OK, I think I get it...maybe. To be honest, as my original question was some time ago, I am having a difficult time reconstructing the source of my earlier confusion. But maybe I was thinking that 4/4 made sense because 4 quarter notes add up to 1 and in 4/4 time, four quarter notes = 1 measure. But in 3/4 time, 3 quarter notes don't add up to 1 even though they also take up 1 measure.

So is the choice of the lower number (if its not a fraction I guess its not really a denominator) at least a little bit arbitrary? What i mean by that is if you had a piece of music that specified 80 bpm and it was in 4/4 time and another piece of music that specified 80 bpm and it was in 4/8 time, wouldn't they sound exactly the same (assuming that all the note values were halved in the 2nd piece of music).