Any number system that forms a commutative ring —for instance, the integers, the real numbers, and the complex numbers—can be extended to a wheel in which division by zero is always possible; however, in such a case, "division" has a slightly different meaning.
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Please advise how best to explain the distinction between the solution to 'zero divided by one' and 'one divided by zero'. I remember being told in school that one of them is undefined and the other is zero but I'm having difficulty with calculating and explaining it to some highly curious 10 year olds! Why some people say it's 1: A number divided by itself is 1. Why some people say it's undefined: Dividing by zero is undefined. Only one of these explanations is valid, and choosing the other explanations can lead to serious contradictions. If you think of money, which seems to help with fractions, 0/1 is $0 divided evenly among 1 person. We have ALL been there. 1/0 is $1 divided evenly among 0 people, well, if there is no one there,how do we know it is $1. 0/1 is easier to think about, because it is a finite answer, but 1/0 can get tricky.