How do I apply the division algorithm with a negative dividend?

[Caldus]

If I have to find the quotient q and the remainder r and:

a = -5286
b = 19

How do I go about writing down the steps for this algorithm? I know what the answer will be, but I need to be able to use the division algorithm to prove my answer. Like I know if:

b > 0 and a < 0 (which in this case is true),

then since -a > 0, a = (-q)b - r (where 0 <= r < b).

But how would I know that q is equal to -279 and that the remainder is 15? (Pretending that I didn't the know answer already.)

Thanks.

 

[HallsofIvy]

I have absolutely no idea how you would "know that q is equal to
-279 and that the remainder is 15" since -(-279)(19)-15 is NOT
-5286 (nor is (-279)(19)-15). You have your signs mixed up.

Did you try actually dividing? That is, after all what the division algorithm is!