The denominator only changes if you're multiplying/dividing. You may need to create an <em>equivalent fraction</em> to add the fractions together, but you <em>don't</em> add or subtract the denominator.
No, you adjust the numerator and denominator to a common denominator, then do the addition/subtraction operations with with the numerator, and finally reduce it to the lowest fraction.
Example:
1/3 + 3/4 = ?
change to a common denominator (12 works for 3 and 4)