1 00:00:00,938 --> 00:00:04,559 Now that we know a little bit about multiplying positive and negative numbers, 2 00:00:04,559 --> 00:00:06,649 Let's think about how how we can divide them. 3 00:00:06,649 --> 00:00:08,562 Now what you'll see is that it's actually 4 00:00:08,562 --> 00:00:10,632 a very similar methodology. 5 00:00:10,632 --> 00:00:12,164 That if both are positive, 6 00:00:12,164 --> 00:00:15,455 you'll get a positive answer. If one is negative, 7 00:00:15,455 --> 00:00:18,890 or the other, but not both, you'll get a negative answer. 8 00:00:18,890 --> 00:00:22,542 And if both are negative, they'll cancel out and you'll get a positive answer. 9 00:00:22,542 --> 00:00:26,359 But let's apply and I encourage you to pause this video and try these out yourself 10 00:00:26,359 --> 00:00:29,473 and then see if you get the same answer that I'm going to get. 11 00:00:29,473 --> 00:00:32,840 So eight (8) divided by negative two (-2). 12 00:00:32,840 --> 00:00:35,957 So if I just said eight (8) divided by two (2), that would be 13 00:00:35,957 --> 00:00:40,326 a positive four (4), but since exactly one of these two numbers 14 00:00:40,326 --> 00:00:45,425 are negative, this one right over here, the answer is going to be negative. 15 00:00:45,425 --> 00:00:49,556 So eight (8) divided by negative two (-2) is negative four (-4). 16 00:00:49,556 --> 00:00:53,425 Now negative sixteen (-16) divided by positive four (4)-- 17 00:00:53,425 --> 00:00:54,423 now be very careful here. 18 00:00:54,423 --> 00:00:59,727 If I just said positive sixteen (16) divided by positive four (4), that would just be four (4). 19 00:00:59,727 --> 00:01:02,675 But because one of these two numbers is negative, 20 00:01:02,675 --> 00:01:05,121 and exactly one of these two numbers is negative, 21 00:01:05,121 --> 00:01:09,104 then I'm going to get a negative answer. 22 00:01:09,104 --> 00:01:12,174 Now I have negative thirty (-30) divided by negative five (-5). 23 00:01:12,174 --> 00:01:17,285 If I just said thirty (30) divided by five (5), I'd get a positive six (6). 24 00:01:17,285 --> 00:01:20,573 And because I have a negative divided by a negative, 25 00:01:20,573 --> 00:01:25,631 the negatives cancel out, so my answer will still be positive six (6)! 26 00:01:25,631 --> 00:01:27,332 And I could even write a positive (+) out there, I don't have to, 27 00:01:27,332 --> 00:01:30,448 but this is a positive six (6). 28 00:01:30,448 --> 00:01:34,065 A negative divided by a negative, just like a negative times a negative, 29 00:01:34,065 --> 00:01:37,063 you're gonna get a positive answer. 30 00:01:37,063 --> 00:01:39,035 Eighteen (18) divided by two (2)! 31 00:01:39,035 --> 00:01:40,612 And this is a little bit of a trick question. 32 00:01:40,612 --> 00:01:43,934 This is what you knew how to do before we even talked about negative numbers: 33 00:01:43,934 --> 00:01:47,067 This is a positive divided by a positive. 34 00:01:47,067 --> 00:01:49,035 Which is going to be a positive. 35 00:01:49,035 --> 00:01:52,918 So that is going to be equal to positive nine (9). 36 00:01:52,918 --> 00:01:55,769 Now we start doing some interesting things, 37 00:01:55,769 --> 00:01:57,967 here's kind of a compound problem. 38 00:01:57,967 --> 00:02:01,464 We have some multiplication and some division going on. 39 00:02:01,464 --> 00:02:03,698 And so first right over here, the way this is written, 40 00:02:03,698 --> 00:02:06,030 we're gonna wanna multiply the numerator out, 41 00:02:06,030 --> 00:02:07,794 and if you're not familiar with this little dot symbol, 42 00:02:07,794 --> 00:02:10,164 it's just another way of writing multiplication. 43 00:02:10,164 --> 00:02:12,381 I could've written this little "x" thing over here 44 00:02:12,381 --> 00:02:15,628 but what you're gonna see in Algebra is that the dot become much more common. 45 00:02:15,628 --> 00:02:17,358 Because the X becomes used for other-- 46 00:02:17,358 --> 00:02:23,383 People don't want to confuse it with the letter X 47 00:02:23,383 --> 00:02:25,584 which gets used a lot in Algebra. 48 00:02:25,584 --> 00:02:27,927 That's why they used the dot very often. 49 00:02:27,927 --> 00:02:31,093 So this just says negative seven (-7) times three (3) 50 00:02:31,093 --> 00:02:33,447 in the numerator, and we're gonna take that product 51 00:02:33,447 --> 00:02:35,597 and divide it by negative one (-1). 52 00:02:35,597 --> 00:02:37,640 So the numerator, negative seven (-7) times three (3), 53 00:02:37,640 --> 00:02:41,437 positive seven (7) times three (3) would be twenty-one (21), 54 00:02:41,437 --> 00:02:45,303 but since exactly one of these two are negative, 55 00:02:45,303 --> 00:02:47,078 this is going to be negative twenty-one (-21), 56 00:02:47,078 --> 00:02:49,732 that's gonna be negative twenty-one (-21) over negative one (-1). 57 00:02:49,732 --> 00:02:51,894 And so negative twenty-one (-21) divided by negative one (-1), 58 00:02:51,894 --> 00:02:54,944 negative divided by a negative is going to be a positive. 59 00:02:54,944 --> 00:02:57,920 So this is going to be a positive twenty-one (21). 60 00:02:57,920 --> 00:02:59,510 Let me write all these things down. 61 00:02:59,510 --> 00:03:03,266 So if I were to take a positive divided by a negative, 62 00:03:03,266 --> 00:03:07,425 that's going to be a negative. 63 00:03:07,425 --> 00:03:11,407 If I had a negative divided by a positive, 64 00:03:11,407 --> 00:03:15,121 that's also going to be a negative. 65 00:03:15,121 --> 00:03:18,020 If I have a negative divided by a negative, 66 00:03:18,020 --> 00:03:20,454 that's going to give me a positive, 67 00:03:20,454 --> 00:03:24,954 and if obviously a positive divided by a positive, 68 00:03:24,954 --> 00:03:27,770 that's also going to give me a positive. 69 00:03:27,770 --> 00:03:29,359 Now let's do this last one over here. 70 00:03:29,359 --> 00:03:30,589 This is actually all multiplication, 71 00:03:30,589 --> 00:03:31,989 but it's interesting, because we're multiplying 72 00:03:31,989 --> 00:03:34,539 three (3) things, which we haven't done yet. 73 00:03:34,539 --> 00:03:37,116 And we could just go from left to right over here, 74 00:03:37,116 --> 00:03:39,405 and we could first think about negative two (-2) times 75 00:03:39,405 --> 00:03:41,089 negative seven (-7). 76 00:03:41,089 --> 00:03:42,627 Negative two (-2) times negative seven (-7). 77 00:03:42,627 --> 00:03:44,043 They are both negatives, and 78 00:03:44,043 --> 00:03:45,094 negatives cancel out, so this would give us, 79 00:03:45,094 --> 00:03:46,844 this part right over here, 80 00:03:46,844 --> 00:03:49,539 will give us positive fourteen (14). 81 00:03:49,539 --> 00:03:51,408 And so we're going to multiply positive fourteen (14) 82 00:03:51,408 --> 00:03:55,207 times this negative one (-1), times -1. 83 00:03:55,207 --> 00:03:57,908 Now we have a positive times a negative. 84 00:03:57,908 --> 00:03:59,590 Exactly one of them is negative, 85 00:03:59,590 --> 00:04:01,470 so this is going to be negative answer, 86 00:04:01,470 --> 00:04:05,020 it's gonna give me negative fourteen (-14). 87 00:04:05,020 --> 00:04:06,087 Now let me give you a couple of more, 88 00:04:06,087 --> 00:04:08,655 I guess we could call these trick problems. 89 00:04:08,655 --> 00:04:12,070 What would happen if I had zero (0) divided by 90 00:04:12,070 --> 00:04:14,252 negative five (-5). 91 00:04:14,252 --> 00:04:16,503 Well this is zero negative fifths 92 00:04:16,503 --> 00:04:19,219 So zero divided by anything that's non-zero 93 00:04:19,219 --> 00:04:22,355 is just going to equal to zero. 94 00:04:22,355 --> 00:04:25,035 But what if it were the other way around? 95 00:04:25,035 --> 00:04:27,371 What happens if we said negative five divided by zero? 96 00:04:27,371 --> 00:04:29,837 Well, we don't know what happens when you divide things by zero. 97 00:04:29,837 --> 00:04:31,522 We haven't defined that. 98 00:04:31,522 --> 00:04:35,254 There's arguments for multiple ways to conceptualize this, 99 00:04:35,254 --> 00:04:38,301 so we traditionally do say that this is undefined. 100 00:04:38,301 --> 00:04:43,213 We haven't defined what happens when something is divided by zero. 101 00:04:43,213 --> 00:04:46,347 And similarly, even when we had zero divided by zero, 102 00:04:46,347 --> 00:04:50,431 this is still, this is still, undefined.