WEBVTT 00:00:00.940 --> 00:00:03.530 Welcome to the presentation on multiplying and 00:00:03.530 --> 00:00:05.270 dividing negative numbers. 00:00:05.270 --> 00:00:06.750 Let's get started. 00:00:06.750 --> 00:00:08.920 I think you're going to find that multiplying and dividing 00:00:08.920 --> 00:00:10.730 negative numbers are a lot easier than it might 00:00:10.760 --> 00:00:13.867 look initially. You just have to remember a couple of rules. 00:00:13.867 --> 00:00:16.168 And I am going to teach probably in the future like I'm actually going 00:00:16.168 --> 00:00:20.840 to give you more intuition on why there rules work. 00:00:20.994 --> 00:00:25.220 So the basic rules are when you multiply two negative numbers, 00:00:25.220 --> 00:00:31.790 so let's say I had negative 2 times negative 2. 00:00:31.790 --> 00:00:33.970 First you just look at each of the numbers as if there 00:00:33.970 --> 00:00:35.240 was no negative sign. 00:00:35.240 --> 00:00:40.150 Well you say well, 2 times 2 that equals 4. 00:00:40.150 --> 00:00:42.670 And it turns out that if you have a negative times a 00:00:42.670 --> 00:00:45.175 negative, that that equals a positive. 00:00:45.175 --> 00:00:47.710 So let's write that first rule down. 00:00:47.710 --> 00:00:54.285 A negative times a negative equals a positive. 00:00:56.854 --> 00:01:01.892 What if it was negative 2 times positive 2? 00:01:01.892 --> 00:01:04.770 Well in this case, let's first of all look at the 00:01:04.770 --> 00:01:06.060 two numbers without signs. 00:01:06.060 --> 00:01:10.170 We know that 2 times 2 is 4. 00:01:10.170 --> 00:01:13.740 But here we have a negative times a positive 2, and it 00:01:13.740 --> 00:01:15.910 turns out that when you multiply a negative times a 00:01:15.910 --> 00:01:18.920 positive you get a negative. 00:01:18.920 --> 00:01:20.260 So that's another rule. 00:01:20.260 --> 00:01:29.009 Negative times positive is equal to negative. 00:01:29.009 --> 00:01:34.786 What happens if you have a positive 2 times a negative 2? 00:01:34.786 --> 00:01:37.140 I think you'll probably guess this one right, as you can tell 00:01:37.140 --> 00:01:41.170 that these two are pretty much the same thing by, I believe 00:01:41.170 --> 00:01:44.800 it's the transitive property -- no, no I think it's the 00:01:44.800 --> 00:01:45.860 communicative property. 00:01:45.860 --> 00:01:47.700 I have to remember that. 00:01:47.700 --> 00:01:51.780 But 2 times negative 2, this also equals negative 4. 00:01:51.780 --> 00:01:57.640 So we have the final rule that a positive times a negative 00:01:57.640 --> 00:01:58.980 also equals the negative. 00:01:58.980 --> 00:02:01.490 And actually these second two rules, they're kind 00:02:03.985 --> 00:02:04.990 of the same thing. 00:02:04.990 --> 00:02:07.570 A negative times a positive is a negative, or a positive 00:02:07.570 --> 00:02:09.140 times a negative is negative. 00:02:09.140 --> 00:02:13.730 You could also say that as when the signs are different and 00:02:13.730 --> 00:02:16.400 you multiply the two numbers, you get a negative number. 00:02:16.400 --> 00:02:18.890 And of course, you already know what happens when you have a 00:02:18.890 --> 00:02:21.550 positive times a positive. 00:02:21.550 --> 00:02:22.840 Well that's just a positive. 00:02:22.840 --> 00:02:23.900 So let's review. 00:02:23.900 --> 00:02:27.970 Negative times a negative is a positive. 00:02:27.970 --> 00:02:30.390 A negative times a positive is a negative. 00:02:30.390 --> 00:02:32.730 A positive times a negative is a negative. 00:02:32.730 --> 00:02:36.290 And positive times each other equals positive. 00:02:36.290 --> 00:02:39.980 I think that last little bit completely confused you. 00:02:39.980 --> 00:02:42.270 Maybe I can simplify it for you. 00:02:42.270 --> 00:02:46.350 What if I just told you if when you're multiplying and they're 00:02:46.350 --> 00:02:55.175 the same signs that gets you a positive result. 00:02:55.175 --> 00:02:57.840 And different signs gets you a negative result. 00:03:11.010 --> 00:03:17.780 So that would be either, let's say a 1 times 1 is equal to 1, 00:03:17.780 --> 00:03:22.120 or if I said negative 1 times negative 1 is equal to 00:03:22.120 --> 00:03:23.510 positive 1 as well. 00:03:23.510 --> 00:03:29.150 Or if I said 1 times negative 1 is equal to negative 1, or 00:03:29.150 --> 00:03:32.600 negative 1 times 1 is equal to negative 1. 00:03:32.600 --> 00:03:36.130 You see how on the bottom two problems I had two different 00:03:36.130 --> 00:03:38.590 signs, positive 1 and negative 1? 00:03:38.590 --> 00:03:41.120 And the top two problems, this one right here 00:03:41.120 --> 00:03:42.680 both 1s are positive. 00:03:42.680 --> 00:03:45.970 And this one right here both 1s are negative. 00:03:45.970 --> 00:03:49.110 So let's do a bunch of problems now, and hopefully it'll hit 00:03:49.110 --> 00:03:51.510 the point home, and you also could try to do along the 00:03:51.510 --> 00:03:56.195 practice problems and also give the hints and give you what rules to you so that should help you as well 00:04:02.855 --> 00:04:06.750 So if I said negative 4 times positive 3, well 4 times 00:04:06.750 --> 00:04:11.820 3 is 12, and we have a negative and a positive. 00:04:11.820 --> 00:04:15.670 So different signs mean negative. 00:04:15.670 --> 00:04:19.060 So negative 4 times 3 is a negative 12. 00:04:19.060 --> 00:04:21.310 That makes sense because we're essentially saying what's 00:04:21.310 --> 00:04:25.070 negative 4 times itself three times, so it's like negative 4 00:04:25.070 --> 00:04:27.800 plus negative 4 plus negative 4, which is negative 12. 00:04:27.800 --> 00:04:31.120 If you've seen the video on adding and subtracting negative 00:04:31.120 --> 00:04:34.200 numbers, you probably should watch first. 00:04:34.200 --> 00:04:35.210 Let's do another one. 00:04:35.210 --> 00:04:40.430 What if I said minus 2 times minus 7. 00:04:40.430 --> 00:04:42.470 And you might want to pause the video at any time to see if you 00:04:42.470 --> 00:04:44.030 know how to do it and then restart it to see 00:04:44.030 --> 00:04:45.420 what the answer is. 00:04:45.420 --> 00:04:51.190 Well, 2 times 7 is 14, and we have the same sign here, so 00:04:51.190 --> 00:04:53.530 it's a positive 14 -- normally you wouldn't have to write the 00:04:53.530 --> 00:04:56.930 positive but that makes it a little bit more explicit. 00:04:56.930 --> 00:05:05.880 And what if I had -- let me think -- 9 times negative 5. 00:05:05.880 --> 00:05:08.800 Well, 9 times 5 is 45. 00:05:08.800 --> 00:05:13.660 And once again, the signs are different so it's a negative. 00:05:13.660 --> 00:05:18.010 And then finally what if it I had -- let me think of some 00:05:18.010 --> 00:05:24.540 good numbers -- minus 6 times minus 11. 00:05:24.540 --> 00:05:29.730 Well, 6 times 11 is 66 and then it's a negative and 00:05:29.730 --> 00:05:31.720 negative, it's a positive. 00:05:31.720 --> 00:05:32.910 Let me give you a trick problem. 00:05:32.910 --> 00:05:39.100 What is 0 times negative 12? 00:05:39.100 --> 00:05:42.740 Well, you might say that the signs are different, but 00:05:42.740 --> 00:05:46.460 0 is actually neither positive nor negative. 00:05:46.460 --> 00:05:48.315 And 0 times anything is still 0. 00:05:48.315 --> 00:05:52.080 It doesn't matter if the thing you multiply it by is a 00:05:52.080 --> 00:05:53.650 negative number or a positive number. 00:05:53.650 --> 00:05:57.630 0 times anything is still 0. 00:05:57.630 --> 00:06:00.020 So let's see if we can apply these same rules to division. 00:06:00.020 --> 00:06:03.080 It actually turns out that the same rules apply. 00:06:03.080 --> 00:06:09.030 If I have 9 divided by negative 3. 00:06:09.030 --> 00:06:11.820 Well, first we say what's 9 divided by 3? 00:06:11.820 --> 00:06:13.640 Well that's 3. 00:06:13.640 --> 00:06:17.920 And they have different signs, positive 9, negative 3. 00:06:17.920 --> 00:06:22.190 So different signs means a negative. 00:06:22.190 --> 00:06:27.520 9 divided by negative 3 is equal to negative 3. 00:06:27.520 --> 00:06:33.830 What is minus 16 divided by 8? 00:06:33.830 --> 00:06:37.790 Well, once again, 16 divided by 8 is 2, but 00:06:37.790 --> 00:06:39.370 the signs are different. 00:06:39.370 --> 00:06:44.830 Negative 16 divided by positive 8, that equals negative 2. 00:06:44.830 --> 00:06:49.140 Remember, different signs will get you a negative result. 00:06:49.140 --> 00:07:00.500 What is minus 54 divided by minus 6? 00:07:00.500 --> 00:07:04.320 Well, 54 divided by 6 is 9. 00:07:04.320 --> 00:07:09.050 And since both terms, the divisor and the dividend, are 00:07:11.470 --> 00:07:13.890 both negative -- negative 54 and negative 6 -- it turns out 00:07:13.930 --> 00:07:18.193 that the answer is positive. Remember, same signs 00:07:18.193 --> 00:07:18.985 result in a positive sign. 00:07:22.470 --> 00:07:24.730 Let's do one more. 00:07:24.730 --> 00:07:30.500 Obviously, 0 divided by anything is still 0. 00:07:30.500 --> 00:07:31.510 That's pretty straightforward. 00:07:31.510 --> 00:07:33.200 And of course, you can't divide anything by 0 00:07:33.200 --> 00:07:36.210 -- that's undefined. 00:07:36.210 --> 00:07:38.420 Let's do one more. 00:07:38.420 --> 00:07:41.890 What is -- I'm just going to think of random numbers -- 00:07:41.890 --> 00:07:44.930 4 divided by negative 1? 00:07:44.930 --> 00:07:50.610 Well, 4 divided by 1 is 4, but the signs are different. 00:07:50.610 --> 00:07:53.130 So it's negative 4. 00:07:53.130 --> 00:07:54.410 I hope that helps. 00:07:54.410 --> 00:07:56.865 Now what I want you to do is actually try 00:07:56.865 --> 00:08:01.380 as many of these multiplying and dividing negative numbers as you can. 00:08:01.380 --> 00:08:03.010 And you click on hints 00:08:03.010 --> 00:08:04.260 and it'll remind you of which rule to use. 00:08:04.260 --> 00:08:09.445 In your own time you might want to actually think about 00:08:09.460 --> 00:08:11.459 why these rules apply and what it means 00:08:11.459 --> 00:08:15.320 to multiply a negative number times a positive number. 00:08:15.320 --> 00:08:16.982 And even more interesting, what it means 00:08:16.982 --> 00:08:20.230 to multiply a negative number times a negative number. 00:08:20.230 --> 00:08:23.215 But I think at this point, 00:08:23.215 --> 00:08:27.160 hopefully, you are ready to start doing some problems. 00:08:27.160 --> 00:08:29.020 Good luck.