Why dividing by zero does not work

This article discusses some fun ways to show your child (or anyone else) that dividing by zero does not work.

dividing by zeroThe four basic operations of arithmetic – addition, subtraction, multiplication and division are all quite intuitive to learn. The hardest one to comprehend for a child is definitely division. The question that really gets a lot of children perplexed is the question of why division by zero does not work.

After all, you can add zero, subtract zero and multiply by zero – so why can’t you divide by it? And how do you explain something that is undefined?

Three ways to think about dividing by zero

Following are the three different ways we have used to explain division by zero:

The story of dividing by zero

The nicest way to explain the concept of division is probably to tell them various stories about sharing. Such as, “There are 9 marbles here (have them physically there), and there are 3 friends who want to play with them. How do you divide the marbles equally among the friends, so that everyone has the same number of marbles?”

That brings us to the first way of explaining why dividing by zero does not work:
“You have nine marbles and nobody wants to play with them. How do you divide the marbles equally among nobody?” This of course does not make sense, because there simply is nobody to give the marbles to. (Which is why the answer cannot be “9”, because that would mean dividing by 1, not zero).

Using Multiplication to explain division by zero

The second way is to look at multiplication. We know that multiplying a number really means adding that number a given number of times. For example, 5 * 3 = 5 + 5 + 5 = 15. And 15 / 5 = 3. In this example, we are really asking, how many times must I add 5 in order to get to 15? However, if we have 15 / 0, we are asking, how many times must I add 0 in order to get to 15. The answer of course is: it’s impossible. No matter how many times we add zero to itself, it will never amount to more than zero.

Looking at fractions

The final way is to look at fractions. For example, ½ means we have one pie and we want to divide it into two pieces. 1/3 means we have 1 pie and divide it into 3 pieces. 1/1 means divide the pie into one piece. But 1/0? No matter how we try and slice the pie, we can never slice it into zero pieces. We could of course, eat the pie, but that would be a different operation to division. 🙂 It would be “eating by one”, rather than “dividing by zero”.

So there you have it – we’ve had a good amount of laughter as a result of these discussions with our children, particularly when we tried via practical examples. So whether you use marbles, a pie or whatever, have some fun dividing by zero and make sure the results are either non-existent or at least edible.

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