Now that we recognize a little bit about multiplying positive and an adverse numbers, Let's think about how just how we deserve to divide them. Now what you'll see is that it's in reality a very comparable methodology. That if both are positive, you'll gain a confident answer. If one is negative, or the other, but not both, you'll acquire a an unfavorable answer. And also if both space negative, they'll publication out and also you'll gain a positive answer. However let's apply and I encourage friend to stop this video and try these out yourself and then see if you acquire the same answer that I'm going come get. For this reason eight (8) split by an adverse two (-2). For this reason if I just said eight (8) divided by two (2), that would certainly be a positive 4 (4), but due to the fact that exactly one of these two numbers room negative, this one right over here, the prize is walking to be negative. For this reason eight (8) divided by an unfavorable two (-2) is negative four (-4). Now an adverse sixteen (-16) separated by positive four (4)-- currently be very careful here. If I simply said optimistic sixteen (16) separated by positive four (4), the would simply be four (4). But since one of these two numbers is negative, and exactly among these two numbers is negative, climate I'm walking to get a an adverse answer. Now I have negative thirty (-30) split by an adverse five (-5). If I simply said thirty (30) divided by five (5), I'd gain a optimistic six (6). And because I have actually a negative divided by a negative, the negative cancel out, so my answer will still be hopeful six (6)! and also I could even compose a optimistic (+) the end there, ns don't have actually to, but this is a optimistic six (6). A negative divided by a negative, just like a an unfavorable times a negative, you're gonna obtain a hopeful answer. Eighteen (18) separated by two (2)! and this is a little bit the a cheat question. This is what you knew how to do prior to we even talked about an unfavorable numbers: This is a positive separated by a positive. Which is walk to be a positive. So the is going come be same to confident nine (9). Now we begin doing some exciting things, here's type of a link problem. We have some multiplication and also some division going on. And so first right end here, the means this is written, we're gonna wanna main point the molecule out, and if you're not acquainted with this small dot symbol, it's simply another means of writing multiplication. Ns could've composed this little "x" thing over here but what you're gonna view in Algebra is the the dot become much an ext common. Due to the fact that the X becomes used for other-- people don't want to confused it v the letter X which gets offered a lot of in Algebra. That's why they supplied the dot really often. Therefore this simply says an unfavorable seven (-7) times three (3) in the numerator, and also we're gonna take that product and divide the by an unfavorable one (-1). So the numerator, an adverse seven (-7) times 3 (3), positive seven (7) times 3 (3) would be twenty-one (21), but due to the fact that exactly one of these two space negative, this is going come be negative twenty-one (-21), that's gonna be negative twenty-one (-21) over negative one (-1). And so an adverse twenty-one (-21) split by an unfavorable one (-1), negative divided by a an adverse is going to be a positive. For this reason this is walking to it is in a optimistic twenty-one (21). Allow me write all these points down. For this reason if ns were to take it a positive divided by a negative, that's walk to be a negative. If I had actually a an unfavorable divided by a positive, that's additionally going to be a negative. If I have a negative divided through a negative, that's going to provide me a positive, and also if clear a positive split by a positive, that's likewise going to give me a positive. Currently let's execute this critical one end here. This is actually all multiplication, yet it's interesting, since we're multiplying 3 (3) things, which us haven't excellent yet. And we could just walk from left to appropriate over here, and also we could first think about negative two (-2) times an unfavorable seven (-7). An adverse two (-2) times an adverse seven (-7). They space both negatives, and negatives publication out, so this would give us, this component right over here, will offer us hopeful fourteen (14). And so we're going to multiply optimistic fourteen (14) time this negative one (-1), times -1. Currently we have actually a hopeful times a negative. Specifically one of castle is negative, so this is going come be an adverse answer, it's gonna offer me an adverse fourteen (-14). Now let me provide you a couple of more, ns guess us could call these cheat problems. What would take place if I had actually zero (0) split by an adverse five (-5). Well this is zero negative fifths for this reason zero separated by anything that's non-zero is simply going to same to zero. However what if it to be the other means around? What happens if us said negative five divided by zero? Well, we don't understand what happens when you divide points by zero. Us haven't identified that. There's arguments for multiple ways to conceptualize this, so us traditionally carry out say that this is undefined.
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We haven't defined what happens once something is separated by zero. And also similarly, even when we had zero separated by zero, this is still, this is still, undefined.