What is the result if you multiply a number of cups by 8fl oz/1 cup and then multiply the result by 1 cup / 8fl oz?

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.