[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.57,0:00:03.11,Default,,0000,0000,0000,,Let's say that we have the\Nnumber 5, and we're asked,
Dialogue: 0,0:00:03.11,0:00:07.87,Default,,0000,0000,0000,,what number do we add to\Nthe number 5 to get to 0?
Dialogue: 0,0:00:07.87,0:00:10.62,Default,,0000,0000,0000,,And you might already know\Nthis, but I'll just draw it out.
Dialogue: 0,0:00:10.62,0:00:13.90,Default,,0000,0000,0000,,So let's say we have a\Nnumber line right over here.
Dialogue: 0,0:00:13.90,0:00:16.30,Default,,0000,0000,0000,,And 0 is sitting\Nright over there.
Dialogue: 0,0:00:16.30,0:00:19.74,Default,,0000,0000,0000,,And we are already\Nsitting here at 5.
Dialogue: 0,0:00:19.74,0:00:23.100,Default,,0000,0000,0000,,So to go from 5 to 0, we have\Nto go five spaces to the left.
Dialogue: 0,0:00:27.71,0:00:29.55,Default,,0000,0000,0000,,And if we're going five\Nspaces to the left,
Dialogue: 0,0:00:29.55,0:00:32.40,Default,,0000,0000,0000,,that means that we\Nare adding negative 5.
Dialogue: 0,0:00:32.40,0:00:34.78,Default,,0000,0000,0000,,So if we add negative\N5 right here,
Dialogue: 0,0:00:34.78,0:00:38.25,Default,,0000,0000,0000,,then that is going\Nto get us back to 0.
Dialogue: 0,0:00:38.25,0:00:40.75,Default,,0000,0000,0000,,That is going to get us\Nback right over here to 0.
Dialogue: 0,0:00:40.75,0:00:42.68,Default,,0000,0000,0000,,And you probably\Nalready knew this.
Dialogue: 0,0:00:42.68,0:00:45.90,Default,,0000,0000,0000,,And this is a pretty maybe\Ncommon sense thing right here.
Dialogue: 0,0:00:45.90,0:00:49.17,Default,,0000,0000,0000,,But there's a fancy word for\Nit called the additive inverse
Dialogue: 0,0:00:49.17,0:00:50.07,Default,,0000,0000,0000,,property.
Dialogue: 0,0:00:50.07,0:00:52.06,Default,,0000,0000,0000,,And all the additive--\NI'll just write it down.
Dialogue: 0,0:00:52.06,0:00:53.77,Default,,0000,0000,0000,,I think it's kind of\Nridiculous that it's
Dialogue: 0,0:00:53.77,0:00:55.94,Default,,0000,0000,0000,,given such a fancy word\Nfor such a simple idea--
Dialogue: 0,0:00:55.94,0:00:58.60,Default,,0000,0000,0000,,additive inverse property.
Dialogue: 0,0:00:58.60,0:01:00.65,Default,,0000,0000,0000,,And it's just the idea\Nthat if you have a number
Dialogue: 0,0:01:00.65,0:01:03.92,Default,,0000,0000,0000,,and you add the additive\Ninverse of the number, which
Dialogue: 0,0:01:03.92,0:01:06.32,Default,,0000,0000,0000,,is what most people call\Nthe negative of the number--
Dialogue: 0,0:01:06.32,0:01:08.53,Default,,0000,0000,0000,,if you add the negative of\Nthe number to your number,
Dialogue: 0,0:01:08.53,0:01:10.92,Default,,0000,0000,0000,,you're going to get back\Nto 0 because they have
Dialogue: 0,0:01:10.92,0:01:13.86,Default,,0000,0000,0000,,the same size, you\Ncould view it that way.
Dialogue: 0,0:01:13.86,0:01:16.19,Default,,0000,0000,0000,,They both have a magnitude\Nof 5, but this is going five
Dialogue: 0,0:01:16.19,0:01:20.06,Default,,0000,0000,0000,,to the right and then you're\Ngoing five back to the left.
Dialogue: 0,0:01:20.06,0:01:24.86,Default,,0000,0000,0000,,Similarly, if you started at--\Nlet me draw another number line
Dialogue: 0,0:01:24.86,0:01:29.31,Default,,0000,0000,0000,,right over here-- if you\Nstarted at negative 3.
Dialogue: 0,0:01:29.31,0:01:31.57,Default,,0000,0000,0000,,If you're starting right\Nover here at negative 3,
Dialogue: 0,0:01:31.57,0:01:34.04,Default,,0000,0000,0000,,so you've already moved\Nthree spaces to the left,
Dialogue: 0,0:01:34.04,0:01:39.03,Default,,0000,0000,0000,,and someone says, well what\Ndo I have to add to negative 3
Dialogue: 0,0:01:39.03,0:01:39.92,Default,,0000,0000,0000,,to get back to 0?
Dialogue: 0,0:01:39.92,0:01:42.66,Default,,0000,0000,0000,,Well, I have to move three\Nspaces to the right now.
Dialogue: 0,0:01:42.66,0:01:45.16,Default,,0000,0000,0000,,And three spaces to the right\Nis in the positive direction.
Dialogue: 0,0:01:45.16,0:01:47.54,Default,,0000,0000,0000,,So I have to add positive 3.
Dialogue: 0,0:01:47.54,0:01:51.27,Default,,0000,0000,0000,,So if I add positive 3 to\Nnegative 3, I will get 0.
Dialogue: 0,0:01:51.27,0:02:00.03,Default,,0000,0000,0000,,So in general, if I have any\Nnumber-- if I have 1,725,314
Dialogue: 0,0:02:00.03,0:02:03.17,Default,,0000,0000,0000,,and I say, what do I need to\Nadd to this to get back to 0?
Dialogue: 0,0:02:03.17,0:02:07.01,Default,,0000,0000,0000,,Well, I have to essentially\Ngo in the opposite direction.
Dialogue: 0,0:02:07.01,0:02:09.18,Default,,0000,0000,0000,,I have to go in the\Nleftwards direction.
Dialogue: 0,0:02:09.18,0:02:11.00,Default,,0000,0000,0000,,So I'm going to subtract\Nthe same amount.
Dialogue: 0,0:02:11.00,0:02:13.88,Default,,0000,0000,0000,,Or I could say, I'm going\Nto add the additive inverse,
Dialogue: 0,0:02:13.88,0:02:16.27,Default,,0000,0000,0000,,or I'm going to add the\Nnegative version of it.
Dialogue: 0,0:02:16.27,0:02:18.69,Default,,0000,0000,0000,,So this is going to be\Nthe same thing as adding
Dialogue: 0,0:02:18.69,0:02:26.23,Default,,0000,0000,0000,,negative 1,725,314 and\Nthat'll just get me back to 0.
Dialogue: 0,0:02:26.23,0:02:29.85,Default,,0000,0000,0000,,Similarly, if I say, what number\Ndo I have to add to negative 7
Dialogue: 0,0:02:29.85,0:02:30.41,Default,,0000,0000,0000,,to get to 0?
Dialogue: 0,0:02:30.41,0:02:33.43,Default,,0000,0000,0000,,Well, if I'm already at negative\N7, I have to go 7 to the right
Dialogue: 0,0:02:33.43,0:02:35.51,Default,,0000,0000,0000,,so I have to add positive 7.
Dialogue: 0,0:02:35.51,0:02:39.08,Default,,0000,0000,0000,,And this is going\Nto be equal to 0.
Dialogue: 0,0:02:39.08,0:02:41.46,Default,,0000,0000,0000,,And this all comes\Nfrom the general idea
Dialogue: 0,0:02:41.46,0:02:44.97,Default,,0000,0000,0000,,5 plus negative 5, 5\Nplus the negative of 5,
Dialogue: 0,0:02:44.97,0:02:47.41,Default,,0000,0000,0000,,or 5 plus the\Nadditive inverse of 5,
Dialogue: 0,0:02:47.41,0:02:51.31,Default,,0000,0000,0000,,you can just view this as\Nanother way of 5 minus 5.
Dialogue: 0,0:02:51.31,0:02:52.73,Default,,0000,0000,0000,,And if you have\Nfive of something,
Dialogue: 0,0:02:52.73,0:02:55.54,Default,,0000,0000,0000,,and you take away five, you've\Nlearned many, many years ago
Dialogue: 0,0:02:55.54,0:02:58.52,Default,,0000,0000,0000,,that that is just\Ngoing to get you to 0.