>I think this is what I mentioned in my other reply, wasn't it? I just want to see if I was right. You do the division first (treat it as a single number - a fraction).

I finally broke down, swallowed my pride, and asked a former coworker who is an actuary. This was his response:

The phrase to remember is “Please Excuse My Dear Aunt Sally,” although the technical term is the mathematical 
“order of operations” (if you do a google).  Order of Operations defines the “order” in which you do the calcs.  The 
phrase above is a memory aid:

P = Do items in Parathesis first (although I’m not sure the 6th grade has done this yet so the students can ignore this step).
E = Do Exponents next (again, not sure if they’ve covered this yet).
M & D = Then do all Multiplication and Division working left to right
A & S = Then Addition and Subtraction working left to right

So, in your example below:

-24 / 4 x -2 would be, working left to right…(-24 / 4) which equals -6, then multiplied by -2, for an answer of 12.

Regarding the negatives and multiplication, you listed all the right rules.  The key is using PEMDAS to break the problem 
down into steps...all multiplication/division, before doing addition/subtraction.  I suspect the left-to-right idea will 
help out a lot.