[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.73,0:00:03.46,Default,,0000,0000,0000,,In this video I want to familiarize ourselves
Dialogue: 0,0:00:03.46,0:00:04.77,Default,,0000,0000,0000,,with negative numbers.
Dialogue: 0,0:00:04.77,0:00:07.56,Default,,0000,0000,0000,,And also learn a bit of how do we add and subtract them.
Dialogue: 0,0:00:07.56,0:00:09.33,Default,,0000,0000,0000,,And when you first encounter them,
Dialogue: 0,0:00:09.33,0:00:11.61,Default,,0000,0000,0000,,they look like this deep and mysterious thing.
Dialogue: 0,0:00:11.61,0:00:14.77,Default,,0000,0000,0000,,When we first count things, we're counting positive numbers.
Dialogue: 0,0:00:14.77,0:00:17.35,Default,,0000,0000,0000,,What does a negative number even mean?
Dialogue: 0,0:00:17.35,0:00:20.84,Default,,0000,0000,0000,,But when we think about it, you probably have encountered
Dialogue: 0,0:00:20.84,0:00:22.90,Default,,0000,0000,0000,,negative numbers in your everyday life.
Dialogue: 0,0:00:22.90,0:00:25.20,Default,,0000,0000,0000,,And let me just give you a few examples.
Dialogue: 0,0:00:25.20,0:00:26.41,Default,,0000,0000,0000,,So before I give the example, the general idea is
Dialogue: 0,0:00:26.41,0:00:30.67,Default,,0000,0000,0000,,a negative number is any number less than zero.
Dialogue: 0,0:00:30.67,0:00:34.84,Default,,0000,0000,0000,,Less than zero.
Dialogue: 0,0:00:34.84,0:00:37.19,Default,,0000,0000,0000,,And if that sounds strange and abstract to you,
Dialogue: 0,0:00:37.19,0:00:39.85,Default,,0000,0000,0000,,let's just think about it in a couple of different contexts.
Dialogue: 0,0:00:39.85,0:00:45.25,Default,,0000,0000,0000,,If I have... if we're measuring the temperature ...
Dialogue: 0,0:00:45.25,0:00:47.11,Default,,0000,0000,0000,,(and it can be in Celsius or Farenheit,
Dialogue: 0,0:00:47.11,0:00:49.88,Default,,0000,0000,0000,,but let's just say we're measuring it in Celsius),
Dialogue: 0,0:00:49.88,0:00:51.88,Default,,0000,0000,0000,,and so let me draw a little scale
Dialogue: 0,0:00:51.88,0:00:53.71,Default,,0000,0000,0000,,that we can measure the temperature on.
Dialogue: 0,0:00:53.71,0:00:57.10,Default,,0000,0000,0000,,So let's say that this is 0° Celsius,
Dialogue: 0,0:00:57.10,0:01:02.91,Default,,0000,0000,0000,,that is 1° Celsius, 2° Celsius, 3° Celsius.
Dialogue: 0,0:01:02.92,0:01:05.82,Default,,0000,0000,0000,,Now, let's say it's a pretty chilly day
Dialogue: 0,0:01:05.82,0:01:10.30,Default,,0000,0000,0000,,and it's currently 3° Celsius.
Dialogue: 0,0:01:10.30,0:01:12.00,Default,,0000,0000,0000,,And someone who predicts the future
Dialogue: 0,0:01:12.00,0:01:16.98,Default,,0000,0000,0000,,tells you that it is going to get 4° colder the next day.
Dialogue: 0,0:01:16.98,0:01:21.50,Default,,0000,0000,0000,,So how cold will it be? How can you represent that coldness?
Dialogue: 0,0:01:21.50,0:01:25.13,Default,,0000,0000,0000,,Well, if it only got 1° colder it would be at 2°,
Dialogue: 0,0:01:25.13,0:01:26.87,Default,,0000,0000,0000,,but we know we have to go 4° colder.
Dialogue: 0,0:01:26.87,0:01:32.07,Default,,0000,0000,0000,,If we got 2° colder, we would be at 1°.
Dialogue: 0,0:01:32.07,0:01:35.31,Default,,0000,0000,0000,,If we got 3° colder, we would be at 0°.
Dialogue: 0,0:01:35.31,0:01:38.45,Default,,0000,0000,0000,,But 3° isn't enough, we have to get 4° colder,
Dialogue: 0,0:01:38.45,0:01:43.96,Default,,0000,0000,0000,,so we actually have to go one more below zero.
Dialogue: 0,0:01:43.96,0:01:50.42,Default,,0000,0000,0000,,And that 1 below 0 we call that "negative 1".
Dialogue: 0,0:01:50.42,0:01:52.91,Default,,0000,0000,0000,,And so you can kind of see that the number line,
Dialogue: 0,0:01:52.91,0:01:57.03,Default,,0000,0000,0000,,as you go to the right of zero increases in positive values,
Dialogue: 0,0:01:57.03,0:02:04.21,Default,,0000,0000,0000,,as you go to the left of zero you're going to have -1, -2, -3.
Dialogue: 0,0:02:04.21,0:02:07.30,Default,,0000,0000,0000,,And you're going to have-depending on how you think about it-
Dialogue: 0,0:02:07.30,0:02:09.95,Default,,0000,0000,0000,,you're going to have larger negative numbers.
Dialogue: 0,0:02:09.95,0:02:15.37,Default,,0000,0000,0000,,But I want to make it very clear: -3 is LESS than -1.
Dialogue: 0,0:02:15.37,0:02:19.49,Default,,0000,0000,0000,,There is less heat in the air at -3° than at -1°.
Dialogue: 0,0:02:19.49,0:02:23.33,Default,,0000,0000,0000,,It is colder---there is less temperature there.
Dialogue: 0,0:02:23.33,0:02:39.82,Default,,0000,0000,0000,,So let me just make it very clear: -100 is much smaller than -1.
Dialogue: 0,0:02:39.82,0:02:41.91,Default,,0000,0000,0000,,You might look at 100 and you might look at 1 and
Dialogue: 0,0:02:41.91,0:02:45.09,Default,,0000,0000,0000,,your gut reaction might be that 100 is much larger than 1.
Dialogue: 0,0:02:45.09,0:02:46.27,Default,,0000,0000,0000,,But when you think about it,
Dialogue: 0,0:02:46.27,0:02:48.85,Default,,0000,0000,0000,,-100 means there is a lack of something.
Dialogue: 0,0:02:48.85,0:02:52.30,Default,,0000,0000,0000,,-100: if it's -100° there is a lack of heat,
Dialogue: 0,0:02:52.30,0:02:55.74,Default,,0000,0000,0000,,so there is much less heat here than if we had -1°.
Dialogue: 0,0:02:55.74,0:02:57.49,Default,,0000,0000,0000,,Let me give you another example.
Dialogue: 0,0:02:57.49,0:03:11.26,Default,,0000,0000,0000,,Let's say in my bank account today I have $10.
Dialogue: 0,0:03:11.26,0:03:13.11,Default,,0000,0000,0000,,Now, let's say I go out there
Dialogue: 0,0:03:13.11,0:03:14.95,Default,,0000,0000,0000,,(because I feel good about my $10),
Dialogue: 0,0:03:14.95,0:03:21.43,Default,,0000,0000,0000,,and let's say I go and spend $30.
Dialogue: 0,0:03:21.43,0:03:22.74,Default,,0000,0000,0000,,And, for the sake of argument
Dialogue: 0,0:03:22.74,0:03:24.28,Default,,0000,0000,0000,,let's say I have a very flexible bank,
Dialogue: 0,0:03:24.28,0:03:26.86,Default,,0000,0000,0000,,one that lets me spend more money than I have
Dialogue: 0,0:03:26.86,0:03:28.35,Default,,0000,0000,0000,,(and these actually exist!).
Dialogue: 0,0:03:28.35,0:03:30.42,Default,,0000,0000,0000,,So I spend $30.
Dialogue: 0,0:03:30.42,0:03:32.91,Default,,0000,0000,0000,,So what's my bank account going to look like?
Dialogue: 0,0:03:32.91,0:03:35.56,Default,,0000,0000,0000,,So let me draw a number line here.
Dialogue: 0,0:03:35.56,0:03:37.84,Default,,0000,0000,0000,,And you may already have an intuitive response:
Dialogue: 0,0:03:37.84,0:03:43.28,Default,,0000,0000,0000,,I will owe the bank some money.
Dialogue: 0,0:03:43.28,0:03:47.13,Default,,0000,0000,0000,,Tomorrow, what is my bank account?
Dialogue: 0,0:03:47.13,0:03:51.64,Default,,0000,0000,0000,,You might immediately say, "if I have $10 and I spend $30,
Dialogue: 0,0:03:51.64,0:03:54.22,Default,,0000,0000,0000,,there's $20 that had to come from some place."
Dialogue: 0,0:03:54.22,0:03:56.49,Default,,0000,0000,0000,,And that $20 is coming from the bank.
Dialogue: 0,0:03:56.49,0:03:59.12,Default,,0000,0000,0000,,So I'm going to owe the bank $20.
Dialogue: 0,0:03:59.12,0:04:00.79,Default,,0000,0000,0000,,And so, in my bank account,
Dialogue: 0,0:04:00.79,0:04:07.20,Default,,0000,0000,0000,,to show how much I have, I could say $10 - $30 is -$20.
Dialogue: 0,0:04:07.20,0:04:13.34,Default,,0000,0000,0000,,So in my bank account tomorrow, I'm going to have -$20.
Dialogue: 0,0:04:13.34,0:04:18.08,Default,,0000,0000,0000,,So, if I say I have -$20, that means that I owe the bank.
Dialogue: 0,0:04:18.08,0:04:19.36,Default,,0000,0000,0000,,---I don't even have it.
Dialogue: 0,0:04:19.36,0:04:20.95,Default,,0000,0000,0000,,Not only do I have nothing, I owe something.
Dialogue: 0,0:04:20.95,0:04:22.54,Default,,0000,0000,0000,,It's going in reverse.
Dialogue: 0,0:04:22.54,0:04:25.59,Default,,0000,0000,0000,,Here, I have something to spend...
Dialogue: 0,0:04:25.59,0:04:29.23,Default,,0000,0000,0000,,if my $10 in my bank account means the bank owes me $10.
Dialogue: 0,0:04:29.23,0:04:31.82,Default,,0000,0000,0000,,I have $10 that I can use to go spend.
Dialogue: 0,0:04:31.82,0:04:33.39,Default,,0000,0000,0000,,Now, all of a sudden I owe the bank.
Dialogue: 0,0:04:33.39,0:04:34.96,Default,,0000,0000,0000,,I've gone the other direction.
Dialogue: 0,0:04:34.96,0:04:36.78,Default,,0000,0000,0000,,If we use a number line here
Dialogue: 0,0:04:36.78,0:04:38.59,Default,,0000,0000,0000,,it should hopefully make more sense.
Dialogue: 0,0:04:38.59,0:04:39.83,Default,,0000,0000,0000,,So that is 0.
Dialogue: 0,0:04:39.83,0:04:43.35,Default,,0000,0000,0000,,I'm starting off with $10,
Dialogue: 0,0:04:43.35,0:04:47.42,Default,,0000,0000,0000,,and spending $30 means I'm moving 30 spaces to the left.
Dialogue: 0,0:04:47.42,0:04:49.85,Default,,0000,0000,0000,,So if I move 10 spaces to the left---
Dialogue: 0,0:04:49.85,0:04:52.80,Default,,0000,0000,0000,,if I only spend $10 I'll be back at $0.
Dialogue: 0,0:04:52.80,0:04:56.83,Default,,0000,0000,0000,,If I spend another $10, I'll be at -$10.
Dialogue: 0,0:04:56.83,0:05:02.21,Default,,0000,0000,0000,,If I spend another $10 after that, I will be at -$20.
Dialogue: 0,0:05:02.21,0:05:04.48,Default,,0000,0000,0000,,So, each of these distances, I spent $10 I'd be at $0.
Dialogue: 0,0:05:04.48,0:05:06.76,Default,,0000,0000,0000,,Another $10 I'd be at -$10.
Dialogue: 0,0:05:06.76,0:05:09.75,Default,,0000,0000,0000,,Another $10 I would be at -$20.
Dialogue: 0,0:05:09.75,0:05:13.14,Default,,0000,0000,0000,,So this whole distance here is how much I spent.
Dialogue: 0,0:05:13.14,0:05:17.27,Default,,0000,0000,0000,,I spent $30.
Dialogue: 0,0:05:17.27,0:05:20.40,Default,,0000,0000,0000,,So the general idea when you spend or if you subtract,
Dialogue: 0,0:05:20.40,0:05:23.33,Default,,0000,0000,0000,,or getting colder, you would move to the left.
Dialogue: 0,0:05:23.33,0:05:24.80,Default,,0000,0000,0000,,The numbers would get smaller.
Dialogue: 0,0:05:24.80,0:05:27.23,Default,,0000,0000,0000,,And we now know they can get even smaller than 0.
Dialogue: 0,0:05:27.23,0:05:31.60,Default,,0000,0000,0000,,They can go to -1, -2---they can even go to -1.5, -1.6.
Dialogue: 0,0:05:31.60,0:05:34.95,Default,,0000,0000,0000,,The more and more negative, the more you lose.
Dialogue: 0,0:05:34.95,0:05:37.27,Default,,0000,0000,0000,,If you're adding, if I go and get my paycheck,
Dialogue: 0,0:05:37.27,0:05:41.39,Default,,0000,0000,0000,,I will move to the right of the number line.
Dialogue: 0,0:05:41.39,0:05:43.06,Default,,0000,0000,0000,,Now, with that out of the way,
Dialogue: 0,0:05:43.06,0:05:46.08,Default,,0000,0000,0000,,let's just do a couple more pure math problems.
Dialogue: 0,0:05:46.08,0:05:52.32,Default,,0000,0000,0000,,What it means, if we were to say...
Dialogue: 0,0:05:52.32,0:05:56.47,Default,,0000,0000,0000,,Let's say, 3 - 4.
Dialogue: 0,0:05:56.47,0:05:57.71,Default,,0000,0000,0000,,So once again,
Dialogue: 0,0:05:57.71,0:06:00.19,Default,,0000,0000,0000,,this is exactly the situation we did with the temperature.
Dialogue: 0,0:06:00.19,0:06:01.94,Default,,0000,0000,0000,,We're starting with 3 and we're subtracting 4,
Dialogue: 0,0:06:01.94,0:06:03.70,Default,,0000,0000,0000,,so we're going to move 4 to the left.
Dialogue: 0,0:06:03.70,0:06:05.85,Default,,0000,0000,0000,,We go 1, 2, 3, 4.
Dialogue: 0,0:06:05.85,0:06:10.42,Default,,0000,0000,0000,,That gets us to -1.
Dialogue: 0,0:06:10.42,0:06:11.77,Default,,0000,0000,0000,,And when you're starting to do this
Dialogue: 0,0:06:11.77,0:06:13.93,Default,,0000,0000,0000,,you really understand what a negative number means.
Dialogue: 0,0:06:13.93,0:06:15.84,Default,,0000,0000,0000,,I really encourage you to visualize the number line
Dialogue: 0,0:06:15.84,0:06:17.75,Default,,0000,0000,0000,,and really move along it depending on
Dialogue: 0,0:06:17.75,0:06:19.96,Default,,0000,0000,0000,,whether you're adding or subtracting.
Dialogue: 0,0:06:19.96,0:06:21.24,Default,,0000,0000,0000,,Let's do a couple more.
Dialogue: 0,0:06:21.24,0:06:27.85,Default,,0000,0000,0000,,Let's say I have 2 - 8
Dialogue: 0,0:06:27.85,0:06:30.55,Default,,0000,0000,0000,,(and we'll think about more ways to do this in future videos),
Dialogue: 0,0:06:30.55,0:06:33.61,Default,,0000,0000,0000,,but once again, you just want to do the number line.
Dialogue: 0,0:06:33.61,0:06:35.08,Default,,0000,0000,0000,,You have a 0 here.
Dialogue: 0,0:06:35.08,0:06:38.73,Default,,0000,0000,0000,,We're at (let me draw the spacing a little bit).
Dialogue: 0,0:06:38.73,0:06:42.03,Default,,0000,0000,0000,,We have 0 here...we're at 1... 2.
Dialogue: 0,0:06:42.03,0:06:43.89,Default,,0000,0000,0000,,If we're subtracting 8,
Dialogue: 0,0:06:43.89,0:06:47.04,Default,,0000,0000,0000,,that means we're going to move 8 to the left.
Dialogue: 0,0:06:47.04,0:06:50.99,Default,,0000,0000,0000,,So we're going to go 1 to the left, 2 to the left.
Dialogue: 0,0:06:50.99,0:06:53.04,Default,,0000,0000,0000,,So, we've gone 2 to the left to get to 0.
Dialogue: 0,0:06:53.04,0:06:55.08,Default,,0000,0000,0000,,We have to move how many more to the left?
Dialogue: 0,0:06:55.08,0:06:56.96,Default,,0000,0000,0000,,We've already moved 2 to the left,
Dialogue: 0,0:06:56.96,0:06:59.01,Default,,0000,0000,0000,,to get to 8, we have to move 6 more to the left.
Dialogue: 0,0:06:59.01,0:07:07.40,Default,,0000,0000,0000,,So we're going to have to move 1-2-3-4-5-6 more to the left.
Dialogue: 0,0:07:07.40,0:07:09.11,Default,,0000,0000,0000,,Well, where is that going to put us?
Dialogue: 0,0:07:09.11,0:07:10.07,Default,,0000,0000,0000,,Well, we were at 0.
Dialogue: 0,0:07:10.07,0:07:18.71,Default,,0000,0000,0000,,This is -1, -2, -3, -4, -5, -6.
Dialogue: 0,0:07:18.71,0:07:24.31,Default,,0000,0000,0000,,So, 2 - 8 is -6.
Dialogue: 0,0:07:24.31,0:07:26.54,Default,,0000,0000,0000,,2-2 would be 0.
Dialogue: 0,0:07:26.54,0:07:29.63,Default,,0000,0000,0000,,When you're subtracting 8 you're subtracting another 6.
Dialogue: 0,0:07:29.63,0:07:33.37,Default,,0000,0000,0000,,So we go to -6, we go 6 below 0.
Dialogue: 0,0:07:33.37,0:07:34.99,Default,,0000,0000,0000,,Let me do one more example.
Dialogue: 0,0:07:34.99,0:07:36.56,Default,,0000,0000,0000,,(and this will be a little less conventional
Dialogue: 0,0:07:36.56,0:07:38.81,Default,,0000,0000,0000,,but hopefully it will make sense).
Dialogue: 0,0:07:38.81,0:07:43.98,Default,,0000,0000,0000,,Let us take... (and I'll do this in a new color)...
Dialogue: 0,0:07:43.98,0:07:47.87,Default,,0000,0000,0000,,Let me take -4 - 2.
Dialogue: 0,0:07:47.87,0:07:49.44,Default,,0000,0000,0000,,So we're starting at a negative number
Dialogue: 0,0:07:49.44,0:07:51.01,Default,,0000,0000,0000,,and then we're subtracting from that.
Dialogue: 0,0:07:51.01,0:07:56.81,Default,,0000,0000,0000,,Now, if this seems confusing just remember the number line!
Dialogue: 0,0:07:56.84,0:07:59.68,Default,,0000,0000,0000,,So this is 0 right here.
Dialogue: 0,0:07:59.68,0:08:07.02,Default,,0000,0000,0000,,This is -1, -2, -3, -4. So that's where we're starting.
Dialogue: 0,0:08:07.02,0:08:09.28,Default,,0000,0000,0000,,Now we're going to subtract 2 from -4,
Dialogue: 0,0:08:09.28,0:08:11.54,Default,,0000,0000,0000,,so we're going to move 2 to the left.
Dialogue: 0,0:08:11.54,0:08:15.39,Default,,0000,0000,0000,,So if we subtract 1 we'll be at -5.
Dialogue: 0,0:08:15.39,0:08:21.72,Default,,0000,0000,0000,,If we subtract another 1 we are going to be at -6.
Dialogue: 0,0:08:21.72,0:08:23.33,Default,,0000,0000,0000,,So this is -6.
Dialogue: 0,0:08:23.33,0:08:24.75,Default,,0000,0000,0000,,Let's do another interesting thing.
Dialogue: 0,0:08:24.75,0:08:30.27,Default,,0000,0000,0000,,Let's start at -3 ... let's say we have -3.
Dialogue: 0,0:08:30.27,0:08:34.26,Default,,0000,0000,0000,,Instead of subtracting something from that, let's add 2.
Dialogue: 0,0:08:34.26,0:08:36.56,Default,,0000,0000,0000,,So where would this put us on the number line?
Dialogue: 0,0:08:36.56,0:08:39.39,Default,,0000,0000,0000,,So we're starting at -3 and we're adding 2.
Dialogue: 0,0:08:39.39,0:08:42.22,Default,,0000,0000,0000,,So we're going to move to the right.
Dialogue: 0,0:08:42.22,0:08:44.75,Default,,0000,0000,0000,,So you add 1, you become -2
Dialogue: 0,0:08:44.75,0:08:46.76,Default,,0000,0000,0000,,But if you add another 1 (which we have to do),
Dialogue: 0,0:08:46.76,0:08:47.97,Default,,0000,0000,0000,,you become -1.
Dialogue: 0,0:08:47.97,0:08:49.39,Default,,0000,0000,0000,,You move 2 to the right.
Dialogue: 0,0:08:49.39,0:08:54.40,Default,,0000,0000,0000,,So, -3 + 2 is -1.
Dialogue: 0,0:08:54.40,0:08:55.96,Default,,0000,0000,0000,,And you can see for yourself,
Dialogue: 0,0:08:55.96,0:08:59.93,Default,,0000,0000,0000,,this all fits our traditional notion of adding and subtracting.
Dialogue: 0,0:08:59.93,0:09:05.40,Default,,0000,0000,0000,,If we start at -1 and we subtract 2, we should get -3.
Dialogue: 0,0:09:05.40,0:09:07.51,Default,,0000,0000,0000,,Kind of reverses this thing up here.
Dialogue: 0,0:09:07.51,0:09:09.64,Default,,0000,0000,0000,,-3 +2 gets us there.
Dialogue: 0,0:09:09.64,0:09:11.23,Default,,0000,0000,0000,,And if we start there and we subtract 2
Dialogue: 0,0:09:11.23,0:09:12.51,Default,,0000,0000,0000,,we should get back to -3.
Dialogue: 0,0:09:12.51,0:09:13.43,Default,,0000,0000,0000,,And we see that happens.
Dialogue: 0,0:09:13.43,0:09:17.63,Default,,0000,0000,0000,,If you start at -1, right over here,
Dialogue: 0,0:09:17.63,0:09:20.47,Default,,0000,0000,0000,,and you subtract 2, you move 2 to the left.
Dialogue: 0,0:09:20.47,0:09:22.11,Default,,0000,0000,0000,,You get back to -3.
Dialogue: 0,0:09:22.11,0:09:25.32,Default,,0000,0000,0000,,So hopefully this starts to give you a sense of what it means
Dialogue: 0,0:09:25.32,0:09:29.03,Default,,0000,0000,0000,,to deal with or add and subtract negative numbers.
Dialogue: 0,0:09:29.03,0:09:31.34,Default,,0000,0000,0000,,But we are going to give a lot more examples in the next video.
Dialogue: 0,0:09:31.34,0:09:32.48,Default,,0000,0000,0000,,And we're actually going to see what it means
Dialogue: 0,0:09:32.48,0:09:35.34,Default,,0000,0000,0000,,to subtract a negative number.