[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.06,0:00:03.37,Default,,0000,0000,0000,,Welcome to the presentation
Dialogue: 0,0:00:03.37,0:00:05.07,Default,,0000,0000,0000,,on adding and subtracting negative numbers.
Dialogue: 0,0:00:05.07,0:00:06.38,Default,,0000,0000,0000,,So let's get started.
Dialogue: 0,0:00:06.38,0:00:08.51,Default,,0000,0000,0000,,So what is a negative number, first of all?
Dialogue: 0,0:00:08.52,0:00:12.08,Default,,0000,0000,0000,,Well, let me draw a number line.
Dialogue: 0,0:00:12.08,0:00:13.30,Default,,0000,0000,0000,,Well it's not much of a line,
Dialogue: 0,0:00:13.30,0:00:15.19,Default,,0000,0000,0000,,but I think you'll get the picture.
Dialogue: 0,0:00:15.19,0:00:18.80,Default,,0000,0000,0000,,So we're used to the positive numbers, so if that's 0
Dialogue: 0,0:00:18.80,0:00:24.67,Default,,0000,0000,0000,,you have one, you have 2, you have 3, you have 4
Dialogue: 0,0:00:24.67,0:00:25.69,Default,,0000,0000,0000,,and you keep going.
Dialogue: 0,0:00:25.69,0:00:28.55,Default,,0000,0000,0000,,And if I were to say what's 2+2
Dialogue: 0,0:00:28.55,0:00:30.78,Default,,0000,0000,0000,,you'd start at 2, and then you'd add 2
Dialogue: 0,0:00:30.78,0:00:31.46,Default,,0000,0000,0000,,you'd get to 4.
Dialogue: 0,0:00:31.46,0:00:32.14,Default,,0000,0000,0000,,I mean most of us it's second nature.
Dialogue: 0,0:00:32.15,0:00:33.93,Default,,0000,0000,0000,,But if you actually drew it on a number line,
Dialogue: 0,0:00:33.93,0:00:36.13,Default,,0000,0000,0000,,you'd say 2+2=4
Dialogue: 0,0:00:36.14,0:00:38.49,Default,,0000,0000,0000,,And if I asked you what's 2-1
Dialogue: 0,0:00:38.49,0:00:39.84,Default,,0000,0000,0000,,or let's say what's 3-2
Dialogue: 0,0:00:39.84,0:00:44.11,Default,,0000,0000,0000,,If you start at 3 and you subtracted 2
Dialogue: 0,0:00:44.11,0:00:45.66,Default,,0000,0000,0000,,you would end up at 1
Dialogue: 0,0:00:45.66,0:00:51.25,Default,,0000,0000,0000,,That's 2+2=4, and 3-2=1
Dialogue: 0,0:00:51.25,0:00:52.98,Default,,0000,0000,0000,,And this is a joke for you.
Dialogue: 0,0:00:52.99,0:00:56.99,Default,,0000,0000,0000,,Now what if I were to say what is 1-3?
Dialogue: 0,0:00:56.99,0:00:58.15,Default,,0000,0000,0000,,Huh.
Dialogue: 0,0:00:58.15,0:01:00.10,Default,,0000,0000,0000,,Well, it's the same thing.
Dialogue: 0,0:01:00.10,0:01:03.85,Default,,0000,0000,0000,,You start at 1 and we're going to go 1--
Dialogue: 0,0:01:03.85,0:01:06.96,Default,,0000,0000,0000,,well, now we're going to go below 0
Dialogue: 0,0:01:06.96,0:01:07.73,Default,,0000,0000,0000,,what happens below 0?
Dialogue: 0,0:01:07.73,0:01:08.50,Default,,0000,0000,0000,,Well then you start going to the negative numbers.
Dialogue: 0,0:01:08.51,0:01:14.93,Default,,0000,0000,0000,,-1, -2, -3, and so on.
Dialogue: 0,0:01:14.93,0:01:20.91,Default,,0000,0000,0000,,So if I start at 1 right here, so 1-3
Dialogue: 0,0:01:20.91,0:01:25.61,Default,,0000,0000,0000,,so I go 1,2,3, I end up at -2
Dialogue: 0,0:01:25.62,0:01:30.68,Default,,0000,0000,0000,,So 1-3=-2
Dialogue: 0,0:01:30.68,0:01:33.08,Default,,0000,0000,0000,,This is something that you're probably already doing
Dialogue: 0,0:01:33.09,0:01:34.73,Default,,0000,0000,0000,,in your everyday life
Dialogue: 0,0:01:34.73,0:01:37.14,Default,,0000,0000,0000,,If I were to tell you that
Dialogue: 0,0:01:37.14,0:01:39.22,Default,,0000,0000,0000,,boy, it's very cold today, it's one degree,
Dialogue: 0,0:01:39.22,0:01:40.73,Default,,0000,0000,0000,,but tomorrow it's going to be three degrees colder,
Dialogue: 0,0:01:40.73,0:01:42.04,Default,,0000,0000,0000,,you might already know intuitively,
Dialogue: 0,0:01:42.04,0:01:44.50,Default,,0000,0000,0000,,well then we're going to be
Dialogue: 0,0:01:44.50,0:01:46.92,Default,,0000,0000,0000,,at a temperature of negative two degrees.
Dialogue: 0,0:01:46.92,0:01:48.04,Default,,0000,0000,0000,,So that's all a negative number means.
Dialogue: 0,0:01:48.04,0:01:51.13,Default,,0000,0000,0000,,And just remember when a negative number is big,
Dialogue: 0,0:01:51.13,0:01:58.09,Default,,0000,0000,0000,,so like -50, that's actually colder than -20, right?
Dialogue: 0,0:01:58.09,0:02:01.71,Default,,0000,0000,0000,,So a -50 is actually even a smaller number than -20
Dialogue: 0,0:02:01.71,0:02:04.93,Default,,0000,0000,0000,,because it's even further to the left of -20
Dialogue: 0,0:02:04.93,0:02:07.16,Default,,0000,0000,0000,,That's just something you'll get an intuitive feel for.
Dialogue: 0,0:02:07.17,0:02:08.71,Default,,0000,0000,0000,,Sometimes when you start you feel like
Dialogue: 0,0:02:08.71,0:02:10.18,Default,,0000,0000,0000,,oh, 50 is a bigger number than 20
Dialogue: 0,0:02:10.18,0:02:13.86,Default,,0000,0000,0000,,but it's a -50 as opposed to a 50
Dialogue: 0,0:02:13.86,0:02:15.31,Default,,0000,0000,0000,,So let's do some problems,
Dialogue: 0,0:02:15.31,0:02:19.27,Default,,0000,0000,0000,,and I'm going to keep using the number line
Dialogue: 0,0:02:19.28,0:02:22.42,Default,,0000,0000,0000,,because I think it's useful
Dialogue: 0,0:02:22.42,0:02:26.87,Default,,0000,0000,0000,,So let's do the problem 5-12
Dialogue: 0,0:02:26.87,0:02:29.78,Default,,0000,0000,0000,,I think you already might have an intuition
Dialogue: 0,0:02:29.78,0:02:34.20,Default,,0000,0000,0000,,of what this equals.
Dialogue: 0,0:02:34.20,0:02:45.14,Default,,0000,0000,0000,,But let me draw a line, 5-12
Dialogue: 0,0:02:45.14,0:02:53.07,Default,,0000,0000,0000,,So let me start with -10, -9, -8--
Dialogue: 0,0:02:53.07,0:02:58.78,Default,,0000,0000,0000,,I think I'm going to run out of space-- -7, -6, -5
Dialogue: 0,0:02:58.78,0:03:05.16,Default,,0000,0000,0000,,I should have this pre-drawn -- -4, -3, -2, -1
Dialogue: 0,0:03:05.16,0:03:12.54,Default,,0000,0000,0000,,0,1,2,3,4, and I'll put 5 right here.
Dialogue: 0,0:03:12.54,0:03:14.49,Default,,0000,0000,0000,,I'm gonna push this arrow out a little bit. Okay.
Dialogue: 0,0:03:14.49,0:03:15.55,Default,,0000,0000,0000,,5-12
Dialogue: 0,0:03:15.56,0:03:18.43,Default,,0000,0000,0000,,So if we start at 5-- let me use a different color--
Dialogue: 0,0:03:18.43,0:03:20.94,Default,,0000,0000,0000,,we start at 5 right here and we're going to go to the left 12
Dialogue: 0,0:03:20.94,0:03:22.80,Default,,0000,0000,0000,,because we're subtracting 12
Dialogue: 0,0:03:22.80,0:03:33.87,Default,,0000,0000,0000,,So then we go 1,2,3...
Dialogue: 0,0:03:33.87,0:03:38.26,Default,,0000,0000,0000,,Negative 7
Dialogue: 0,0:03:38.26,0:03:39.99,Default,,0000,0000,0000,,That's pretty interesting.
Dialogue: 0,0:03:40.00,0:03:42.79,Default,,0000,0000,0000,,Because it also happens to be
Dialogue: 0,0:03:42.79,0:03:45.58,Default,,0000,0000,0000,,that 12 - 5 = +7
Dialogue: 0,0:03:45.59,0:03:48.90,Default,,0000,0000,0000,,So, I want you to think a little bit about why that is.
Dialogue: 0,0:03:48.90,0:03:52.94,Default,,0000,0000,0000,,Why the difference between 12 and 5 is 7,
Dialogue: 0,0:03:52.94,0:03:58.92,Default,,0000,0000,0000,,and the difference between
Dialogue: 0,0:03:58.92,0:04:00.04,Default,,0000,0000,0000,,-- well, I guess it's either way.
Dialogue: 0,0:04:00.04,0:04:01.10,Default,,0000,0000,0000,,In this situation we're also saying
Dialogue: 0,0:04:01.10,0:04:03.81,Default,,0000,0000,0000,,that the difference between 5 and 12 is -7,
Dialogue: 0,0:04:03.81,0:04:05.16,Default,,0000,0000,0000,,but the numbers are that far apart,
Dialogue: 0,0:04:05.16,0:04:07.50,Default,,0000,0000,0000,,but now we're starting with the lower number.
Dialogue: 0,0:04:07.50,0:04:09.54,Default,,0000,0000,0000,,I think that last sentence just completely confused you,
Dialogue: 0,0:04:09.54,0:04:11.79,Default,,0000,0000,0000,,but we'll keep moving forward.
Dialogue: 0,0:04:11.79,0:04:18.06,Default,,0000,0000,0000,,We just said 5-12=-7
Dialogue: 0,0:04:18.06,0:04:19.43,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:04:19.43,0:04:25.84,Default,,0000,0000,0000,,What's -3+5?
Dialogue: 0,0:04:25.84,0:04:28.05,Default,,0000,0000,0000,,Well, let's use the same number line.
Dialogue: 0,0:04:28.06,0:04:31.49,Default,,0000,0000,0000,,Let's go to -3 plus 5
Dialogue: 0,0:04:31.49,0:04:33.58,Default,,0000,0000,0000,,So we're going to go to the right 5
Dialogue: 0,0:04:33.58,0:04:38.42,Default,,0000,0000,0000,,One, two, three, four, five.
Dialogue: 0,0:04:38.42,0:04:42.60,Default,,0000,0000,0000,,It's a two.
Dialogue: 0,0:04:42.60,0:04:44.36,Default,,0000,0000,0000,,It equals two.
Dialogue: 0,0:04:44.36,0:04:48.79,Default,,0000,0000,0000,,So -3 + 5 = 2
Dialogue: 0,0:04:48.79,0:04:53.84,Default,,0000,0000,0000,,That's interesting because 5 - 3 is also equal to 2
Dialogue: 0,0:04:53.84,0:04:57.01,Default,,0000,0000,0000,,Well, it turns out that 5 - 3 is the same thing,
Dialogue: 0,0:04:57.01,0:05:00.25,Default,,0000,0000,0000,,it's just another way of writing 5 plus -3
Dialogue: 0,0:05:00.25,0:05:04.05,Default,,0000,0000,0000,,or -3 plus 5
Dialogue: 0,0:05:04.05,0:05:07.05,Default,,0000,0000,0000,,A general, easy way to always do negative numbers
Dialogue: 0,0:05:07.05,0:05:11.64,Default,,0000,0000,0000,,is it's just like regular addition and subtraction,
Dialogue: 0,0:05:11.64,0:05:15.46,Default,,0000,0000,0000,,but now when we subtract
Dialogue: 0,0:05:15.46,0:05:18.63,Default,,0000,0000,0000,,we can go to the left below zero
Dialogue: 0,0:05:18.63,0:05:19.83,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:05:19.83,0:05:21.59,Default,,0000,0000,0000,,So what happens when you get
Dialogue: 0,0:05:21.59,0:05:27.11,Default,,0000,0000,0000,,let's say, 2 minus -3?
Dialogue: 0,0:05:27.11,0:05:30.75,Default,,0000,0000,0000,,Well, if you think about how it should work out,
Dialogue: 0,0:05:30.75,0:05:32.08,Default,,0000,0000,0000,,I think this will make sense.
Dialogue: 0,0:05:32.08,0:05:34.14,Default,,0000,0000,0000,,But it turns out that the negative number,
Dialogue: 0,0:05:34.14,0:05:36.14,Default,,0000,0000,0000,,the negative signs actually cancel out.
Dialogue: 0,0:05:36.14,0:05:40.42,Default,,0000,0000,0000,,So this is the same thing as 2 plus +3
Dialogue: 0,0:05:40.42,0:05:43.05,Default,,0000,0000,0000,,and that just equals 5
Dialogue: 0,0:05:43.06,0:05:46.30,Default,,0000,0000,0000,,Another way you could say is-- let's do another one--
Dialogue: 0,0:05:46.30,0:05:52.87,Default,,0000,0000,0000,,what is -7 minus -2?
Dialogue: 0,0:05:52.87,0:05:58.01,Default,,0000,0000,0000,,Well that's the same thing as -7 + 2
Dialogue: 0,0:05:58.02,0:06:00.14,Default,,0000,0000,0000,,And remember, so we're doing to start at -7
Dialogue: 0,0:06:00.14,0:06:03.56,Default,,0000,0000,0000,,and we're going to move 2 to the right.
Dialogue: 0,0:06:03.56,0:06:06.22,Default,,0000,0000,0000,,So if we move 1 to the right we go to -6
Dialogue: 0,0:06:06.22,0:06:11.39,Default,,0000,0000,0000,,and then we move 2 to the right we get -5
Dialogue: 0,0:06:11.39,0:06:13.76,Default,,0000,0000,0000,,That makes sense because -7 + 2
Dialogue: 0,0:06:13.76,0:06:16.54,Default,,0000,0000,0000,,that's the same thing as 2 - 7
Dialogue: 0,0:06:16.55,0:06:19.35,Default,,0000,0000,0000,,If it's two degrees and
Dialogue: 0,0:06:19.35,0:06:22.48,Default,,0000,0000,0000,,it gets seven degrees colder, it's -5
Dialogue: 0,0:06:22.48,0:06:23.23,Default,,0000,0000,0000,,Let's do a bunch of these.
Dialogue: 0,0:06:23.24,0:06:25.25,Default,,0000,0000,0000,,I think the more you do, the more practice you have,
Dialogue: 0,0:06:25.25,0:06:26.85,Default,,0000,0000,0000,,and the modules explain it pretty well.
Dialogue: 0,0:06:26.85,0:06:29.06,Default,,0000,0000,0000,,Probably better than I do.
Dialogue: 0,0:06:29.06,0:06:31.10,Default,,0000,0000,0000,,So let's just do a ton of problems.
Dialogue: 0,0:06:31.10,0:06:36.47,Default,,0000,0000,0000,,So if I said -7 - 3
Dialogue: 0,0:06:36.47,0:06:39.40,Default,,0000,0000,0000,,Well, now we're going to go 3 to the left of -7
Dialogue: 0,0:06:39.41,0:06:41.39,Default,,0000,0000,0000,,We're going to get 3 less than -7
Dialogue: 0,0:06:41.39,0:06:45.42,Default,,0000,0000,0000,,so that's -10, right?
Dialogue: 0,0:06:45.43,0:06:49.06,Default,,0000,0000,0000,,That makes sense, because if we had 7 + 3
Dialogue: 0,0:06:49.06,0:06:50.76,Default,,0000,0000,0000,,we're at 7 to the right of 0
Dialogue: 0,0:06:50.76,0:06:52.50,Default,,0000,0000,0000,,and we're going to go 3 more to the right of 0
Dialogue: 0,0:06:52.50,0:06:54.54,Default,,0000,0000,0000,,and we get positive 10
Dialogue: 0,0:06:54.54,0:06:57.38,Default,,0000,0000,0000,,So for 7 to the left of 0 and go 3 more to the left,
Dialogue: 0,0:06:57.38,0:06:58.68,Default,,0000,0000,0000,,we're going to get -10
Dialogue: 0,0:06:58.68,0:06:59.46,Default,,0000,0000,0000,,Let's do a bunch more.
Dialogue: 0,0:06:59.47,0:07:01.05,Default,,0000,0000,0000,,I know I'm probably confusing you,
Dialogue: 0,0:07:01.05,0:07:04.22,Default,,0000,0000,0000,,but practice is what's going to really help us.
Dialogue: 0,0:07:04.22,0:07:09.12,Default,,0000,0000,0000,,So let's say 3 minus -3
Dialogue: 0,0:07:09.12,0:07:12.36,Default,,0000,0000,0000,,well, these negatives cancel out,
Dialogue: 0,0:07:12.36,0:07:14.57,Default,,0000,0000,0000,,so that just equals 6
Dialogue: 0,0:07:14.57,0:07:17.09,Default,,0000,0000,0000,,What's 3-3?
Dialogue: 0,0:07:17.09,0:07:18.69,Default,,0000,0000,0000,,Well, 3-3, that's easy.
Dialogue: 0,0:07:18.69,0:07:20.69,Default,,0000,0000,0000,,That's just 0
Dialogue: 0,0:07:20.69,0:07:23.98,Default,,0000,0000,0000,,What's -3 nimus 3?
Dialogue: 0,0:07:23.99,0:07:26.42,Default,,0000,0000,0000,,Well now we're going to get 3 less than -3
Dialogue: 0,0:07:26.42,0:07:28.88,Default,,0000,0000,0000,,well that's -6
Dialogue: 0,0:07:28.88,0:07:34.03,Default,,0000,0000,0000,,What's -3 minus -3
Dialogue: 0,0:07:34.04,0:07:35.50,Default,,0000,0000,0000,,Interesting.
Dialogue: 0,0:07:35.50,0:07:40.79,Default,,0000,0000,0000,,Well, the minuses cancel out, so you get -3 plus 3
Dialogue: 0,0:07:40.80,0:07:44.03,Default,,0000,0000,0000,,Well, if we start 3 to the left of 0 and we move 3 to the right,
Dialogue: 0,0:07:44.03,0:07:46.06,Default,,0000,0000,0000,,we end up at 0 again.
Dialogue: 0,0:07:46.06,0:07:48.24,Default,,0000,0000,0000,,So that makes sense, right?
Dialogue: 0,0:07:48.25,0:07:49.36,Default,,0000,0000,0000,,Let me do that again.
Dialogue: 0,0:07:49.37,0:07:53.29,Default,,0000,0000,0000,,-3 minus -3
Dialogue: 0,0:07:53.29,0:07:56.39,Default,,0000,0000,0000,,Anything minus itself should equal 0, right?
Dialogue: 0,0:07:56.39,0:07:57.95,Default,,0000,0000,0000,,That's why that equals 0
Dialogue: 0,0:07:57.95,0:08:00.87,Default,,0000,0000,0000,,And that's why it makes sense that
Dialogue: 0,0:08:00.87,0:08:03.18,Default,,0000,0000,0000,,those two negatives cancel out
Dialogue: 0,0:08:03.18,0:08:05.50,Default,,0000,0000,0000,,and that's the same thing as this.
Dialogue: 0,0:08:05.50,0:08:07.43,Default,,0000,0000,0000,,Let's do a bunch more.
Dialogue: 0,0:08:07.43,0:08:12.14,Default,,0000,0000,0000,,Let's do 12 - 13
Dialogue: 0,0:08:12.14,0:08:13.61,Default,,0000,0000,0000,,That's pretty easy.
Dialogue: 0,0:08:13.62,0:08:17.94,Default,,0000,0000,0000,,Well, 12 - 12 = 0, so12 - 13 = -1
Dialogue: 0,0:08:17.94,0:08:20.92,Default,,0000,0000,0000,,because we're going to go 1 the left of 0
Dialogue: 0,0:08:20.93,0:08:24.67,Default,,0000,0000,0000,,Let's do 8 - 5
Dialogue: 0,0:08:24.67,0:08:27.27,Default,,0000,0000,0000,,Well, this one is just a normal problem, that's 3
Dialogue: 0,0:08:27.27,0:08:29.64,Default,,0000,0000,0000,,What's 5 - 8?
Dialogue: 0,0:08:29.64,0:08:31.99,Default,,0000,0000,0000,,Well, we're going to go all the way to 0
Dialogue: 0,0:08:31.99,0:08:35.42,Default,,0000,0000,0000,,and then 3 more to the left of 0, so it's -3
Dialogue: 0,0:08:35.42,0:08:38.50,Default,,0000,0000,0000,,I could draw a number line here.
Dialogue: 0,0:08:38.50,0:08:43.47,Default,,0000,0000,0000,,If this is 0, this is 5
Dialogue: 0,0:08:43.47,0:08:47.23,Default,,0000,0000,0000,,and now we're going to go to left 8,
Dialogue: 0,0:08:47.23,0:08:48.29,Default,,0000,0000,0000,,then we end up at -3
Dialogue: 0,0:08:48.30,0:08:49.40,Default,,0000,0000,0000,,You could do that for all of these.
Dialogue: 0,0:08:49.40,0:08:51.77,Default,,0000,0000,0000,,That actually might be a good exercise.
Dialogue: 0,0:08:51.77,0:08:54.11,Default,,0000,0000,0000,,I think this will give you good introduction
Dialogue: 0,0:08:54.11,0:08:56.22,Default,,0000,0000,0000,,and I recommend that you just do the modules,
Dialogue: 0,0:08:56.22,0:08:58.28,Default,,0000,0000,0000,,because the modules actually
Dialogue: 0,0:08:58.28,0:08:58.98,Default,,0000,0000,0000,,especially if you do the hints
Dialogue: 0,0:08:58.98,0:08:59.67,Default,,0000,0000,0000,,it has a pretty nice graphic
Dialogue: 0,0:08:59.67,0:09:01.58,Default,,0000,0000,0000,,that's a lot nicer than
Dialogue: 0,0:09:01.58,0:09:03.99,Default,,0000,0000,0000,,anything I could draw on this chalkboard.
Dialogue: 0,0:09:03.99,0:09:05.46,Default,,0000,0000,0000,,So, try that out
Dialogue: 0,0:09:05.46,0:09:07.49,Default,,0000,0000,0000,,and I'm going to try to record some more modules
Dialogue: 0,0:09:07.51,0:09:09.14,Default,,0000,0000,0000,,that hopefully won't confuse you as badly.
Dialogue: 0,0:09:09.14,0:09:10.53,Default,,0000,0000,0000,,You could also attend the seminar
Dialogue: 0,0:09:10.53,0:09:12.70,Default,,0000,0000,0000,,on adding and subtracting negative numbers.
Dialogue: 0,0:09:12.70,0:09:14.16,Default,,0000,0000,0000,,I hope you have fun!
Dialogue: 0,0:09:14.16,0:09:15.46,Default,,0000,0000,0000,,Bye.