Why is 12 divided by 0 undefined?

Answer 1

Undefined: You cannot divide by zero

Answer 2

There are two ways this can be explained. The first is the simplest explanation, but if you're still curious- or just need something to do- feel free to read the second.

* Say you have twelve objects- or, for this example, $12. You want to divide these twelve dollars among several people. If you happened to be the only one who receives these twelve dollars (12 divided by 1), the $12 remains $12, and is undivided. If there's two people, it's 12 divided by 2; if it's one million people, it's 12 divided by one million (ignore the fact that $12 probably won't be worth much if it's divided by so many people). But what if you divide $12 by zero people? No one would get anything, right? If you divide any number of objects into zero groups, it will apparently cease to exist, which doesn't really make sense. So, 12/0 becomes a paradox. * You have a number, X, divided by another number, Y (so X / Y). When Y is equal to 1, X is unchanged. If you set Y equal to a number bigger than 1, such as 100, X, no matter its initial value, is decreased. Now, if Y is smaller than 1 (and still positive), such as 0.5, X is greater than its original value. Now, say you keep decreasing Y, so it is getting constantly smaller, and even approaches zero, but never actually reaches zero. X would start getting larger, and the closer Y gets to zero, the more incredibly large X becomes. So, what would happen if Y actually reachedzero? X would suddenly become extremely big- in a sense, X would become infinity. So let's say X/0 is infinity. Now what? There's not much you can do with a number that defies half the mathematical laws ever created. So infinity is labeled as "undefined" and is henceforth banned from mathematical reasoning, destined to exile from the world of numbers. And there you have it.