Gather round, children, I'll tell you something they won't teach you in math class. (Because math nerds are thick in some ways.)
This thing is, dividing by zero isn't that hard to do. All you do is convert the numbers back into their original concepts and then logically surmise based off of what it is you are trying to do what the proper course of action is.
* You have $1337 dollars and you will divide this evenly amongst the participants. If there are zero participants, do you attempt to divide $1337 by zero participants? Of course not: circumstances have called for no division to be necessary.
* Over 1337 minutes, you measure the number of people to cross the street and divide 1337 by those people to determine the average number of minutes per people to cross the street. As it turns out, zero people cross the street in those 1337 minutes. Do you attempt to divide 1337 by zero to get your average? Of course not: you obviously have an insufficient sample to get the answer you need, so no division occurs.
* You're noticing that as your projectile weighing 1337 kgs approaches the event horizon of a black hole, the amount of energy required to break the speed of light approaches infinity. Do you surmise, then, that division by zero has occurred and therefore it is impossible to break the speed of light because the math fails at that point? Of course not: rather, your understanding of time/space is lacking a fundamental detail to explain why this happens.
Basically, math exists solely in your head. It's used as a technique of measurement. Measurement can be a powerful thing that allows us to make accurate predictions in many cases. However, at the point where we find our measurements to be more real than what we've measured, math ceases being an effective tool, and becomes a trap of narrow minds. Dwelling on how to divide by zero is the epitome of this.