That would make you feel comfortable that you are getting this right. and later we can think about other ways to get the intitution of what these might be allowed you to actually make sense but to make this make consistent with the rest of mathematics that you know, you go into a little bit of a thought experiment you say, well, what should five times three plus negative three equal well you already have a philosophy of adding negative numbers or adding positive numbers to negative numbers, you know negative three is the opposite of three, but you add three to negative three you're going to get zero, so this is going to be equal to five times zero based on how you already thought about adding a negative number to a positive, and anything times zero is going to be zero, so this expression right over here should be zero but you see, I want to multiply positive and negative numbers to be consistent with this distributive property so