[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.85,0:00:05.08,Default,,0000,0000,0000,,Welcome to the presentation on\Nwhy, not how, borrowing works.
Dialogue: 0,0:00:05.08,0:00:06.75,Default,,0000,0000,0000,,And I think this is very\Nimportant because a lot of
Dialogue: 0,0:00:06.75,0:00:11.50,Default,,0000,0000,0000,,people who even know math\Nfairly well or have an advanced
Dialogue: 0,0:00:11.50,0:00:15.63,Default,,0000,0000,0000,,degree still aren't completely\Nsure on why borrowing works.
Dialogue: 0,0:00:15.63,0:00:17.71,Default,,0000,0000,0000,,That's the focus of\Nthis presentation.
Dialogue: 0,0:00:17.71,0:00:20.50,Default,,0000,0000,0000,,Let's say I have the\Nsubtraction problem
Dialogue: 0,0:00:20.50,0:00:23.45,Default,,0000,0000,0000,,1,000-- that's a 0.
Dialogue: 0,0:00:23.45,0:00:31.84,Default,,0000,0000,0000,,1,005 minus 616.
Dialogue: 0,0:00:31.84,0:00:34.05,Default,,0000,0000,0000,,What I'm going to do is I'm\Ngoing to write the same problem
Dialogue: 0,0:00:34.05,0:00:35.30,Default,,0000,0000,0000,,in a slightly different way.
Dialogue: 0,0:00:35.30,0:00:37.64,Default,,0000,0000,0000,,We could call this\Nthe expanded form.
Dialogue: 0,0:00:37.64,0:00:40.08,Default,,0000,0000,0000,,1,005-- what I'm going to do\Nis I'm going to separate
Dialogue: 0,0:00:40.08,0:00:42.33,Default,,0000,0000,0000,,the digits out into\Ntheir respective places.
Dialogue: 0,0:00:42.33,0:00:49.72,Default,,0000,0000,0000,,So that is equal to 1,000\Nplus let's say zero 100's
Dialogue: 0,0:00:49.72,0:00:53.55,Default,,0000,0000,0000,,plus zero 10's plus 5.
Dialogue: 0,0:00:53.55,0:00:56.83,Default,,0000,0000,0000,,1,005 is just 1,000\Nplus 0 plus 0 plus 5.
Dialogue: 0,0:00:56.83,0:01:00.34,Default,,0000,0000,0000,,And then that's minus 616.
Dialogue: 0,0:01:00.34,0:01:08.91,Default,,0000,0000,0000,,So that's minus 600\Nminus 10 minus 6.
Dialogue: 0,0:01:08.91,0:01:13.44,Default,,0000,0000,0000,,616 could be rewritten\Nas 600 plus 10 plus 6.
Dialogue: 0,0:01:13.44,0:01:15.15,Default,,0000,0000,0000,,And I put a minus there\Nbecause we're subtracting
Dialogue: 0,0:01:15.15,0:01:16.13,Default,,0000,0000,0000,,the whole thing.
Dialogue: 0,0:01:16.13,0:01:18.94,Default,,0000,0000,0000,,So let's do this problem.
Dialogue: 0,0:01:18.94,0:01:23.22,Default,,0000,0000,0000,,Well, if you're familiar with\Nhow you borrow is, this 5 is
Dialogue: 0,0:01:23.22,0:01:25.94,Default,,0000,0000,0000,,less than this 6, so we have to\Nsomehow make this 5 a bigger
Dialogue: 0,0:01:25.94,0:01:28.22,Default,,0000,0000,0000,,number so that we could\Nsubtract the 6 from it.
Dialogue: 0,0:01:28.22,0:01:31.06,Default,,0000,0000,0000,,Well, we know from traditional\Nborrowing that we have to
Dialogue: 0,0:01:31.06,0:01:33.89,Default,,0000,0000,0000,,borrow 1 from someplace and\Nmake this it into a 15.
Dialogue: 0,0:01:33.89,0:01:36.24,Default,,0000,0000,0000,,But what I want to see\Nactually, is understand where
Dialogue: 0,0:01:36.24,0:01:38.53,Default,,0000,0000,0000,,that 1 or actually where\Nthat 10 comes from.
Dialogue: 0,0:01:38.53,0:01:41.09,Default,,0000,0000,0000,,Because if you're turning this\N5 into a 15 you actually
Dialogue: 0,0:01:41.09,0:01:43.09,Default,,0000,0000,0000,,have to add 10 to it.
Dialogue: 0,0:01:43.09,0:01:45.55,Default,,0000,0000,0000,,Well, if we look at this top\Nnumber, the only place that
Dialogue: 0,0:01:45.55,0:01:49.97,Default,,0000,0000,0000,,a 10 could come from is\Nhere, is from this 1,000.
Dialogue: 0,0:01:49.97,0:01:52.95,Default,,0000,0000,0000,,But what we're going to do\Nsince this is the 1,000's
Dialogue: 0,0:01:52.95,0:01:57.04,Default,,0000,0000,0000,,place, instead of borrowing 10\Nfrom here, which would make it
Dialogue: 0,0:01:57.04,0:01:59.48,Default,,0000,0000,0000,,kind of a very messy problem,\NI'm going to borrow
Dialogue: 0,0:01:59.48,0:02:02.43,Default,,0000,0000,0000,,1,000 from here.
Dialogue: 0,0:02:02.43,0:02:03.96,Default,,0000,0000,0000,,I'm going to get\Nrid of this 1,000.
Dialogue: 0,0:02:03.96,0:02:08.11,Default,,0000,0000,0000,,And I have a 1,000 that\NI took from this 1,000.
Dialogue: 0,0:02:08.11,0:02:12.74,Default,,0000,0000,0000,,I have 1,000 now that\NI can distribute into
Dialogue: 0,0:02:12.74,0:02:14.79,Default,,0000,0000,0000,,these 3 buckets.
Dialogue: 0,0:02:14.79,0:02:17.36,Default,,0000,0000,0000,,Into the 100's, 10's\Nand 1's buckets.
Dialogue: 0,0:02:17.36,0:02:21.27,Default,,0000,0000,0000,,Well, we need 10 here,\Nso let's put 10 here.
Dialogue: 0,0:02:21.27,0:02:24.32,Default,,0000,0000,0000,,So it's 10 plus 5\Nis equal to 15.
Dialogue: 0,0:02:24.32,0:02:25.04,Default,,0000,0000,0000,,We got our 15.
Dialogue: 0,0:02:25.04,0:02:31.54,Default,,0000,0000,0000,,If we took 10 from the 1,000\Nthen we have 990 left.
Dialogue: 0,0:02:32.03,0:02:37.96,Default,,0000,0000,0000,,So we could put 900\Nhere and 90 here.
Dialogue: 0,0:02:37.96,0:02:41.25,Default,,0000,0000,0000,,Notice, we just said-- so we\Nhad 1,000 and we just rewrote
Dialogue: 0,0:02:41.25,0:02:44.04,Default,,0000,0000,0000,,it as 900 plus 90 plus 10.
Dialogue: 0,0:02:44.04,0:02:45.67,Default,,0000,0000,0000,,And we added this 10 to this 5.
Dialogue: 0,0:02:45.67,0:02:47.67,Default,,0000,0000,0000,,And now we could do this\Nsubtraction just how we
Dialogue: 0,0:02:47.67,0:02:49.11,Default,,0000,0000,0000,,would do a normal problem.
Dialogue: 0,0:02:49.11,0:02:52.71,Default,,0000,0000,0000,,15 minus 6 is 9.
Dialogue: 0,0:02:52.71,0:02:56.30,Default,,0000,0000,0000,,90 minus 10 is 80.
Dialogue: 0,0:02:56.30,0:03:00.73,Default,,0000,0000,0000,,900 minus 600 is 300.
Dialogue: 0,0:03:00.73,0:03:06.55,Default,,0000,0000,0000,,So 300 plus 80 plus 9 is 389.
Dialogue: 0,0:03:06.55,0:03:08.94,Default,,0000,0000,0000,,And let's see how we would have\Ndone it traditionally and make
Dialogue: 0,0:03:08.94,0:03:12.79,Default,,0000,0000,0000,,sure that it would have kind of\Ntranslated into the same way.
Dialogue: 0,0:03:12.79,0:03:15.21,Default,,0000,0000,0000,,Well, the way I teach it and I\Ndon't know if this is actually
Dialogue: 0,0:03:15.21,0:03:20.44,Default,,0000,0000,0000,,the traditional way of teaching\Nborrowing, is I say, OK, I need
Dialogue: 0,0:03:20.44,0:03:23.48,Default,,0000,0000,0000,,to turn this 5 into a 15.
Dialogue: 0,0:03:23.48,0:03:25.22,Default,,0000,0000,0000,,So I have to borrow\Na 1 from someplace.
Dialogue: 0,0:03:25.22,0:03:26.84,Default,,0000,0000,0000,,Well, we know from this side of\Nthe problem that we actually
Dialogue: 0,0:03:26.84,0:03:28.63,Default,,0000,0000,0000,,borrowed a 10 because that's\Nwhy it turned to 15.
Dialogue: 0,0:03:28.63,0:03:30.54,Default,,0000,0000,0000,,If we're going to borrow\N1, I'd say, well, can I
Dialogue: 0,0:03:30.54,0:03:31.66,Default,,0000,0000,0000,,borrow the 1 from the 0?
Dialogue: 0,0:03:31.66,0:03:32.10,Default,,0000,0000,0000,,No.
Dialogue: 0,0:03:32.10,0:03:33.73,Default,,0000,0000,0000,,Can I borrow the 1 from this 0?
Dialogue: 0,0:03:33.73,0:03:34.44,Default,,0000,0000,0000,,No.
Dialogue: 0,0:03:34.44,0:03:36.63,Default,,0000,0000,0000,,I could borrow it from\Nhere, but I'm borrowing
Dialogue: 0,0:03:36.63,0:03:38.98,Default,,0000,0000,0000,,it from 100, right?
Dialogue: 0,0:03:38.98,0:03:43.11,Default,,0000,0000,0000,,So 100 minus 1 is 99.
Dialogue: 0,0:03:43.11,0:03:44.50,Default,,0000,0000,0000,,So that's the how I do it.
Dialogue: 0,0:03:44.50,0:03:47.56,Default,,0000,0000,0000,,And I say 15 minus 6 is 9.
Dialogue: 0,0:03:47.56,0:03:49.37,Default,,0000,0000,0000,,9 minus 1 is 8.
Dialogue: 0,0:03:49.37,0:03:51.57,Default,,0000,0000,0000,,And 9 minus 6 is 300.
Dialogue: 0,0:03:51.57,0:03:55.60,Default,,0000,0000,0000,,So this way that I just did it\Nis clearly faster and, I guess
Dialogue: 0,0:03:55.60,0:03:57.78,Default,,0000,0000,0000,,you could say it's easier, but\Na lot of people might say, well
Dialogue: 0,0:03:57.78,0:03:59.20,Default,,0000,0000,0000,,Sal, that looks like a\Nlittle bit of magic.
Dialogue: 0,0:03:59.20,0:04:02.16,Default,,0000,0000,0000,,You just took that 5, put a 1\Non it, and then you borrowed
Dialogue: 0,0:04:02.16,0:04:04.60,Default,,0000,0000,0000,,a 1 from this 100 here.
Dialogue: 0,0:04:04.60,0:04:07.08,Default,,0000,0000,0000,,But really, what I\Ndid is right here.
Dialogue: 0,0:04:07.08,0:04:12.60,Default,,0000,0000,0000,,I took 1,000 from this 1\Nand I redistributed that
Dialogue: 0,0:04:12.60,0:04:17.05,Default,,0000,0000,0000,,1,000 amongst the 100's,\N10's, and 1's place.
Dialogue: 0,0:04:17.05,0:04:18.30,Default,,0000,0000,0000,,Let me do another example.
Dialogue: 0,0:04:18.30,0:04:20.42,Default,,0000,0000,0000,,I think it might make it a\Nlittle bit more clearer
Dialogue: 0,0:04:20.42,0:04:22.53,Default,,0000,0000,0000,,of why borrowing works.
Dialogue: 0,0:04:25.33,0:04:27.42,Default,,0000,0000,0000,,Let me do a simpler problem.
Dialogue: 0,0:04:27.44,0:04:29.21,Default,,0000,0000,0000,,I actually started off with a\Nproblem that tends to confuse
Dialogue: 0,0:04:29.21,0:04:30.67,Default,,0000,0000,0000,,the most number of people.
Dialogue: 0,0:04:30.67,0:04:32.72,Default,,0000,0000,0000,,Let's say I had
Dialogue: 0,0:04:34.32,0:04:38.45,Default,,0000,0000,0000,,732
Dialogue: 0,0:04:40.90,0:04:45.29,Default,,0000,0000,0000,,minus-- Let\Nme do a fairly simple one.
Dialogue: 0,0:04:45.29,0:04:48.96,Default,,0000,0000,0000,,Minus 23.
Dialogue: 0,0:04:48.96,0:04:51.18,Default,,0000,0000,0000,,Sometimes those 3's\Njust come out weird.
Dialogue: 0,0:04:51.18,0:04:55.12,Default,,0000,0000,0000,,Well, we just learned that's\Nthe same thing as 700 plus
Dialogue: 0,0:04:55.12,0:05:03.24,Default,,0000,0000,0000,,30 plus 2 minus 20 minus 3.
Dialogue: 0,0:05:03.24,0:05:07.15,Default,,0000,0000,0000,,Well, we see this 2, 2 is less\Nthan 3, so we can't subtract.
Dialogue: 0,0:05:07.15,0:05:09.05,Default,,0000,0000,0000,,Wouldn't it be great if we\Ncould get a 10 from someplace?
Dialogue: 0,0:05:09.05,0:05:10.87,Default,,0000,0000,0000,,We could get a 10 from here.
Dialogue: 0,0:05:10.87,0:05:16.96,Default,,0000,0000,0000,,We make this into 20 and add\Nthe 10 to the 2 and we get 12.
Dialogue: 0,0:05:16.96,0:05:21.94,Default,,0000,0000,0000,,And notice, 700 plus 20\Nplus 12 is still 732.
Dialogue: 0,0:05:21.94,0:05:24.42,Default,,0000,0000,0000,,So we really didn't change\Nthe number up top at all.
Dialogue: 0,0:05:24.42,0:05:28.52,Default,,0000,0000,0000,,We just redistributed its\Nquantity amongst the
Dialogue: 0,0:05:28.52,0:05:29.20,Default,,0000,0000,0000,,different places.
Dialogue: 0,0:05:29.20,0:05:30.26,Default,,0000,0000,0000,,And now we're ready\Nto subtract.
Dialogue: 0,0:05:30.26,0:05:32.34,Default,,0000,0000,0000,,12 minus 3 is 9.
Dialogue: 0,0:05:32.34,0:05:36.61,Default,,0000,0000,0000,,20 minus 20 is 0 and then you\Njust bring down the 700.
Dialogue: 0,0:05:36.61,0:05:42.19,Default,,0000,0000,0000,,You get 700 plus 0 plus 9,\Nwhich is the same thing as 709.
Dialogue: 0,0:05:42.19,0:05:45.26,Default,,0000,0000,0000,,And that's the reason why\Nthis borrowing will work.
Dialogue: 0,0:05:45.26,0:05:47.38,Default,,0000,0000,0000,,Well, we say, oh, let's\Nborrow 1 from the 3.
Dialogue: 0,0:05:47.38,0:05:48.29,Default,,0000,0000,0000,,Makes it a 2.
Dialogue: 0,0:05:48.29,0:05:49.75,Default,,0000,0000,0000,,This becomes a 12.
Dialogue: 0,0:05:49.75,0:05:52.20,Default,,0000,0000,0000,,And then we subtract.
Dialogue: 0,0:05:52.20,0:05:54.52,Default,,0000,0000,0000,,9 0 7.
Dialogue: 0,0:05:54.52,0:05:57.37,Default,,0000,0000,0000,,Let's do another\Nproblem, one last one.
Dialogue: 0,0:05:57.37,0:05:59.16,Default,,0000,0000,0000,,And once again, you don't\Nhave to do it this way.
Dialogue: 0,0:05:59.16,0:06:00.85,Default,,0000,0000,0000,,You don't have to every\Ntime you do a subtraction
Dialogue: 0,0:06:00.85,0:06:01.48,Default,,0000,0000,0000,,problem do it this way.
Dialogue: 0,0:06:01.48,0:06:03.52,Default,,0000,0000,0000,,Although if you ever get\Nconfused, you can do it this
Dialogue: 0,0:06:03.52,0:06:05.70,Default,,0000,0000,0000,,way and you won't make a\Nmistake, and you'll actually
Dialogue: 0,0:06:05.70,0:06:06.99,Default,,0000,0000,0000,,understand what you're doing.
Dialogue: 0,0:06:06.99,0:06:08.93,Default,,0000,0000,0000,,But if you're on a test and you\Nhave to do things really fast
Dialogue: 0,0:06:08.93,0:06:10.86,Default,,0000,0000,0000,,you should do it the\Nconventional way.
Dialogue: 0,0:06:10.86,0:06:13.57,Default,,0000,0000,0000,,But it takes a lot of practice\Nto make sure you never are
Dialogue: 0,0:06:13.57,0:06:15.71,Default,,0000,0000,0000,,doing something improper.
Dialogue: 0,0:06:15.71,0:06:16.39,Default,,0000,0000,0000,,And that's the problem.
Dialogue: 0,0:06:16.39,0:06:18.28,Default,,0000,0000,0000,,People learn just the rules,\Nand then they forget the
Dialogue: 0,0:06:18.28,0:06:19.98,Default,,0000,0000,0000,,rules, and then they\Nforgot how to do it.
Dialogue: 0,0:06:19.98,0:06:22.62,Default,,0000,0000,0000,,If you learn what you're doing,\Nyou'll never really forget it
Dialogue: 0,0:06:22.62,0:06:25.54,Default,,0000,0000,0000,,because it should make\Nsome sense to you.
Dialogue: 0,0:06:26.19,0:06:28.70,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:06:28.70,0:06:32.18,Default,,0000,0000,0000,,If I had 512
Dialogue: 0,0:06:32.18,0:06:36.18,Default,,0000,0000,0000,,minus 38
Dialogue: 0,0:06:36.18,0:06:38.35,Default,,0000,0000,0000,,Well, let's keep doing it\Nthat way I just showed you.
Dialogue: 0,0:06:38.35,0:06:45.02,Default,,0000,0000,0000,,That's the same thing\Nas 500 plus 10 plus
Dialogue: 0,0:06:45.02,0:06:51.08,Default,,0000,0000,0000,,2 minus 30 minus 8.
Dialogue: 0,0:06:51.08,0:06:52.13,Default,,0000,0000,0000,,Well, 2 is less than 8.
Dialogue: 0,0:06:52.13,0:06:53.29,Default,,0000,0000,0000,,I need a 10 from someplace.
Dialogue: 0,0:06:53.29,0:06:55.29,Default,,0000,0000,0000,,Well, one option we can\Ndo is we can just get
Dialogue: 0,0:06:55.29,0:06:56.60,Default,,0000,0000,0000,,the 10 from here.
Dialogue: 0,0:06:56.60,0:06:58.72,Default,,0000,0000,0000,,So then that becomes 0.
Dialogue: 0,0:06:58.72,0:07:00.22,Default,,0000,0000,0000,,And then this will become a 12.
Dialogue: 0,0:07:00.22,0:07:05.37,Default,,0000,0000,0000,,Notice that 500 plus 0 plus\N12, same thing as 512 still.
Dialogue: 0,0:07:05.37,0:07:06.27,Default,,0000,0000,0000,,So we could subtract.
Dialogue: 0,0:07:06.27,0:07:09.77,Default,,0000,0000,0000,,12 minus 8 is 4.
Dialogue: 0,0:07:09.77,0:07:14.86,Default,,0000,0000,0000,,But here we see this 0 is less\Nthan 30, so we can't subtract.
Dialogue: 0,0:07:14.86,0:07:17.29,Default,,0000,0000,0000,,But we can borrow from the 500.
Dialogue: 0,0:07:17.29,0:07:22.93,Default,,0000,0000,0000,,Well, all we need is 100, so if\Nwe turn this into 100 then we
Dialogue: 0,0:07:22.93,0:07:25.26,Default,,0000,0000,0000,,took the 100 from the 500.
Dialogue: 0,0:07:25.26,0:07:28.07,Default,,0000,0000,0000,,This becomes 400.
Dialogue: 0,0:07:28.07,0:07:31.43,Default,,0000,0000,0000,,I just rewrote 500\Nas 400 plus 100.
Dialogue: 0,0:07:31.43,0:07:32.34,Default,,0000,0000,0000,,Now I can subtract.
Dialogue: 0,0:07:32.34,0:07:35.51,Default,,0000,0000,0000,,100 minus 30 is 70.
Dialogue: 0,0:07:35.51,0:07:38.79,Default,,0000,0000,0000,,Bring down the 400.
Dialogue: 0,0:07:38.79,0:07:42.56,Default,,0000,0000,0000,,And this is the\Nsame thing as 474.
Dialogue: 0,0:07:42.56,0:07:44.49,Default,,0000,0000,0000,,And the way you learn how to do\Nit in school is you say, oh,
Dialogue: 0,0:07:44.49,0:07:47.82,Default,,0000,0000,0000,,well, 2 is less than 8,\Nso let me borrow the 1.
Dialogue: 0,0:07:47.82,0:07:48.93,Default,,0000,0000,0000,,It becomes 12.
Dialogue: 0,0:07:48.93,0:07:50.89,Default,,0000,0000,0000,,This becomes a 0.
Dialogue: 0,0:07:50.89,0:07:56.12,Default,,0000,0000,0000,,0 is less than 3, so let\Nme borrow 1 from this 5.
Dialogue: 0,0:07:56.12,0:07:57.14,Default,,0000,0000,0000,,Make this 4.
Dialogue: 0,0:07:57.14,0:07:58.71,Default,,0000,0000,0000,,This becomes 10.
Dialogue: 0,0:07:58.71,0:08:01.27,Default,,0000,0000,0000,,So then you say\N12 minus 8 is 4.
Dialogue: 0,0:08:01.27,0:08:05.78,Default,,0000,0000,0000,,10 minus 3 is 7 and\Nyou bring down the 4.
Dialogue: 0,0:08:05.78,0:08:09.40,Default,,0000,0000,0000,,Hopefully what I've done here\Nwill give you an intuition
Dialogue: 0,0:08:09.40,0:08:10.51,Default,,0000,0000,0000,,of why borrowing works.
Dialogue: 0,0:08:10.51,0:08:12.76,Default,,0000,0000,0000,,And this is something that\Nactually I didn't quite
Dialogue: 0,0:08:12.76,0:08:16.69,Default,,0000,0000,0000,,understand until a while after\NI learned how to borrow.
Dialogue: 0,0:08:16.69,0:08:19.65,Default,,0000,0000,0000,,And if you learned this, you'll\Nrealize that what you're doing
Dialogue: 0,0:08:19.65,0:08:21.26,Default,,0000,0000,0000,,here isn't really magic.
Dialogue: 0,0:08:21.26,0:08:23.78,Default,,0000,0000,0000,,And hopefully, you'll never\Nforget what you're actually
Dialogue: 0,0:08:23.78,0:08:25.40,Default,,0000,0000,0000,,doing and you can always\Nkind of think about what's
Dialogue: 0,0:08:25.40,0:08:28.90,Default,,0000,0000,0000,,fundamentally happening to\Nthe numbers when you borrow.
Dialogue: 0,0:08:28.90,0:08:31.58,Default,,0000,0000,0000,,I hope you found that useful.
Dialogue: 0,0:08:31.58,0:08:32.40,Default,,0000,0000,0000,,Talk to later.
Dialogue: 0,0:08:32.40,0:08:33.70,Default,,0000,0000,0000,,Bye.