[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.78,0:00:05.70,Default,,0000,0000,0000,,Welcome to the video\Non basic subtraction.
Dialogue: 0,0:00:05.70,0:00:10.34,Default,,0000,0000,0000,,Let's do a little bit a review\Nof basic addition first.
Dialogue: 0,0:00:10.34,0:00:15.57,Default,,0000,0000,0000,,If I said 4 plus 3,\Nwhat did this mean?
Dialogue: 0,0:00:19.05,0:00:20.70,Default,,0000,0000,0000,,What did that equal?
Dialogue: 0,0:00:20.70,0:00:22.94,Default,,0000,0000,0000,,Well, there were a couple of\Nways we could have viewed this.
Dialogue: 0,0:00:22.94,0:00:24.64,Default,,0000,0000,0000,,We could have said I\Nhad 4 of something.
Dialogue: 0,0:00:24.64,0:00:28.10,Default,,0000,0000,0000,,Let's say I had 4 circles\Nor I don't know, I had
Dialogue: 0,0:00:28.10,0:00:30.16,Default,,0000,0000,0000,,4 lemons for breakfast.
Dialogue: 0,0:00:30.16,0:00:36.18,Default,,0000,0000,0000,,So 1, 2, 3, 4 lemons\Nfor breakfast.
Dialogue: 0,0:00:36.18,0:00:40.76,Default,,0000,0000,0000,,And let's say, I had another\N3 lemons for lunch.
Dialogue: 0,0:00:40.76,0:00:46.00,Default,,0000,0000,0000,,1, 2, 3, and so you could\Nview 4 plus 3 as how many
Dialogue: 0,0:00:46.00,0:00:47.75,Default,,0000,0000,0000,,total lemons did I have?
Dialogue: 0,0:00:47.75,0:00:49.64,Default,,0000,0000,0000,,I'm adding 3 to 4.
Dialogue: 0,0:00:49.64,0:00:50.90,Default,,0000,0000,0000,,So how many total did I have?
Dialogue: 0,0:00:50.90,0:00:55.36,Default,,0000,0000,0000,,Well, it's 1, 2, 3, 4, 5, 6, 7.
Dialogue: 0,0:00:55.36,0:00:59.19,Default,,0000,0000,0000,,So I had a total of 7 lemons.
Dialogue: 0,0:00:59.19,0:01:01.44,Default,,0000,0000,0000,,Another way we could have\Nviewed that is we could have
Dialogue: 0,0:01:01.44,0:01:04.06,Default,,0000,0000,0000,,drawn our number line.
Dialogue: 0,0:01:04.06,0:01:07.24,Default,,0000,0000,0000,,And I'll draw it in yellow\Nbecause-- now that's
Dialogue: 0,0:01:07.24,0:01:09.72,Default,,0000,0000,0000,,not wide enough.
Dialogue: 0,0:01:09.72,0:01:13.71,Default,,0000,0000,0000,,I'll draw it in yellow because\Nwe're talking about lemons.
Dialogue: 0,0:01:13.71,0:01:15.36,Default,,0000,0000,0000,,So let's say that's\Nour number line.
Dialogue: 0,0:01:18.07,0:01:21.35,Default,,0000,0000,0000,,And if I start at the number--\Nlet me draw all of the numbers.
Dialogue: 0,0:01:21.35,0:01:32.02,Default,,0000,0000,0000,,0, 1, 2, 3, 4, 5, 6, 7.
Dialogue: 0,0:01:32.02,0:01:34.47,Default,,0000,0000,0000,,So you could think about\Nthis as saying, well,
Dialogue: 0,0:01:34.47,0:01:35.38,Default,,0000,0000,0000,,we're on the number line.
Dialogue: 0,0:01:35.38,0:01:37.95,Default,,0000,0000,0000,,We start at the number 4.
Dialogue: 0,0:01:37.95,0:01:39.13,Default,,0000,0000,0000,,That's this number 4.
Dialogue: 0,0:01:39.13,0:01:40.70,Default,,0000,0000,0000,,And we're adding 3 to it.
Dialogue: 0,0:01:40.70,0:01:44.17,Default,,0000,0000,0000,,So we'll increase, along\Nthe number line by 3.
Dialogue: 0,0:01:44.17,0:01:48.65,Default,,0000,0000,0000,,So we'll go 1, 2, 3\Nand you end up at 7.
Dialogue: 0,0:01:48.65,0:01:51.92,Default,,0000,0000,0000,,So you could say if I have 4\Nand I get 3 more, I get 7.
Dialogue: 0,0:01:51.92,0:01:57.13,Default,,0000,0000,0000,,Or if I increase 4\Nby 3 I also get 7.
Dialogue: 0,0:01:57.13,0:01:59.35,Default,,0000,0000,0000,,So what's subtraction now?
Dialogue: 0,0:01:59.35,0:02:00.45,Default,,0000,0000,0000,,Because that's what\Nthis video is about.
Dialogue: 0,0:02:00.45,0:02:03.03,Default,,0000,0000,0000,,I shouldn't waste all of our\Ntime talking about addition.
Dialogue: 0,0:02:03.03,0:02:05.92,Default,,0000,0000,0000,,So let's take the\Nexample of 4 minus 3.
Dialogue: 0,0:02:05.92,0:02:08.50,Default,,0000,0000,0000,,What is that equal to?
Dialogue: 0,0:02:08.50,0:02:11.54,Default,,0000,0000,0000,,Let me switch colors just to\Nkeep things interesting.
Dialogue: 0,0:02:11.54,0:02:18.86,Default,,0000,0000,0000,,So what is 4 minus 3 equal to?
Dialogue: 0,0:02:18.86,0:02:23.05,Default,,0000,0000,0000,,Subtraction or minus is\Nthe opposite of addition.
Dialogue: 0,0:02:23.05,0:02:26.99,Default,,0000,0000,0000,,So in addition you're doing\Nsomething more, you're adding.
Dialogue: 0,0:02:26.99,0:02:29.85,Default,,0000,0000,0000,,I don't want to use the word\Nadding to define addition, but
Dialogue: 0,0:02:29.85,0:02:31.04,Default,,0000,0000,0000,,that's what you're doing.
Dialogue: 0,0:02:31.04,0:02:33.89,Default,,0000,0000,0000,,I had 4 lemons and\Nthen I had 3 more.
Dialogue: 0,0:02:33.89,0:02:36.28,Default,,0000,0000,0000,,In subtraction\Nyou're taking away.
Dialogue: 0,0:02:36.28,0:02:42.92,Default,,0000,0000,0000,,So this example, if I started\Nwith 4 lemons, let's say I
Dialogue: 0,0:02:42.92,0:02:45.21,Default,,0000,0000,0000,,had 4 lemons on a plate.
Dialogue: 0,0:02:45.21,0:02:50.07,Default,,0000,0000,0000,,If I'm subtracting 3, if I'm\Nsaying minus 3, instead of
Dialogue: 0,0:02:50.07,0:02:53.72,Default,,0000,0000,0000,,adding these 3 and getting 7,\NI'm going to take 3 away.
Dialogue: 0,0:02:53.72,0:02:55.91,Default,,0000,0000,0000,,So maybe I'm eating them\Nor maybe I'm giving them
Dialogue: 0,0:02:55.91,0:02:59.76,Default,,0000,0000,0000,,to you in exchange for\Nwatching these videos.
Dialogue: 0,0:02:59.76,0:03:04.26,Default,,0000,0000,0000,,So to take away 3 from this 4,\Nlet's say this one goes away,
Dialogue: 0,0:03:04.26,0:03:06.91,Default,,0000,0000,0000,,this one goes away, and\Nthis one goes away.
Dialogue: 0,0:03:06.91,0:03:09.90,Default,,0000,0000,0000,,How many lemons\Nwould we have left?
Dialogue: 0,0:03:09.90,0:03:11.82,Default,,0000,0000,0000,,Well, this is the only one\Nthat I haven't crossed out.
Dialogue: 0,0:03:11.82,0:03:13.98,Default,,0000,0000,0000,,So we would have 1 lemon left.
Dialogue: 0,0:03:16.57,0:03:18.12,Default,,0000,0000,0000,,And this would be the\Nlemon that's left.
Dialogue: 0,0:03:18.12,0:03:19.44,Default,,0000,0000,0000,,Didn't have to be that\None, I could have crossed
Dialogue: 0,0:03:19.44,0:03:21.21,Default,,0000,0000,0000,,out any of the 3.
Dialogue: 0,0:03:21.21,0:03:24.52,Default,,0000,0000,0000,,Another way to view that,\Nlet's draw the same lemon
Dialogue: 0,0:03:24.52,0:03:28.04,Default,,0000,0000,0000,,colored number line.
Dialogue: 0,0:03:28.04,0:03:30.81,Default,,0000,0000,0000,,Let's say that this is the\Nnumber line right here.
Dialogue: 0,0:03:34.40,0:03:36.18,Default,,0000,0000,0000,,And I'll draw all\Nthe same numbers.
Dialogue: 0,0:03:36.18,0:03:47.24,Default,,0000,0000,0000,,So that's 0, 1, 2,\N3, 4, 5, 6, 7.
Dialogue: 0,0:03:47.24,0:03:49.53,Default,,0000,0000,0000,,Of course, the number\Nline keeps going.
Dialogue: 0,0:03:49.53,0:03:51.14,Default,,0000,0000,0000,,There's no largest number.
Dialogue: 0,0:03:51.14,0:03:55.19,Default,,0000,0000,0000,,And you can imagine, any number\Nthat you can think of, I can
Dialogue: 0,0:03:55.19,0:03:56.58,Default,,0000,0000,0000,,think of one higher than that.
Dialogue: 0,0:03:56.58,0:03:57.67,Default,,0000,0000,0000,,So there is no largest number.
Dialogue: 0,0:03:57.67,0:03:59.04,Default,,0000,0000,0000,,So that's why we draw\Nthat arrow there.
Dialogue: 0,0:03:59.04,0:04:00.73,Default,,0000,0000,0000,,I could never draw the\Nentire number line.
Dialogue: 0,0:04:00.73,0:04:03.02,Default,,0000,0000,0000,,But anyway, back\Nto subtraction.
Dialogue: 0,0:04:03.02,0:04:06.71,Default,,0000,0000,0000,,So we're starting at\N4 lemons, right?
Dialogue: 0,0:04:06.71,0:04:12.13,Default,,0000,0000,0000,,When we added 3-- plus 3-- we\Nwent to the right 4 spaces
Dialogue: 0,0:04:12.13,0:04:12.84,Default,,0000,0000,0000,,on the number line.
Dialogue: 0,0:04:12.84,0:04:15.09,Default,,0000,0000,0000,,And that's because the\Nright is increasing value.
Dialogue: 0,0:04:15.09,0:04:16.27,Default,,0000,0000,0000,,So we went from 4 to 5.
Dialogue: 0,0:04:16.27,0:04:17.45,Default,,0000,0000,0000,,That was one more.
Dialogue: 0,0:04:17.45,0:04:20.99,Default,,0000,0000,0000,,5 to 6 was two more,\Nand 7 was 3 more.
Dialogue: 0,0:04:20.99,0:04:23.51,Default,,0000,0000,0000,,Now we're taking away from 4.
Dialogue: 0,0:04:23.51,0:04:24.86,Default,,0000,0000,0000,,So what do we do?
Dialogue: 0,0:04:24.86,0:04:26.69,Default,,0000,0000,0000,,What would you think we do?
Dialogue: 0,0:04:26.69,0:04:29.58,Default,,0000,0000,0000,,Well, since we're taking away\Nwe're going to decrease the
Dialogue: 0,0:04:29.58,0:04:31.79,Default,,0000,0000,0000,,total number of lemons we have.
Dialogue: 0,0:04:31.79,0:04:33.68,Default,,0000,0000,0000,,So we take away\None, we get to 3.
Dialogue: 0,0:04:33.68,0:04:35.55,Default,,0000,0000,0000,,Take away two, get to 2.
Dialogue: 0,0:04:35.55,0:04:38.91,Default,,0000,0000,0000,,Take away three, we took\Naway three, right?
Dialogue: 0,0:04:38.91,0:04:41.98,Default,,0000,0000,0000,,So we'll go back 1, 2, 3\Nalong the number line
Dialogue: 0,0:04:41.98,0:04:44.21,Default,,0000,0000,0000,,and we'll end up at 1.
Dialogue: 0,0:04:44.21,0:04:47.34,Default,,0000,0000,0000,,And that's this 1 right here.
Dialogue: 0,0:04:47.34,0:04:52.34,Default,,0000,0000,0000,,So just to review, addition is\Nyou're doing more or something.
Dialogue: 0,0:04:52.34,0:04:55.12,Default,,0000,0000,0000,,Subtraction is you\Nare taking away.
Dialogue: 0,0:04:55.12,0:04:58.18,Default,,0000,0000,0000,,If you think about it on the\Nnumber line, addition is
Dialogue: 0,0:04:58.18,0:05:00.74,Default,,0000,0000,0000,,increasing along the number\Nline by that amount.
Dialogue: 0,0:05:00.74,0:05:04.20,Default,,0000,0000,0000,,So in this case we increased\Nalong the number line by 3.
Dialogue: 0,0:05:04.20,0:05:06.34,Default,,0000,0000,0000,,And so we went from 4 to 7.
Dialogue: 0,0:05:06.34,0:05:10.17,Default,,0000,0000,0000,,In the subtraction case\Nwe decrease back on
Dialogue: 0,0:05:10.17,0:05:11.35,Default,,0000,0000,0000,,the number line.
Dialogue: 0,0:05:11.35,0:05:13.55,Default,,0000,0000,0000,,So we decrease by the amount\Nthat you're subtracting.
Dialogue: 0,0:05:13.55,0:05:17.48,Default,,0000,0000,0000,,So in this case we\Ndecreased by 3.
Dialogue: 0,0:05:17.48,0:05:21.18,Default,,0000,0000,0000,,We went back 1, 2,\N3 and we had 1.
Dialogue: 0,0:05:21.18,0:05:22.74,Default,,0000,0000,0000,,And the other way to view it,\Nif I have 4 of something.
Dialogue: 0,0:05:22.74,0:05:26.58,Default,,0000,0000,0000,,If I give 3 away or if I ate\N3 of them or I don't know
Dialogue: 0,0:05:26.58,0:05:27.68,Default,,0000,0000,0000,,what I did to 3 of them.
Dialogue: 0,0:05:27.68,0:05:31.05,Default,,0000,0000,0000,,If I lost 3 of them I\Nwould have 1 left.
Dialogue: 0,0:05:31.05,0:05:33.26,Default,,0000,0000,0000,,Now let me show you some\Ninteresting things
Dialogue: 0,0:05:33.26,0:05:34.84,Default,,0000,0000,0000,,about subtraction.
Dialogue: 0,0:05:34.84,0:05:38.51,Default,,0000,0000,0000,,So we know that 4 minus\N3 is equal to 1.
Dialogue: 0,0:05:38.51,0:05:40.90,Default,,0000,0000,0000,,Let me show you something\Nelse that's interesting.
Dialogue: 0,0:05:40.90,0:05:46.05,Default,,0000,0000,0000,,What is 4 minus 1?
Dialogue: 0,0:05:46.05,0:05:49.51,Default,,0000,0000,0000,,Well, we could use\Neither example.
Dialogue: 0,0:05:49.51,0:05:51.44,Default,,0000,0000,0000,,Let's do the lemon example.
Dialogue: 0,0:05:51.44,0:05:54.13,Default,,0000,0000,0000,,Let's do apples now; I'm\Nbored of the lemons.
Dialogue: 0,0:05:54.13,0:06:01.16,Default,,0000,0000,0000,,Let's say I 1, 2, 3, 4.
Dialogue: 0,0:06:01.16,0:06:03.62,Default,,0000,0000,0000,,I have a new pen, sometimes\Nit doesn't draw right.
Dialogue: 0,0:06:03.62,0:06:05.39,Default,,0000,0000,0000,,Let's say I had 4 apples.
Dialogue: 0,0:06:05.39,0:06:07.14,Default,,0000,0000,0000,,This is the example\Nwe're dealing with.
Dialogue: 0,0:06:07.14,0:06:09.45,Default,,0000,0000,0000,,And I were to eat one of them.
Dialogue: 0,0:06:09.45,0:06:10.83,Default,,0000,0000,0000,,So one of them were to go away.
Dialogue: 0,0:06:10.83,0:06:12.64,Default,,0000,0000,0000,,How many apples\Nwould I have left?
Dialogue: 0,0:06:12.64,0:06:15.56,Default,,0000,0000,0000,,Well, 3-- 1, 2, 3.
Dialogue: 0,0:06:15.56,0:06:18.60,Default,,0000,0000,0000,,So 4 minus 1 is equal to 3.
Dialogue: 0,0:06:18.60,0:06:21.64,Default,,0000,0000,0000,,And if we did it on the number\Nline, if we started at 4 and we
Dialogue: 0,0:06:21.64,0:06:23.78,Default,,0000,0000,0000,,subtracted 1-- we took 1 away.
Dialogue: 0,0:06:23.78,0:06:26.02,Default,,0000,0000,0000,,So we're going to\Nbecome one smaller.
Dialogue: 0,0:06:26.02,0:06:28.38,Default,,0000,0000,0000,,We go back one, we get 3.
Dialogue: 0,0:06:28.38,0:06:29.57,Default,,0000,0000,0000,,Either way works.
Dialogue: 0,0:06:29.57,0:06:30.82,Default,,0000,0000,0000,,But isn't this interesting?
Dialogue: 0,0:06:30.82,0:06:37.52,Default,,0000,0000,0000,,4 minus 3 is equal to 1 and\N4 minus 1 is equal to 3.
Dialogue: 0,0:06:37.52,0:06:41.07,Default,,0000,0000,0000,,You might say, well, did I pick\Nthe numbers just so it worked?
Dialogue: 0,0:06:41.07,0:06:42.79,Default,,0000,0000,0000,,Well, it turns out that\Nit's always true.
Dialogue: 0,0:06:45.36,0:06:47.44,Default,,0000,0000,0000,,Well, I don't want to get too\Ntechnical, but we're already
Dialogue: 0,0:06:47.44,0:06:50.86,Default,,0000,0000,0000,,touching on something that\Nyou'll learn later, maybe
Dialogue: 0,0:06:50.86,0:06:52.21,Default,,0000,0000,0000,,in algebra one day.
Dialogue: 0,0:06:52.21,0:06:54.84,Default,,0000,0000,0000,,But actually I don't want to\Ngo into all that right now.
Dialogue: 0,0:06:54.84,0:06:56.46,Default,,0000,0000,0000,,So where does this come from?
Dialogue: 0,0:06:56.46,0:07:02.17,Default,,0000,0000,0000,,Well, this is also based on\Nthe fact that 3 plus 1-- I
Dialogue: 0,0:07:02.17,0:07:03.66,Default,,0000,0000,0000,,didn't want to confuse you.
Dialogue: 0,0:07:03.66,0:07:05.70,Default,,0000,0000,0000,,So I apologize if I did.
Dialogue: 0,0:07:05.70,0:07:07.44,Default,,0000,0000,0000,,But I'll show you another\Ninteresting thing.
Dialogue: 0,0:07:07.44,0:07:10.61,Default,,0000,0000,0000,,What is 3 plus 1?
Dialogue: 0,0:07:10.61,0:07:12.71,Default,,0000,0000,0000,,3 plus 1 is equal to what?
Dialogue: 0,0:07:12.71,0:07:13.37,Default,,0000,0000,0000,,Well, that's easy.
Dialogue: 0,0:07:13.37,0:07:15.40,Default,,0000,0000,0000,,You know that from\Nbasic addition.
Dialogue: 0,0:07:15.40,0:07:20.72,Default,,0000,0000,0000,,You can start on the number\Nline at 3 and add 1 do it.
Dialogue: 0,0:07:20.72,0:07:22.00,Default,,0000,0000,0000,,And where do you end up?
Dialogue: 0,0:07:22.00,0:07:23.31,Default,,0000,0000,0000,,You end up at 4.
Dialogue: 0,0:07:23.31,0:07:25.06,Default,,0000,0000,0000,,3 plus 1 is equal to 4.
Dialogue: 0,0:07:25.06,0:07:29.42,Default,,0000,0000,0000,,Or you could have started at 1\Non the number line and added 3.
Dialogue: 0,0:07:29.42,0:07:33.16,Default,,0000,0000,0000,,1, 2, 3 and you would\Nhave also ended up at 4.
Dialogue: 0,0:07:33.16,0:07:36.69,Default,,0000,0000,0000,,So we also know that you could\Nhave switch this either way.
Dialogue: 0,0:07:36.69,0:07:38.88,Default,,0000,0000,0000,,Both of those are equal 4.
Dialogue: 0,0:07:38.88,0:07:40.14,Default,,0000,0000,0000,,What do you see here?
Dialogue: 0,0:07:40.14,0:07:42.63,Default,,0000,0000,0000,,Well, there's a bunch of things\NI've written here and they all
Dialogue: 0,0:07:42.63,0:07:43.93,Default,,0000,0000,0000,,kind of relate to each other.
Dialogue: 0,0:07:43.93,0:07:45.66,Default,,0000,0000,0000,,1 plus 3 is equal to 4.
Dialogue: 0,0:07:45.66,0:07:47.78,Default,,0000,0000,0000,,3 plus 1 is equal to 4.
Dialogue: 0,0:07:47.78,0:07:49.74,Default,,0000,0000,0000,,4 minus 1 is 3.
Dialogue: 0,0:07:49.74,0:07:53.92,Default,,0000,0000,0000,,Essentially, 4 minus 1 and\Ngetting 3 is the exact same--
Dialogue: 0,0:07:53.92,0:07:59.20,Default,,0000,0000,0000,,you're saying the same thing\Nas 3 plus 1 is equal to 4.
Dialogue: 0,0:07:59.20,0:08:03.17,Default,,0000,0000,0000,,This statement says if\NI add 1 to 3 I get 4.
Dialogue: 0,0:08:03.17,0:08:08.12,Default,,0000,0000,0000,,This is saying if I take\Naway 1 from 4 I get 3.
Dialogue: 0,0:08:08.12,0:08:10.60,Default,,0000,0000,0000,,So if I start at 4,\Nmove back, I get 3.
Dialogue: 0,0:08:10.60,0:08:15.28,Default,,0000,0000,0000,,This is saying if I start at\N3, and I move up 1, I get 4.
Dialogue: 0,0:08:15.28,0:08:17.60,Default,,0000,0000,0000,,Hopefully that gives you a\Nlittle bit of intuition
Dialogue: 0,0:08:17.60,0:08:19.67,Default,,0000,0000,0000,,about what subtraction is.
Dialogue: 0,0:08:19.67,0:08:24.87,Default,,0000,0000,0000,,In the next video I'll just do\Nas many basic subtraction
Dialogue: 0,0:08:24.87,0:08:27.80,Default,,0000,0000,0000,,problems I can do\Nin 10 minutes.
Dialogue: 0,0:08:27.80,0:08:30.03,Default,,0000,0000,0000,,And then you'll be ready\Nto do the exercises.
Dialogue: 0,0:08:30.03,0:08:31.53,Default,,0000,0000,0000,,See you soon.