Euclideans Algorithm to reduce fractions

Hi my teacher gave us an assignment and I have gotten every thing taken care of except for understanding where to apply the Euclidean Algorithm to reduce my fractions... below is the source code and where i have attempted to use the algorithm are commented out. Please help me figure out how and where to apply it..

#include <iostream>
using namespace std;

int main ()

{
char operation = ' ';
int numerator1;
int denominator1;
int numerator2;
int denominator2;
int finalNumerator;
int finalDenominator;
int small;
int large;
int remainder;

//enter operation number code
cout << "Addition -- 1" << endl;
cout << "Subtraction -- 2" << endl;
cout << "Multiplication -- 3" << endl;
cout << "Division -- 4" << endl;
cout << "Please enter the number of operation you want: ";
cin >> operation;

cout << "Please enter the numerator of the first value: ";
cin >> numerator1;
cout << "Please enter the denominator of the first value: ";
cin >> denominator1;
cout << "Please enter the numerator of the second value: ";
cin >> numerator2;
cout << "Please enter the denominator of the second value: ";
cin >> denominator2;

if (denominator1 == 0 || denominator2 == 0)
{
cout << "Invalid value for denominator"<< endl;
}
else
//endif
switch (operation)
{
case '1': //addition

finalNumerator = (numerator1 * denominator2) + (numerator2 * denominator1);
finalDenominator = denominator1 * denominator2;

if (finalNumerator > finalDenominator)
{
int wholeNumber;
int mixedNumerator;

wholeNumber = finalNumerator / finalDenominator;
mixedNumerator = finalNumerator % finalDenominator;

// mixedNumerator = small;
// finalDenominator = large;
// while (large % small != 0)
// {
// remainder = large % small ;
// large = small;
// small = remainder;
// }

if (mixedNumerator == 0)
{
cout <<"Result is: " << wholeNumber; // for when the answer is only whole number
}
else
{

cout << "Result is: " << wholeNumber << " " << mixedNumerator << "/" << finalDenominator;
}
}
else if (finalNumerator == finalDenominator)
{
int equals1;
equals1 = finalNumerator / finalDenominator;
cout << "Result is: " << equals1;
}
else
{
cout << "Result: " << finalNumerator << '/' << finalDenominator << endl;
}
break;

case '2': //subtraction

finalNumerator = (numerator1 * denominator2) - (numerator2 * denominator1);
finalDenominator = denominator1 * denominator2;
if (finalNumerator > finalDenominator)
{
int wholeNumber = 0;
int mixedNumerator = 0;
int mixedDenominator = 0;

wholeNumber = finalNumerator / finalDenominator;
mixedNumerator = finalNumerator % finalDenominator;
if (mixedNumerator == 0)
{
cout <<"Result is: " << wholeNumber; // for when the answer is only whole number
}
else
{
cout << "Result is: " << wholeNumber << " " << mixedNumerator << "/" << finalDenominator;
}
}
else if (finalNumerator == finalDenominator)
{
int equals1;
equals1 = finalNumerator / finalDenominator;
cout << "Result is: " << equals1;
}
else
{
cout << "Result: " << finalNumerator << '/' << finalDenominator << endl;
}
break;

case '3': //multiplication

finalNumerator = numerator1 * numerator2;
finalDenominator = denominator1 * denominator2;

if (finalNumerator > finalDenominator)
{
int wholeNumber = 0;
int mixedNumerator = 0;

wholeNumber = finalNumerator / finalDenominator;
mixedNumerator = finalNumerator % finalDenominator;

if (mixedNumerator == 0)
{
cout <<"Result is: " << wholeNumber; // for when the answer is only whole number
} // end if
else
{
mixedNumerator = small;
finalDenominator = large;

while (large % small != 0)
{
remainder = large % small ;
large = small;
small = remainder;
}

cout << "Result is: " << wholeNumber << " " << mixedNumerator << "/" << finalDenominator;
}
}// end if
else if (finalNumerator == finalDenominator)
{
int equals1;
equals1 = finalNumerator / finalDenominator;
cout << "Result is: " << equals1;
}
else
{
// finalNumerator = small;
// finalDenominator = large;

// while (large % small != 0)
// {
// remainder = large % small ;
// large = small;
// small = remainder;
// }// end while
// cout << "Result is: " << remainder << '/' << large << endl;
}
break;

case '4': //division

finalNumerator = numerator1 * denominator2;
finalDenominator = denominator1 * numerator2;
if (finalNumerator > finalDenominator)
{
int wholeNumber = 0;
int mixedNumerator = 0;
int mixedDenominator = 0;

wholeNumber = finalNumerator / finalDenominator;
mixedNumerator = finalNumerator % finalDenominator;
if (mixedNumerator == 0)
{
cout <<"Result is: " << wholeNumber; // for when the answer is only whole number
}
else
{
cout << "Result is: " << wholeNumber << " " << mixedNumerator << "/" << finalDenominator;
}
}
else if (finalNumerator == finalDenominator)
{
int equals1;
equals1 = finalNumerator / finalDenominator;
cout << "Result is: " << equals1;
}
else
{
cout << "Result: " << finalNumerator << '/' << finalDenominator << endl;
}
break;

default:
cout << "Invalid selection";
} //end switch

return 0;
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