We all know that we cannot divide by zero, but why?

Mar 5, 2022 | Red Deer

Try googling the answer. You’ll find lots of answers, and they like to use fancy and complex reasons that often can only be understood by a math nerd ðŸ¤“ We are lucky that Larry Martinek, the man behind the Mathnasium method, can give us a fairly straightforward explanation. 

Division by any number can be thought of as a fraction having that number as the denominator. For example, 2 divided by 5 can be written as 2/5; 1 divided by 2 can be expressed as ½, and 3 divided by 0 as 3/0.

Recall that the denominator of a fraction tells us how many equal parts make up the whole, and that the numerator tells us how many of these parts to consider. So, 2/5 means that the whole has 5 equal parts, and that we are currently considering 2 of them. Similarly, ½ means that the whole has 2 equal parts, and that we are using 1 of them.

Now, 3/0 means that the whole has zero parts … hey, wait a minute. Something is wrong here. Something doesn’t make sense. How can a whole have no parts?? ðŸ¤”

It can’t. To say that we have a whole means that at the very least we have one part, that is, the minimum case is that a whole has at least one part, namely, itself. That one part may be very small, but unless we have at least one part, we cannot say that we have a whole to start with.

Therefore, it is meaningless to speak of division by zero, because we cannot have a whole that has no parts.


Mathnasium of Red Deer is your neighbourhood’s math-only learning centre, and we are here to help your child. Our centre director, Riwan, would be happy to meet you! We are conveniently located in the shopping destination area in Red Deer: 5250 22nd St, Unit 30 B – at the Gaetz Avenue Crossing shopping centre, in the same area as Chapters Indigo/Starbucks, Michael Arts, Petland and Ashley, and the phone number is 403-872 MATH (6284). 

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