Dividing by Zero

We have all learned as students that dividing any number by zero is undefined, but why is that so?  To understand this, we first have to define division. 

So what is division really?  Division is splitting a number into equal groups.  For example, if three children are fighting over a bag of candy that contains nine pieces, we would split that bag into three groups of three, so that we're fair to all three kids.  Knowing that then, to divide by zero would mean to split a number into zero groups.  To go back to the idea of children fighting over candy, would we be able to split that bag into zero kids?  Does that even make sense?  Not quite! 

The other nice thing about division is that we can always check our answer by multiplying the two numbers to get the third.  For example, if we just figured out that 10 divided by 5 is 2, we can multiply 5 and 2 to verify that the answer is indeed 10.  Having zero, that concept does not work:

10 divided by 0 DOES NOT EQUAL 0 divided by 10

Hence, dividing by zero is undefined simply because it doesn't have any mathematical or logical sense.