Why do fractions need to have a common denominator before you add or subtract them?

Fractions need to have a common denominator because it tells how many pieces the whole is divided into. If one whole is divided into two parts, and another whole the same size is divided in to three parts, one out of the two parts will not be the same size as one out of the three parts.

If we use a common denominator, it ensures each piece is the same size.

The denominator of a fraction tells you the relative size of the pieces. For instance, 1/2 is bigger than 1/4 because it only takes 2 pieces to make a whole, as opposed to 4 pieces to make a whole. One might connect the need for a common denominator to the need for having common units before adding or subtracting (you wouldn't add 12 inches to 12 feet and get 24 for an answer). Therefore, the reason fractions need a common denominator before adding or subtracting is so that the number of pieces you are adding/subtracting are all the same size. By the way, the numerator of a fraction just tells you how many pieces you have of that size.