Adding two negative numbers makes a negative sum: (-a)+(-b)=-a-b=-(a+b). Example: if the temperature yesterday was -1° and today it's two degrees lower, then the temperature today is -1-2=-3°C. -1-2=-(1+2)=-3. The sum just becomes more negative..
Multiplying two negative numbers makes a positive product. To understand this, consider -1 on a number line, which is 1 unit to the left of zero. If we multiply -1 by 1, it doesn't change, so -1×1=-1; multiplying anything by 1 doesn't change that thing. Now consider 1 on a number line (1 unit to the right of zero.) Since -1×1 is the same as 1×(-1)=-1, so multiplying by -1 has reflected 1 (which was 1 unit to the right of zero) to 1 unit to the left of zero, which is -1. Therefore -1×(-1) causes -1 (1 unit to the left of zero) to be reflected to become 1 (1 unit to the right of zero). A negative number -a is a units to the left of zero. Multiplying it by -1 causes it to be reflected, making it a units to the right of zero, that is, positive a. Multiplying -a by -b causes it to be reflected AND multiplied so that it's ab units to the right of zero.