[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.66,0:00:04.09,Default,,0000,0000,0000,,We've got 24 triangle\Nthings right over here.
Dialogue: 0,0:00:04.09,0:00:05.55,Default,,0000,0000,0000,,And what I want to\Ndo in this video
Dialogue: 0,0:00:05.55,0:00:09.13,Default,,0000,0000,0000,,is to divide it into\Ndifferent numbers of groups.
Dialogue: 0,0:00:09.13,0:00:10.60,Default,,0000,0000,0000,,So the first thing\NI want to do is
Dialogue: 0,0:00:10.60,0:00:16.76,Default,,0000,0000,0000,,I want to divide this 24\Ntriangle things into 3 groups
Dialogue: 0,0:00:16.76,0:00:20.02,Default,,0000,0000,0000,,and think about how many\Ndo I end up per group.
Dialogue: 0,0:00:20.02,0:00:21.66,Default,,0000,0000,0000,,So let's try that out.
Dialogue: 0,0:00:21.66,0:00:24.37,Default,,0000,0000,0000,,So I'm going to divide\Nit into 3 equal groups.
Dialogue: 0,0:00:24.37,0:00:28.45,Default,,0000,0000,0000,,So that is one equal\Ngroup right over there.
Dialogue: 0,0:00:28.45,0:00:32.47,Default,,0000,0000,0000,,Then I have another equal\Ngroup right over here.
Dialogue: 0,0:00:32.47,0:00:36.34,Default,,0000,0000,0000,,And then I have a third\Nequal group right over here.
Dialogue: 0,0:00:36.34,0:00:42.28,Default,,0000,0000,0000,,So if I divide 24 into 3 equal\Ngroups-- 1, 2, 3-- how many
Dialogue: 0,0:00:42.28,0:00:43.89,Default,,0000,0000,0000,,are going to be in each group?
Dialogue: 0,0:00:43.89,0:00:44.97,Default,,0000,0000,0000,,Well, we can count that.
Dialogue: 0,0:00:44.97,0:00:52.50,Default,,0000,0000,0000,,We have 1, 2, 3, 4, 5,\N6, 7, 8 in each group.
Dialogue: 0,0:00:52.50,0:00:59.24,Default,,0000,0000,0000,,So we could say that 24\Ndivided by 3 is equal to 8.
Dialogue: 0,0:00:59.24,0:01:00.78,Default,,0000,0000,0000,,Now, you might say,\Nhey, this is very
Dialogue: 0,0:01:00.78,0:01:02.49,Default,,0000,0000,0000,,similar to what we\Nsaw in multiplication.
Dialogue: 0,0:01:02.49,0:01:06.83,Default,,0000,0000,0000,,In multiplication, we said\Nif we have 3 groups of 8,
Dialogue: 0,0:01:06.83,0:01:10.72,Default,,0000,0000,0000,,we could view that as\N3 times 8 and get 24.
Dialogue: 0,0:01:10.72,0:01:12.04,Default,,0000,0000,0000,,And you are exactly right.
Dialogue: 0,0:01:14.67,0:01:18.94,Default,,0000,0000,0000,,Let me do those same colors--\Nwe could also write that 3
Dialogue: 0,0:01:18.94,0:01:25.62,Default,,0000,0000,0000,,times 8-- so if I\Nhave 3 groups of 8,
Dialogue: 0,0:01:25.62,0:01:32.04,Default,,0000,0000,0000,,that that is going\Nto be equal to 24.
Dialogue: 0,0:01:32.04,0:01:34.58,Default,,0000,0000,0000,,So when we started in this\Nvideo, we had 24 things.
Dialogue: 0,0:01:34.58,0:01:37.44,Default,,0000,0000,0000,,We want to divide it\Ninto 3 equal groups.
Dialogue: 0,0:01:37.44,0:01:42.78,Default,,0000,0000,0000,,We got 8 in each group, or you\Ncould say 3 equal groups of 8
Dialogue: 0,0:01:42.78,0:01:45.16,Default,,0000,0000,0000,,is equal to 24.
Dialogue: 0,0:01:45.16,0:01:47.62,Default,,0000,0000,0000,,But there's even other ways\Nof thinking about this.
Dialogue: 0,0:01:47.62,0:01:49.84,Default,,0000,0000,0000,,So let me clear this\Nup a little bit.
Dialogue: 0,0:01:49.84,0:01:51.39,Default,,0000,0000,0000,,So let me clear that.
Dialogue: 0,0:01:54.45,0:01:59.46,Default,,0000,0000,0000,,So in the first example, I\Ndivided 24 into 3 equal groups.
Dialogue: 0,0:01:59.46,0:02:02.73,Default,,0000,0000,0000,,But you could also\Nview 24 divided by 3
Dialogue: 0,0:02:02.73,0:02:05.50,Default,,0000,0000,0000,,as dividing 24 into groups of 3.
Dialogue: 0,0:02:05.50,0:02:07.89,Default,,0000,0000,0000,,So let's think about\Nwhat that looks like.
Dialogue: 0,0:02:07.89,0:02:10.68,Default,,0000,0000,0000,,So if we divide it\Ninto groups of 3,
Dialogue: 0,0:02:10.68,0:02:15.27,Default,,0000,0000,0000,,then, for example,\Nthis is a group of 3.
Dialogue: 0,0:02:15.27,0:02:17.86,Default,,0000,0000,0000,,That is a group of 3.
Dialogue: 0,0:02:17.86,0:02:19.49,Default,,0000,0000,0000,,This is a group of 3.
Dialogue: 0,0:02:19.49,0:02:20.91,Default,,0000,0000,0000,,You might see where\Nthis is going.
Dialogue: 0,0:02:20.91,0:02:23.05,Default,,0000,0000,0000,,That's a group of 3.
Dialogue: 0,0:02:23.05,0:02:25.43,Default,,0000,0000,0000,,That is another group of 3.
Dialogue: 0,0:02:25.43,0:02:27.57,Default,,0000,0000,0000,,And we're going to think\Nabout how many groups of 3
Dialogue: 0,0:02:27.57,0:02:29.19,Default,,0000,0000,0000,,we're actually going to get.
Dialogue: 0,0:02:29.19,0:02:32.78,Default,,0000,0000,0000,,So this is another group of 3.
Dialogue: 0,0:02:32.78,0:02:35.75,Default,,0000,0000,0000,,And that's another group of 3.
Dialogue: 0,0:02:35.75,0:02:38.49,Default,,0000,0000,0000,,So how many groups\Nof 3 did we get?
Dialogue: 0,0:02:38.49,0:02:45.12,Default,,0000,0000,0000,,Let's see, we have 1, 2, 3,\N4, 5, 6, 7, 8 groups of 3.
Dialogue: 0,0:02:45.12,0:02:50.58,Default,,0000,0000,0000,,So another way of\Nviewing 24 divided by 3
Dialogue: 0,0:02:50.58,0:02:54.45,Default,,0000,0000,0000,,is divide 24 into groups of 3.
Dialogue: 0,0:02:54.45,0:02:57.12,Default,,0000,0000,0000,,And then you will\Nhave 8 groups of 3.
Dialogue: 0,0:02:57.12,0:02:58.62,Default,,0000,0000,0000,,And one way of\Nthinking about this--
Dialogue: 0,0:02:58.62,0:03:01.90,Default,,0000,0000,0000,,if you want to express\Nthe same thing in terms
Dialogue: 0,0:03:01.90,0:03:03.55,Default,,0000,0000,0000,,of multiplication--\Nis if you have
Dialogue: 0,0:03:03.55,0:03:13.07,Default,,0000,0000,0000,,8 groups of 3, that is also\Ngoing to be equal to 24.
Dialogue: 0,0:03:13.07,0:03:18.14,Default,,0000,0000,0000,,Whether you have 3 groups\Nof 8 or 8 groups of 3,
Dialogue: 0,0:03:18.14,0:03:21.82,Default,,0000,0000,0000,,either way, you're\Ngoing to have 24.
Dialogue: 0,0:03:21.82,0:03:25.83,Default,,0000,0000,0000,,Now, let's make things\Nmore interesting.
Dialogue: 0,0:03:25.83,0:03:30.65,Default,,0000,0000,0000,,What I want you to think about\Nis, based on what we just saw,
Dialogue: 0,0:03:30.65,0:03:37.64,Default,,0000,0000,0000,,what is 24 divided by 12?
Dialogue: 0,0:03:37.64,0:03:39.33,Default,,0000,0000,0000,,And I encourage you\Nto pause the video,
Dialogue: 0,0:03:39.33,0:03:42.05,Default,,0000,0000,0000,,draw out 24 triangles\Nlike this, and try
Dialogue: 0,0:03:42.05,0:03:46.46,Default,,0000,0000,0000,,to figure out what\N24 divided by 12 is.
Dialogue: 0,0:03:46.46,0:03:48.17,Default,,0000,0000,0000,,Well, I assume you've\Npaused the video.
Dialogue: 0,0:03:48.17,0:03:51.26,Default,,0000,0000,0000,,And there's two ways to\Nthink about 24 divided by 12.
Dialogue: 0,0:03:51.26,0:03:55.86,Default,,0000,0000,0000,,You could say, well, let's\Ndivide 24 into groups of 12
Dialogue: 0,0:03:55.86,0:03:57.72,Default,,0000,0000,0000,,and think about how\Nmany groups we have.
Dialogue: 0,0:03:57.72,0:03:58.66,Default,,0000,0000,0000,,So we could do that.
Dialogue: 0,0:03:58.66,0:03:59.20,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:03:59.20,0:04:04.53,Default,,0000,0000,0000,,This is one group of\N12 right over here.
Dialogue: 0,0:04:04.53,0:04:10.00,Default,,0000,0000,0000,,That's one group of 12, and then\Nhere is another group of 12.
Dialogue: 0,0:04:10.00,0:04:13.08,Default,,0000,0000,0000,,So how many groups\Nof 12 do we have?
Dialogue: 0,0:04:13.08,0:04:14.78,Default,,0000,0000,0000,,Well, we have 2 groups of 12.
Dialogue: 0,0:04:14.78,0:04:19.12,Default,,0000,0000,0000,,So we could say 24\Ndivided by 12 is 2.
Dialogue: 0,0:04:19.12,0:04:23.01,Default,,0000,0000,0000,,But another just as reasonable\Nway of doing this is you
Dialogue: 0,0:04:23.01,0:04:27.19,Default,,0000,0000,0000,,could have said,\Nwell, let me divide 24
Dialogue: 0,0:04:27.19,0:04:30.46,Default,,0000,0000,0000,,into 12 groups instead\Nof groups of 12.
Dialogue: 0,0:04:30.46,0:04:32.24,Default,,0000,0000,0000,,So if I want to divide\Nit into 12 groups,
Dialogue: 0,0:04:32.24,0:04:34.53,Default,,0000,0000,0000,,12 equal groups--\Nwell, let's see.
Dialogue: 0,0:04:34.53,0:04:38.75,Default,,0000,0000,0000,,This is 1 equal group,\N2 equal groups--
Dialogue: 0,0:04:38.75,0:04:40.04,Default,,0000,0000,0000,,actually let me do it this way.
Dialogue: 0,0:04:40.04,0:04:54.60,Default,,0000,0000,0000,,Well, let me do this-- 2 equal\Ngroups, 3 4, 5, 6, 7, 8, 9, 10,
Dialogue: 0,0:04:54.60,0:04:56.84,Default,,0000,0000,0000,,11, 12.
Dialogue: 0,0:04:56.84,0:04:59.91,Default,,0000,0000,0000,,So once again, if you say, oh,\NI'm going to divide 24 into 12
Dialogue: 0,0:04:59.91,0:05:02.48,Default,,0000,0000,0000,,equal groups, how many do\Nyou have in each group?
Dialogue: 0,0:05:02.48,0:05:03.62,Default,,0000,0000,0000,,Well, you have 2.
Dialogue: 0,0:05:03.62,0:05:05.10,Default,,0000,0000,0000,,So once again, 24\Ncould be viewed
Dialogue: 0,0:05:05.10,0:05:07.58,Default,,0000,0000,0000,,as 24 divided into\N12 equal groups.
Dialogue: 0,0:05:07.58,0:05:09.21,Default,,0000,0000,0000,,And how many do you\Nhave in each group?
Dialogue: 0,0:05:09.21,0:05:12.86,Default,,0000,0000,0000,,Or 24 divided into groups of\N12, and how many groups would
Dialogue: 0,0:05:12.86,0:05:13.42,Default,,0000,0000,0000,,you have?
Dialogue: 0,0:05:13.42,0:05:16.02,Default,,0000,0000,0000,,And that's what we saw\Nin the last example.
Dialogue: 0,0:05:16.02,0:05:18.94,Default,,0000,0000,0000,,So now, let's make things\Neven more interesting.
Dialogue: 0,0:05:18.94,0:05:21.84,Default,,0000,0000,0000,,What I want you to think\Nabout-- a couple of things.
Dialogue: 0,0:05:21.84,0:05:31.10,Default,,0000,0000,0000,,I want you think about\Nwhat 24 divided by 6 is.
Dialogue: 0,0:05:31.10,0:05:36.22,Default,,0000,0000,0000,,And I also want you to figure\Nout what 24 divided by--
Dialogue: 0,0:05:36.22,0:05:41.07,Default,,0000,0000,0000,,let me use that\Nsame color-- 4 is.
Dialogue: 0,0:05:41.07,0:05:43.45,Default,,0000,0000,0000,,And once again, I encourage\Nyou to pause the video,
Dialogue: 0,0:05:43.45,0:05:45.17,Default,,0000,0000,0000,,draw these triangles,\Nand figure it out.
Dialogue: 0,0:05:45.17,0:05:49.21,Default,,0000,0000,0000,,What is 24 divided by\N6 and 24 divided by 4?
Dialogue: 0,0:05:49.21,0:05:51.36,Default,,0000,0000,0000,,So let's tackle 24\Ndivided by 6 first.
Dialogue: 0,0:05:51.36,0:05:59.24,Default,,0000,0000,0000,,And let's try to divide\N24 into 6 equal groups.
Dialogue: 0,0:05:59.24,0:05:59.78,Default,,0000,0000,0000,,So let's see.
Dialogue: 0,0:05:59.78,0:06:05.31,Default,,0000,0000,0000,,This could be 1 equal group,\N2 equal groups-- in fact,
Dialogue: 0,0:06:05.31,0:06:09.49,Default,,0000,0000,0000,,each group here is a group of 4.
Dialogue: 0,0:06:09.49,0:06:11.30,Default,,0000,0000,0000,,And we have 6 rows.
Dialogue: 0,0:06:11.30,0:06:19.19,Default,,0000,0000,0000,,So 3 equal groups, 4, 5, and 6.
Dialogue: 0,0:06:19.19,0:06:23.15,Default,,0000,0000,0000,,And so if you divide\N24 into 6 equal groups,
Dialogue: 0,0:06:23.15,0:06:24.69,Default,,0000,0000,0000,,how many do you\Nhave in each group?
Dialogue: 0,0:06:24.69,0:06:27.78,Default,,0000,0000,0000,,Well, it's pretty\Nclear you have 4.
Dialogue: 0,0:06:27.78,0:06:29.41,Default,,0000,0000,0000,,You have 4 In each group.
Dialogue: 0,0:06:29.41,0:06:30.78,Default,,0000,0000,0000,,Another way we\Ncould have thought
Dialogue: 0,0:06:30.78,0:06:39.71,Default,,0000,0000,0000,,about that is we\Ncould have said,
Dialogue: 0,0:06:39.71,0:06:43.22,Default,,0000,0000,0000,,let me divide 24\Ninto groups of 6.
Dialogue: 0,0:06:43.22,0:06:45.86,Default,,0000,0000,0000,,So if you divided\N24 into groups of 6,
Dialogue: 0,0:06:45.86,0:06:49.00,Default,,0000,0000,0000,,you could have\Nviewed it like this.
Dialogue: 0,0:06:49.00,0:06:53.49,Default,,0000,0000,0000,,So that's 1 group\Nof 6 right there.
Dialogue: 0,0:06:53.49,0:06:57.09,Default,,0000,0000,0000,,That's another group\Nof 6 right over here.
Dialogue: 0,0:06:57.09,0:06:58.48,Default,,0000,0000,0000,,That's another group of 6.
Dialogue: 0,0:06:58.48,0:07:01.48,Default,,0000,0000,0000,,And I think you see how\Nmany groups of 6 we have.
Dialogue: 0,0:07:01.48,0:07:03.06,Default,,0000,0000,0000,,How many groups of 6 do we have?
Dialogue: 0,0:07:03.06,0:07:04.48,Default,,0000,0000,0000,,We have 4.
Dialogue: 0,0:07:04.48,0:07:10.12,Default,,0000,0000,0000,,We have 4 groups of 6.
Dialogue: 0,0:07:10.12,0:07:13.37,Default,,0000,0000,0000,,Well, now let's think about\Nwhat 24 divided by 4 is.
Dialogue: 0,0:07:13.37,0:07:18.40,Default,,0000,0000,0000,,Well, if I view 24 divided by\N4 as taking 24 and dividing it
Dialogue: 0,0:07:18.40,0:07:20.78,Default,,0000,0000,0000,,into 4 equal groups,\NI've just drawn that.
Dialogue: 0,0:07:20.78,0:07:23.96,Default,,0000,0000,0000,,I have 4 equal groups, and\Nin each group I have 6.
Dialogue: 0,0:07:27.74,0:07:30.45,Default,,0000,0000,0000,,So notice 24 divided by 6 is 4.
Dialogue: 0,0:07:30.45,0:07:33.90,Default,,0000,0000,0000,,24 divided by 4 is 6.
Dialogue: 0,0:07:33.90,0:07:38.10,Default,,0000,0000,0000,,And that's because I could\Nview this as 4 groups of 6
Dialogue: 0,0:07:38.10,0:07:44.14,Default,,0000,0000,0000,,or say that 4 times\N6 is equal to 24.
Dialogue: 0,0:07:47.14,0:07:50.89,Default,,0000,0000,0000,,Or you could just as\Nequivalently say that 6 times 4
Dialogue: 0,0:07:50.89,0:07:52.57,Default,,0000,0000,0000,,is 24.
Dialogue: 0,0:07:52.57,0:08:00.20,Default,,0000,0000,0000,,You could equivalently say\Nthat 6 times 4 is equal to 24.