We can only do arithmetic in the usual way. To calculate 5(−2), we have to do 5· 2 = 10 -- and then decide on the sign. Is it +10 or −10? For the answer, we have the followng Rule of Signs.
When you multiply two negative signed answers the overall answer will be positive. But when you multiply one number that is positive and one number that is negative, the overall answer will be negative. I hope this was what you were looking for!
