WEBVTT 00:00:01.060 --> 00:00:03.366 Welcome to the presentation 00:00:03.366 --> 00:00:05.066 on adding and subtracting negative numbers. 00:00:05.066 --> 00:00:06.380 So let's get started. 00:00:06.380 --> 00:00:08.510 So what is a negative number, first of all? 00:00:08.520 --> 00:00:12.080 Well, let me draw a number line. 00:00:12.080 --> 00:00:13.295 Well it's not much of a line, 00:00:13.295 --> 00:00:15.190 but I think you'll get the picture. 00:00:15.190 --> 00:00:18.797 So we're used to the positive numbers, so if that's 0 00:00:18.797 --> 00:00:24.670 you have one, you have 2, you have 3, you have 4 00:00:24.670 --> 00:00:25.686 and you keep going. 00:00:25.686 --> 00:00:28.548 And if I were to say what's 2+2 00:00:28.548 --> 00:00:30.780 you'd start at 2, and then you'd add 2 00:00:30.780 --> 00:00:31.460 you'd get to 4. 00:00:31.460 --> 00:00:32.140 I mean most of us it's second nature. 00:00:32.150 --> 00:00:33.930 But if you actually drew it on a number line, 00:00:33.930 --> 00:00:36.130 you'd say 2+2=4 00:00:36.140 --> 00:00:38.490 And if I asked you what's 2-1 00:00:38.490 --> 00:00:39.840 or let's say what's 3-2 00:00:39.840 --> 00:00:44.111 If you start at 3 and you subtracted 2 00:00:44.111 --> 00:00:45.658 you would end up at 1 00:00:45.658 --> 00:00:51.248 That's 2+2=4, and 3-2=1 00:00:51.248 --> 00:00:52.980 And this is a joke for you. 00:00:52.990 --> 00:00:56.990 Now what if I were to say what is 1-3? 00:00:56.990 --> 00:00:58.150 Huh. 00:00:58.150 --> 00:01:00.100 Well, it's the same thing. 00:01:00.100 --> 00:01:03.847 You start at 1 and we're going to go 1-- 00:01:03.847 --> 00:01:06.960 well, now we're going to go below 0 00:01:06.960 --> 00:01:07.730 what happens below 0? 00:01:07.730 --> 00:01:08.500 Well then you start going to the negative numbers. 00:01:08.510 --> 00:01:14.930 -1, -2, -3, and so on. 00:01:14.930 --> 00:01:20.909 So if I start at 1 right here, so 1-3 00:01:20.909 --> 00:01:25.610 so I go 1,2,3, I end up at -2 00:01:25.620 --> 00:01:30.680 So 1-3=-2 00:01:30.680 --> 00:01:33.080 This is something that you're probably already doing 00:01:33.090 --> 00:01:34.729 in your everyday life 00:01:34.729 --> 00:01:37.137 If I were to tell you that 00:01:37.137 --> 00:01:39.225 boy, it's very cold today, it's one degree, 00:01:39.225 --> 00:01:40.728 but tomorrow it's going to be three degrees colder, 00:01:40.728 --> 00:01:42.038 you might already know intuitively, 00:01:42.038 --> 00:01:44.502 well then we're going to be 00:01:44.502 --> 00:01:46.925 at a temperature of negative two degrees. 00:01:46.925 --> 00:01:48.040 So that's all a negative number means. 00:01:48.040 --> 00:01:51.132 And just remember when a negative number is big, 00:01:51.132 --> 00:01:58.090 so like -50, that's actually colder than -20, right? 00:01:58.090 --> 00:02:01.710 So a -50 is actually even a smaller number than -20 00:02:01.710 --> 00:02:04.926 because it's even further to the left of -20 00:02:04.926 --> 00:02:07.160 That's just something you'll get an intuitive feel for. 00:02:07.170 --> 00:02:08.708 Sometimes when you start you feel like 00:02:08.708 --> 00:02:10.185 oh, 50 is a bigger number than 20 00:02:10.185 --> 00:02:13.860 but it's a -50 as opposed to a 50 00:02:13.860 --> 00:02:15.306 So let's do some problems, 00:02:15.306 --> 00:02:19.270 and I'm going to keep using the number line 00:02:19.280 --> 00:02:22.415 because I think it's useful 00:02:22.415 --> 00:02:26.872 So let's do the problem 5-12 00:02:26.872 --> 00:02:29.785 I think you already might have an intuition 00:02:29.785 --> 00:02:34.195 of what this equals. 00:02:34.195 --> 00:02:45.144 But let me draw a line, 5-12 00:02:45.144 --> 00:02:53.068 So let me start with -10, -9, -8-- 00:02:53.068 --> 00:02:58.780 I think I'm going to run out of space-- -7, -6, -5 00:02:58.780 --> 00:03:05.155 I should have this pre-drawn -- -4, -3, -2, -1 00:03:05.155 --> 00:03:12.537 0,1,2,3,4, and I'll put 5 right here. 00:03:12.537 --> 00:03:14.494 I'm gonna push this arrow out a little bit. Okay. 00:03:14.494 --> 00:03:15.548 5-12 00:03:15.560 --> 00:03:18.430 So if we start at 5-- let me use a different color-- 00:03:18.430 --> 00:03:20.945 we start at 5 right here and we're going to go to the left 12 00:03:20.945 --> 00:03:22.805 because we're subtracting 12 00:03:22.805 --> 00:03:33.870 So then we go 1,2,3... 00:03:33.870 --> 00:03:38.262 Negative 7 00:03:38.262 --> 00:03:39.993 That's pretty interesting. 00:03:40.000 --> 00:03:42.789 Because it also happens to be 00:03:42.789 --> 00:03:45.580 that 12 - 5 = +7 00:03:45.590 --> 00:03:48.900 So, I want you to think a little bit about why that is. 00:03:48.900 --> 00:03:52.939 Why the difference between 12 and 5 is 7, 00:03:52.939 --> 00:03:58.918 and the difference between 00:03:58.918 --> 00:04:00.038 -- well, I guess it's either way. 00:04:00.038 --> 00:04:01.097 In this situation we're also saying 00:04:01.097 --> 00:04:03.812 that the difference between 5 and 12 is -7, 00:04:03.812 --> 00:04:05.162 but the numbers are that far apart, 00:04:05.162 --> 00:04:07.496 but now we're starting with the lower number. 00:04:07.496 --> 00:04:09.538 I think that last sentence just completely confused you, 00:04:09.538 --> 00:04:11.789 but we'll keep moving forward. 00:04:11.789 --> 00:04:18.060 We just said 5-12=-7 00:04:18.060 --> 00:04:19.434 Let's do another one. 00:04:19.434 --> 00:04:25.843 What's -3+5? 00:04:25.843 --> 00:04:28.050 Well, let's use the same number line. 00:04:28.060 --> 00:04:31.490 Let's go to -3 plus 5 00:04:31.490 --> 00:04:33.580 So we're going to go to the right 5 00:04:33.580 --> 00:04:38.425 One, two, three, four, five. 00:04:38.425 --> 00:04:42.602 It's a two. 00:04:42.602 --> 00:04:44.363 It equals two. 00:04:44.363 --> 00:04:48.790 So -3 + 5 = 2 00:04:48.790 --> 00:04:53.843 That's interesting because 5 - 3 is also equal to 2 00:04:53.843 --> 00:04:57.007 Well, it turns out that 5 - 3 is the same thing, 00:04:57.007 --> 00:05:00.252 it's just another way of writing 5 plus -3 00:05:00.252 --> 00:05:04.050 or -3 plus 5 00:05:04.050 --> 00:05:07.052 A general, easy way to always do negative numbers 00:05:07.052 --> 00:05:11.640 is it's just like regular addition and subtraction, 00:05:11.640 --> 00:05:15.456 but now when we subtract 00:05:15.456 --> 00:05:18.634 we can go to the left below zero 00:05:18.634 --> 00:05:19.826 Let's do another one. 00:05:19.826 --> 00:05:21.587 So what happens when you get 00:05:21.587 --> 00:05:27.111 let's say, 2 minus -3? 00:05:27.111 --> 00:05:30.747 Well, if you think about how it should work out, 00:05:30.747 --> 00:05:32.079 I think this will make sense. 00:05:32.079 --> 00:05:34.135 But it turns out that the negative number, 00:05:34.135 --> 00:05:36.140 the negative signs actually cancel out. 00:05:36.140 --> 00:05:40.425 So this is the same thing as 2 plus +3 00:05:40.425 --> 00:05:43.050 and that just equals 5 00:05:43.060 --> 00:05:46.305 Another way you could say is-- let's do another one-- 00:05:46.305 --> 00:05:52.866 what is -7 minus -2? 00:05:52.866 --> 00:05:58.010 Well that's the same thing as -7 + 2 00:05:58.020 --> 00:06:00.144 And remember, so we're doing to start at -7 00:06:00.144 --> 00:06:03.560 and we're going to move 2 to the right. 00:06:03.560 --> 00:06:06.224 So if we move 1 to the right we go to -6 00:06:06.224 --> 00:06:11.392 and then we move 2 to the right we get -5 00:06:11.392 --> 00:06:13.755 That makes sense because -7 + 2 00:06:13.755 --> 00:06:16.540 that's the same thing as 2 - 7 00:06:16.550 --> 00:06:19.351 If it's two degrees and 00:06:19.351 --> 00:06:22.475 it gets seven degrees colder, it's -5 00:06:22.475 --> 00:06:23.230 Let's do a bunch of these. 00:06:23.240 --> 00:06:25.253 I think the more you do, the more practice you have, 00:06:25.253 --> 00:06:26.847 and the modules explain it pretty well. 00:06:26.847 --> 00:06:29.056 Probably better than I do. 00:06:29.056 --> 00:06:31.104 So let's just do a ton of problems. 00:06:31.104 --> 00:06:36.473 So if I said -7 - 3 00:06:36.473 --> 00:06:39.396 Well, now we're going to go 3 to the left of -7 00:06:39.410 --> 00:06:41.386 We're going to get 3 less than -7 00:06:41.386 --> 00:06:45.420 so that's -10, right? 00:06:45.430 --> 00:06:49.055 That makes sense, because if we had 7 + 3 00:06:49.055 --> 00:06:50.762 we're at 7 to the right of 0 00:06:50.762 --> 00:06:52.504 and we're going to go 3 more to the right of 0 00:06:52.504 --> 00:06:54.538 and we get positive 10 00:06:54.538 --> 00:06:57.385 So for 7 to the left of 0 and go 3 more to the left, 00:06:57.385 --> 00:06:58.680 we're going to get -10 00:06:58.680 --> 00:06:59.460 Let's do a bunch more. 00:06:59.470 --> 00:07:01.048 I know I'm probably confusing you, 00:07:01.048 --> 00:07:04.218 but practice is what's going to really help us. 00:07:04.218 --> 00:07:09.118 So let's say 3 minus -3 00:07:09.118 --> 00:07:12.360 well, these negatives cancel out, 00:07:12.360 --> 00:07:14.570 so that just equals 6 00:07:14.570 --> 00:07:17.088 What's 3-3? 00:07:17.088 --> 00:07:18.687 Well, 3-3, that's easy. 00:07:18.687 --> 00:07:20.687 That's just 0 00:07:20.687 --> 00:07:23.980 What's -3 nimus 3? 00:07:23.990 --> 00:07:26.420 Well now we're going to get 3 less than -3 00:07:26.420 --> 00:07:28.880 well that's -6 00:07:28.880 --> 00:07:34.030 What's -3 minus -3 00:07:34.040 --> 00:07:35.500 Interesting. 00:07:35.500 --> 00:07:40.790 Well, the minuses cancel out, so you get -3 plus 3 00:07:40.800 --> 00:07:44.028 Well, if we start 3 to the left of 0 and we move 3 to the right, 00:07:44.028 --> 00:07:46.060 we end up at 0 again. 00:07:46.060 --> 00:07:48.240 So that makes sense, right? 00:07:48.250 --> 00:07:49.360 Let me do that again. 00:07:49.370 --> 00:07:53.290 -3 minus -3 00:07:53.290 --> 00:07:56.390 Anything minus itself should equal 0, right? 00:07:56.390 --> 00:07:57.950 That's why that equals 0 00:07:57.950 --> 00:08:00.868 And that's why it makes sense that 00:08:00.868 --> 00:08:03.183 those two negatives cancel out 00:08:03.183 --> 00:08:05.498 and that's the same thing as this. 00:08:05.498 --> 00:08:07.429 Let's do a bunch more. 00:08:07.429 --> 00:08:12.140 Let's do 12 - 13 00:08:12.140 --> 00:08:13.610 That's pretty easy. 00:08:13.620 --> 00:08:17.940 Well, 12 - 12 = 0, so12 - 13 = -1 00:08:17.940 --> 00:08:20.920 because we're going to go 1 the left of 0 00:08:20.930 --> 00:08:24.670 Let's do 8 - 5 00:08:24.670 --> 00:08:27.270 Well, this one is just a normal problem, that's 3 00:08:27.270 --> 00:08:29.640 What's 5 - 8? 00:08:29.640 --> 00:08:31.988 Well, we're going to go all the way to 0 00:08:31.988 --> 00:08:35.420 and then 3 more to the left of 0, so it's -3 00:08:35.420 --> 00:08:38.500 I could draw a number line here. 00:08:38.500 --> 00:08:43.468 If this is 0, this is 5 00:08:43.468 --> 00:08:47.233 and now we're going to go to left 8, 00:08:47.233 --> 00:08:48.290 then we end up at -3 00:08:48.300 --> 00:08:49.400 You could do that for all of these. 00:08:49.400 --> 00:08:51.770 That actually might be a good exercise. 00:08:51.770 --> 00:08:54.113 I think this will give you good introduction 00:08:54.113 --> 00:08:56.220 and I recommend that you just do the modules, 00:08:56.220 --> 00:08:58.281 because the modules actually 00:08:58.281 --> 00:08:58.977 especially if you do the hints 00:08:58.977 --> 00:08:59.673 it has a pretty nice graphic 00:08:59.673 --> 00:09:01.578 that's a lot nicer than 00:09:01.578 --> 00:09:03.990 anything I could draw on this chalkboard. 00:09:03.990 --> 00:09:05.463 So, try that out 00:09:05.463 --> 00:09:07.494 and I'm going to try to record some more modules 00:09:07.509 --> 00:09:09.140 that hopefully won't confuse you as badly. 00:09:09.140 --> 00:09:10.533 You could also attend the seminar 00:09:10.533 --> 00:09:12.700 on adding and subtracting negative numbers. 00:09:12.700 --> 00:09:14.160 I hope you have fun! 00:09:14.160 --> 00:09:15.460 Bye.