Division action with negative numbers

How to understand division with negative numbers? Not be able to follow the rules, but understand in practice.

Exactly the same as we were taught in the ABC book – on apples.

If I have 12 apples and I need to share them between myself and two comrades, then I and everyone will have four apples.

What if minus nine apples need to be divided by three?

It is necessary to introduce the concept of “debt”: There is a debt of 12 apples and I have two comrades who are ready to share this burden with me. Now each of us needs four apples.

The fun begins when 12 apples have to be divided by -3. Here again three appear, but now they are harmful collectors and the only thing they can do is create debt obligations out of everything. These are such negative, in all senses, personalities. They found out that I have 12 apples and now everyone wants their 4.

In fact, the last two examples are identical. Only in the penultimate debt is there already, and in the latter it arises. Result one – three promissory notes, 4 apples each. Therefore, dividing with one negative always results in negative.

Well, -12 / -3 are the collectors that have collected the debt.