The result will always be less than what you started with. Consider
2/3 * 15/16
the result is 5/8.
2/3 has a decimal equivalent of .6666666
5/8 has a decimal equivalent of 0.625 it is moving smaller. I would offer you a more "mathematical"proof, but I don't think that's what you are asking for.
This is actually a pretty good question.