Why can 0 be divided by any other number but any number cannot be divided by 0?

Answer 1

Undefined: You cannot divide by zero

Answer 2

Think of it this way:

• If you have nothing and give an equal part to a group of people, how much does each get? Answer: Nothing, because you have nothing to give away to each person. This works no matter how many people are there, because you are still giving nothing to each one. This is related to the idea of multiplication by zero and is pretty much identical except for the fact it is division instead.
• If you have 10 apples to give to nobody, how many would you give to one person? This is where the 'undefined' comes in, because the same could be asked with 3 apples or a million apples, or by going from 0 to 2 people or 0 to 50 people. Hence, division by zero must have either the same answer for every question, or have no answer at all. It couldn't be zero, because where did your apples go otherwise. It couldn't be 1, because only dividing by the same number gives 1. In fact, we can't define it, because it breaches the inverse property; dividing by something, then multiplying by that same something, must give the original number. But multiplication by zero will always return 0, when we started with 10 (or 3 or a million). So division by zero cannot be defined, because we do not have anything to define it as.