We know that when we multiply two integers with the same sign together, the sign of the product is positive. When we multiply to integers with differing signs together, the sign of the product is negative. Similar rules apply to division (presumably because of the inverse relationship of the two operations). By viewing the process of multiplication as being equivalent to successive additions, I can see why the product of two positive numbers is a positive and why the product of a positive number and a negative number is a negative. I'm having trouble wrapping my mind around the sign of the product of two negative numbers. Can someone please guide me as to how I would deduce that result?
Thanks for any input.