If you divide by zero on a mechanical calculator, bad things can happen. You've probably seen the video:
This chaos of churning gears comes down to a fairly simple explanation. Division is just a series of sequential subtraction, and division by zero is the sequential subtraction of zero, over and over and over again into infinity. It's an endless loop.
Today, calculators like kids use in school or the apps you find on your phone know better than to get themselves into this kind of trouble. Instead of walking into an infinite loop, they'll spit you a boring error. The calculators of yesteryear, on the other hand, were not quite so smart and reacted in a variety of different ways.
Here are five examples of adding (and subtracting) machines that are taking it less than well.