Relating multiplication and division with negative numbers

0:00- [Presenter] We're told to fill in the blanks. Pause this video, see if you could do this on your own before we do this together. Okay. Well, they're saying that something divided by 0.25 is equal to negative eight because negative eight times 0.25 is equal to that same something.

0:19So for a lot of us, including for me, it's easier for me to think about what negative eight times 0.25 is, than to initially think about what dividing by 0.25 means. So if we take negative eight times 0.25, 0.25 is also the same thing as one-fourth. So if we said one-fourth of negative eight, that's going to be negative two.

0:43Remember, a negative times a positive is going to be a negative. If you have different signs, you're going to have a negative. If you have the same sign, both negatives or both positives, you're going to get a positive. So that would also tell us that if we took negative two, and if we were to divide it by 0.25, then we would get to negative eight.

1:01So we could fill this in right over here. And just to make sure this is making sense to you, remember, negative two divided by 0.25, that is the same thing as negative two divided by one-fourth, which is the same thing when you divide by a fraction, that's the same thing as multiplying by its reciprocal, times four over one or just four.

1:24And so that's why it makes sense that that is equal to negative eight.