Details and caveats of the rules of basic mathematics. Can you divide by a negative number?

Question

I heard a while back, I dont know if its true or not, that division by a negative is "technically" not allowed.

Mathematically, you have to move the negative factor (-1) from the denominator to the numerator before dividing. Its algebraically the same exact thing and produces the same result... one can get away with not even consciously thinking about it. But the rule exists because it matters in higher level mathematics like number theory and whatnot.

Is this true? What do the rules of mathematics actually say about this... about division by negative values?

Likewise, what other odd caveats apply to mathematics that people dont often think about but can easily get away with ignoring?

Answer 1

Division by a negative number is certainly allowed:
6 / (-2) = -3

This is the same thing as saying
(-6) / 2 = -3
but neither form is more correct than the other. The reason for this is that multiplication is commutative:

(-2)*(3) is the same as (2)*(-3). They both equal (-6).

Answer 2

You are allowed to divide by a negative number.

here's a rule: + divide by + is=positive
- divide by -=positive
- divide by +=negative..
+ divide by -=negative