Parts of the Fraction:Why We Need Them???

To explain to my students why they need a common denominator when adding and subtracting fraction I would tell them the following information.First, I would tell my students what a common denominator is.the common denominator is the bottom number of the fraction and when adding and subtracting fractions the bottom number should be a multiple of both numbers meaning that both numbers can divide into the denominator. I would than explain that now the fractions is a whole of both numbers and the proper procedure for adding and subtracting fractions can be done.I would remind them that the product of adding and subtracting fractions is determined by the denominator.If the denominator is not the same you may not add or subtract them.  When explaining to my students about why you don't need a common denominator in multiplying and dividing fractions I would say that multiplication problems are already division problems so you don't need a common denominator because if the numerator has any divisor in common with a denominator than just as reducing in a single fraction we can cancel that common divsor.  I am not sure if this is agood way to explain it but I think this is a good way for them to understand it.