int int2 ){

    return int1 * int2;

}

int quotient( int int1, int int2 ){

    return int1 / int2;

}

int main(){

cout << "\nWelcome to the calculator.\n\n";
cout << "Please enter two numbers.\n\n";

int a;
int b;
cin >> a >> b;

cout << "What would you like to do with these numbers?\nHere are your options: add, subtract, multiply, or divide.\n\n";

string add;
string subtract;
string multiply;
string divide;

string choice;
cin >> choice;


if( choice == add )
    cout << sum( a, b );
else if ( choice == subtract )
    cout << difference( a, b );
else if ( choice == multiply )
    cout << product( a, b );
else if ( choice == divide )
    cout << quotient( a, b );
else 
    cout << "Invalid entry.\n"; 

return 0;

}