Expert: Socrates - 9/29/2005

Question
Do you have a suggestion of how I can prove to my 8th grade Algebra I class that a zero in the denominator of a fraction is undefined or infinite?  Thanks so much!

Answer
I can think of two ways to try and show this. I will keep it as simple as I can.


If your students believe in the cancellation rule for fractions , tell them to suppose that 5/0 is some number n

so 5/0 = n

multiply both sides by 0

(0) (5/0) = (0) (n)

cancelling 0's on the left side, this means

5 = (0) (n) = 0

so 5 = 0, which is obviously wrong.

This means you can't define 5/0 as any number, so it's undefined.

Another way is to put smaller and smaller numbers in for x in the fraction 5/x.

5/ .01  = 500

5/.0001 = 50,000

5/.0000001 = 50,000,000

so they see that as the denominator gets smaller and smaller , or closer to 0, the value of the fraction gets bigger and bigger. So if you put the smallest number in for x ,  which will be 0, you should get the biggest number for 5/0. But there is no biggest number, so 5/0 is  undefined . Or else you can say infinity is the biggest number , so 5/0 = infinity.

I am sure you can find other ways to explain why division by zero is undefined by doing a little research in the resources for secondary school teachers, but the above arguments, or some variation on them, might help.