Why can't I just add fractions by adding the numerators and denominators, like I do with integers?
Because fractions represent parts of different-sized wholes. 1/2 is one of two parts, and 1/3 is one of three parts—they're not the same size, so you can't simply add them. You must first convert them to the same-sized parts (common denominator) before adding. Applaa shows this visually so it makes sense.
