# Division By Zero

## Published on Nov. 23, 2012, 7:40 p.m.

In a former life (while a GA in graduate school), I was forced to had the pleasure to teach elementary and intermediate algebra. These courses are essentially the algebra curriculum you should learn during High School in the United States. Unfortunately, many college-bound students don't master the material, and find themselves in a remedial class during their college career. That's the class I was teaching.

There are many concepts that are difficult for students to understand, but one of the most perplexing is the concept of Division by Zero. Interestingly enough, Multiplication by Zero is relatively easy for students to master:`a × 0 = 0`

## But what is Division?

We start out teaching division by disguising it as a multiplication problem.

``` 3 × ____ = 12 ```

Read in english, this is "three times what number is twelve?" Then, somewhere along the line, we introduce this new notation:

``` 12 / 3 = ____ ```

In english, this is "twelve divided by three is what number?" It can also be read as "three times what number is twelve?" Hey! this is the same as the equation above!

So, now we get to this:

``` 5 / 0 = ____ ```

I've seen so many people answer this with "zero" (which is incorrect). In english, we're asking, "zero times what number is five?"

This is essentially: `0 × ____ = 5`. This problem makes no sense. It's analogous to asking "Which part of the turkey makes a spaceship?" (OK, that's a bad analogy, but Thanksgiving was yesterday, and I like spaceships).

Since any number multiplied by zero is zero, there is no answer to this equation. Mathematicians say the solution is undefined.

I'm pretty sure these kinds of problems are just practical jokes played on us by the Mathematicians of old.