Order of evaluating an a fraction's components - 0/0

1. May 28, 2015

Square1

Just wondering if I've forgotten a rule here, or there is some new terminology I can learn.

We know 0/x when x > 0, is equal to 0. x/0 is undefined..since we "blow up" dividing any value by a value that is more than infinitely small...by zero.

We say that 0/0 is also undefined. We choose to consider the denominator 0 here first to say, "dividing by zero...can't be defined", instead of first considering the numerator and saying maybe, "zero is gonna be divided. It's gonna be equal to zero no matter what since we started with nothing".

Question: Is there an algebraic rule, or convention, that generally states you should start to evaluate the denominators first? Or is x/0 simply its own case where we can begin and end evaluating the parts that make up an expression?

2. May 28, 2015

Staff: Mentor

The basic rule is that division by 0 is not allowed.
0/0 is called an indeterminate form. It shows up in limits where both the numerator and denominator are approaching zero. This is indeterminate, because some quotients with this form actually have a limit, which can be literally any number or even $\infty$ or $-\infty$.
No. The rule is that division by zero is not allowed.