0:00:00.938,0:00:04.559 Now that we know a little bit about multiplying positive and negative numbers, 0:00:04.559,0:00:06.649 Let's think about how how we can divide them. 0:00:06.649,0:00:08.562 Now what you'll see is that it's actually 0:00:08.562,0:00:10.632 a very similar methodology. 0:00:10.632,0:00:12.164 That if both are positive, 0:00:12.164,0:00:15.455 you'll get a positive answer. If one is negative, 0:00:15.455,0:00:18.890 or the other, but not both, you'll get a negative answer. 0:00:18.890,0:00:22.542 And if both are negative, they'll cancel out and you'll get a positive answer. 0:00:22.542,0:00:26.359 But let's apply and I encourage you to pause this video and try these out yourself 0:00:26.359,0:00:29.473 and then see if you get the same answer that I'm going to get. 0:00:29.473,0:00:32.840 So eight (8) divided by negative two (-2). 0:00:32.840,0:00:35.957 So if I just said eight (8) divided by two (2), that would be 0:00:35.957,0:00:40.326 a positive four (4), but since exactly one of these two numbers 0:00:40.326,0:00:45.425 are negative, this one right over here, the answer is going to be negative. 0:00:45.425,0:00:49.556 So eight (8) divided by negative two (-2) is negative four (-4). 0:00:49.556,0:00:53.425 Now negative sixteen (-16) divided by positive four (4)-- 0:00:53.425,0:00:54.423 now be very careful here. 0:00:54.423,0:00:59.727 If I just said positive sixteen (16) divided by positive four (4), that would just be four (4). 0:00:59.727,0:01:02.675 But because one of these two numbers is negative, 0:01:02.675,0:01:05.121 and exactly one of these two numbers is negative, 0:01:05.121,0:01:09.104 then I'm going to get a negative answer. 0:01:09.104,0:01:12.174 Now I have negative thirty (-30) divided by negative five (-5). 0:01:12.174,0:01:17.285 If I just said thirty (30) divided by five (5), I'd get a positive six (6). 0:01:17.285,0:01:20.573 And because I have a negative divided by a negative, 0:01:20.573,0:01:25.631 the negatives cancel out, so my answer will still be positive six (6)! 0:01:25.631,0:01:27.332 And I could even write a positive (+) out there, I don't have to, 0:01:27.332,0:01:30.448 but this is a positive six (6). 0:01:30.448,0:01:34.065 A negative divided by a negative, just like a negative times a negative, 0:01:34.065,0:01:37.063 you're gonna get a positive answer. 0:01:37.063,0:01:39.035 Eighteen (18) divided by two (2)! 0:01:39.035,0:01:40.612 And this is a little bit of a trick question. 0:01:40.612,0:01:43.934 This is what you knew how to do before we even talked about negative numbers: 0:01:43.934,0:01:47.067 This is a positive divided by a positive. 0:01:47.067,0:01:49.035 Which is going to be a positive. 0:01:49.035,0:01:52.918 So that is going to be equal to positive nine (9). 0:01:52.918,0:01:55.769 Now we start doing some interesting things, 0:01:55.769,0:01:57.967 here's kind of a compound problem. 0:01:57.967,0:02:01.464 We have some multiplication and some division going on. 0:02:01.464,0:02:03.698 And so first right over here, the way this is written, 0:02:03.698,0:02:06.030 we're gonna wanna multiply the numerator out, 0:02:06.030,0:02:07.794 and if you're not familiar with this little dot symbol, 0:02:07.794,0:02:10.164 it's just another way of writing multiplication. 0:02:10.164,0:02:12.381 I could've written this little "x" thing over here 0:02:12.381,0:02:15.628 but what you're gonna see in Algebra is that the dot become much more common. 0:02:15.628,0:02:17.358 Because the X becomes used for other-- 0:02:17.358,0:02:23.383 People don't want to confuse it with the letter X 0:02:23.383,0:02:25.584 which gets used a lot in Algebra. 0:02:25.584,0:02:27.927 That's why they used the dot very often. 0:02:27.927,0:02:31.093 So this just says negative seven (-7) times three (3) 0:02:31.093,0:02:33.447 in the numerator, and we're gonna take that product 0:02:33.447,0:02:35.597 and divide it by negative one (-1). 0:02:35.597,0:02:37.640 So the numerator, negative seven (-7) times three (3), 0:02:37.640,0:02:41.437 positive seven (7) times three (3) would be twenty-one (21), 0:02:41.437,0:02:45.303 but since exactly one of these two are negative, 0:02:45.303,0:02:47.078 this is going to be negative twenty-one (-21), 0:02:47.078,0:02:49.732 that's gonna be negative twenty-one (-21) over negative one (-1). 0:02:49.732,0:02:51.894 And so negative twenty-one (-21) divided by negative one (-1), 0:02:51.894,0:02:54.944 negative divided by a negative is going to be a positive. 0:02:54.944,0:02:57.920 So this is going to be a positive twenty-one (21). 0:02:57.920,0:02:59.510 Let me write all these things down. 0:02:59.510,0:03:03.266 So if I were to take a positive divided by a negative, 0:03:03.266,0:03:07.425 that's going to be a negative. 0:03:07.425,0:03:11.407 If I had a negative divided by a positive, 0:03:11.407,0:03:15.121 that's also going to be a negative. 0:03:15.121,0:03:18.020 If I have a negative divided by a negative, 0:03:18.020,0:03:20.454 that's going to give me a positive, 0:03:20.454,0:03:24.954 and if obviously a positive divided by a positive, 0:03:24.954,0:03:27.770 that's also going to give me a positive. 0:03:27.770,0:03:29.359 Now let's do this last one over here. 0:03:29.359,0:03:30.589 This is actually all multiplication, 0:03:30.589,0:03:31.989 but it's interesting, because we're multiplying 0:03:31.989,0:03:34.539 three (3) things, which we haven't done yet. 0:03:34.539,0:03:37.116 And we could just go from left to right over here, 0:03:37.116,0:03:39.405 and we could first think about negative two (-2) times 0:03:39.405,0:03:41.089 negative seven (-7). 0:03:41.089,0:03:42.627 Negative two (-2) times negative seven (-7). 0:03:42.627,0:03:44.043 They are both negatives, and 0:03:44.043,0:03:45.094 negatives cancel out, so this would give us, 0:03:45.094,0:03:46.844 this part right over here, 0:03:46.844,0:03:49.539 will give us positive fourteen (14). 0:03:49.539,0:03:51.408 And so we're going to multiply positive fourteen (14) 0:03:51.408,0:03:55.207 times this negative one (-1), times -1. 0:03:55.207,0:03:57.908 Now we have a positive times a negative. 0:03:57.908,0:03:59.590 Exactly one of them is negative, 0:03:59.590,0:04:01.470 so this is going to be negative answer, 0:04:01.470,0:04:05.020 it's gonna give me negative fourteen (-14). 0:04:05.020,0:04:06.087 Now let me give you a couple of more, 0:04:06.087,0:04:08.655 I guess we could call these trick problems. 0:04:08.655,0:04:12.070 What would happen if I had zero (0) divided by 0:04:12.070,0:04:14.252 negative five (-5). 0:04:14.252,0:04:16.503 Well this is zero negative fifths 0:04:16.503,0:04:19.219 So zero divided by anything that's non-zero 0:04:19.219,0:04:22.355 is just going to equal to zero. 0:04:22.355,0:04:25.035 But what if it were the other way around? 0:04:25.035,0:04:27.371 What happens if we said negative five divided by zero? 0:04:27.371,0:04:29.837 Well, we don't know what happens when you divide things by zero. 0:04:29.837,0:04:31.522 We haven't defined that. 0:04:31.522,0:04:35.254 There's arguments for multiple ways to conceptualize this, 0:04:35.254,0:04:38.301 so we traditionally do say that this is undefined. 0:04:38.301,0:04:43.213 We haven't defined what happens when something is divided by zero. 0:04:43.213,0:04:46.347 And similarly, even when we had zero divided by zero, 0:04:46.347,0:04:50.431 this is still, this is still, undefined.