That might actually work if both halves of the $20 didn't have the serial # on it...

Taping the two 'smaller' halves together would produce a bill with TWO DIFFERENT serial numbers. Nobody would accept it.

Yeah except who the fark is going to compare the serial numbers on both halfs of the thing? Chances are you could pull it off at some store where the cashier doesn't give a crud, which is pretty much any place with a miserable looking teenager at the register.