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.
