Expert: Paul Klarreich - 9/29/2005

Question
How can I relate to my 8th grade algebra I students that a fraction with a value of zero in the denominator is undefined or infinite?  

They are a very bright group of kids who want to understand WHY. I need help to find a way to clearly explain this to them....Thanks so much!

~Kellie Palmer

Answer
Hi, Kellie,
Try this approach:
What is division, really?  What does it mean to, say, divide 56 by 7?
It means 'find a number (the quotient) that you can multiply 7 (the divisor) by so the product is 56 (the dividend).'  Since we know 7 times 8 is 56, the answer is 8.

When we look at a fraction,  a/b, that is an indicated division.  The divisor is b, the dividend is a, and the answer will be the quotient.  So when we write:

a/b = q,  we mean we have found 'q' that satisfies bq = a.

So how about  15/0?  This means 'find q that satisfies 0q = 15?'

But zero times any number never gives 15, or for that matter, anything but zero.

I hope this helps.  

And you can write me again when some wise guy asks about 0/0.

Paul