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A very way to understand this very logically.

First know what is multiplication?

It is recurring addition.

So if we multiply 3 by (-2), that means:-

(-2)+(-2)+(-2)= -6

Now see the examples below:

4 X (-4) = -16

3 X (-4) = -12

2 X (-4) = -8

1 X (-4) = -4

0 X (-4) = 0

Have you noticed a trend. Notice carefully that as the numbers which are being multiplied by (-4) are decreasing 1 by 1 the product is increasing by (+4).

So for the numbers 4,3,2,1,0 the products are:-

-16

-16+4= -12

-12+4= -8

-8+4= -4

-4+4=0

So what will be in the next step when we do:

(-1) X (-4)=?

The series will continue 0+4 an will result to a positive 4

and it will go like this:

(-1) X (-4)= 4

(-2) X (-4)= 8

(-3) X (-4)= 12

+4 is added in each step. This was the best explanation to this according to me which was told to me by my teacher which he made himself.

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