The result is the number of cups.
Let x be the number of cups:
multiply a number of cups by 8fl oz / 1 cup
x * 8fl.oz/1 cup = (8floz * x)/1cup
multiply the result by 1cup/8fl oz
(8fl.oz * x)/1cup * 1 cup / 8 fl oz = x ; the original number multiplied is the answer. The multiplier cancels itself.