Division by zero

Hi.  One topic I cover in week one of a college algebra course is division by zero.  We are going to see this later on in the chapter on rational functions, so I think we ought to settle this issue sooner rather than later.  Most people reading this blog are well-aware that division by zero is an undefined operation in the rules of real and complex number arithmetic.  3/0 = undefined.

This is often quite a surprise to my students, who apparently never learned this anywhere in their K-12 educations.  Truthfully, I can't remember learning it in my K-12 education either.  I think my fourth grade teacher is on Facebook, and I'm going to ask her if she remembers teaching it.

I invite my students to try 3/0 on as many calculators as they own.  Sometimes the calculator will show "Error" (which is descriptive, but is not a correct answer), and sometimes it will show zero (which is worse).  Students are even more surprised when I tell them both of these calculator results are incorrect.  However, we also experiment on calculators with Order of Operations problems, so students discover that not every calculator follows those rules.

I can picture Reverend Jim on the TV show Taxi:  "3/0 = undefined?  You're blowing my mind!"  I'd love to hear from some K-8 teachers or some high school algebra teachers on whether they teach division by zero.