How to explain that division by $0$ yields infinity to a 2nd grader How do we explain that dividing a positive number by $0$ yields positive infinity to a 2nd grader? The way I intuitively understand this is $\lim_{x \to 0}{a/x}$ but that's asking too much of a child. There's got to be an easier way.
In response to the comments about it being undefined, granted, it is undefined, but it's undefined because of flipping around $0$ in positive or negative values and is in any case either positive or negative infinity.
Yet, $|\frac{2}{0}|$ equals positive infinity in my book. How do you convey this idea? 

The first thing to point out is that division by zero is not defined! You cannot divide by zero. Consider the number $1/x$ where $x$ is a negative number. You will find that $1/x$ is negative for all negative $x$. As $x$ gets closer and closer to zero, $1/x$ gets bigger and bigger in the negative direction: $1/x \to -\infty$ as $x \to 0$ from the negative side. Next, consider the number $1/x$ where $x$ is a positive number. You will find that $1/x$ is positive for all positive $x$. As $x$ gets closer and closer to zero, $1/x$ gets bigger and bigger in the positive direction: $1/x \to +\infty$ as $x \to 0$ from the positive side.
$$\lim_{x \to 0^-} \frac{1}{x} \neq \lim_{x \to 0^+} \frac{1}{x}$$
Informally: what does $6 \div 3$ mean? It means, how many times do you add $3$ together to get $6$, and the answer is $2$. What does $7 \div 2$ mean? It means, how many times do you add $2$ together to get $7$, and the answer is $3\frac{1}{2}.$ What does $1 \div 0$ mean? It means, how many times do you add $0$ together to get $1$? Well: $0 = 0+0 = 0+0+0$, etc.
You have to keep adding zeros for all of eternity. In reality, you never get to $1$ and so there is no answer. It is not infinity: you can't have "infinitly many" zeros. But some people might say "You add $0$ together infinitely many times".
