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.

I teach high school math--and yes, I teach that division by zero is undefined. (I tell students that is why they get an error message when they try.) We also relate the fact that division by zero is undefined to the fact that the slope of a vertical line is undefined.

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