Math teachers tell you not to divide by zero because if you do, the world will explode. I mean, why else would calculators refuse to perform a division by zero? Try it: find a calculator and type in 1/0; you’ll get an error. The calculator manufacturers don’t want to take the chance of the world exploding when you try to do such a calculation because if the teachers are right and the world does explode, then they’ll lose out on sales. Less sales means less money to make more calculators, and less calculators means that people can’t do math (“Mental math? Never heard of it.”). Everyone would be unhappy, so it’s probably a good thing that they stop you from trying.
Ben Orlin even attempts to explain why you can’t divide by zero using math (complete with drawings!). That’s nice and all, and it even seems to work, but I’ve got something that makes a little more sense, and no, it’s not 42. Don’t think about it too much and you’ll be fine.
Division is taught to students by putting objects into groups. For the sake of example, I’m going to use marbles put into bags.
Let’s say you want to calculate 10/2. You would visualize this as 10 marbles being put into 2 bags:
Very simply, you’d put five marbles in each bag:
From that, you can clearly tell that 10/2=5.
That’s all well and good, but what about division by zero? It’s a similar process. Suppose we have 10/0; we would visualize that with 10 marbles and 0 bags:
Well, there’s only one way to do this: leave it as it is. Therefore, the answer must be 1. That is, 10/0=1.
I propose that anything divided by zero is 1. Here, let’s try 5/0:
Again, the only option is to leave it alone, so 5 divided by 0 must be 1.
This consistency is very nice. Multiplication by zero also yields a consistent answer, and since multiplication and division are related, this consistency is yet another piece of evidence for the proposition’s validity.
That’s it, then: division by zero yields one, and the world didn’t explode. At least, not physically, as far as I can tell. Perhaps this “world” that the teachers speak of is your mind, which I’m sure has just been blown. You should probably get that checked.
Clip art from the Open Clipart Library.