0:00:00.000,0:00:00.660


0:00:00.660,0:00:04.092
We've got 24 triangle[br]things right over here.

0:00:04.092,0:00:05.550
And what I want to[br]do in this video

0:00:05.550,0:00:09.130
is to divide it into[br]different numbers of groups.

0:00:09.130,0:00:10.600
So the first thing[br]I want to do is

0:00:10.600,0:00:16.760
I want to divide this 24[br]triangle things into 3 groups

0:00:16.760,0:00:20.020
and think about how many[br]do I end up per group.

0:00:20.020,0:00:21.660
So let's try that out.

0:00:21.660,0:00:24.370
So I'm going to divide[br]it into 3 equal groups.

0:00:24.370,0:00:28.450
So that is one equal[br]group right over there.

0:00:28.450,0:00:32.470
Then I have another equal[br]group right over here.

0:00:32.470,0:00:36.340
And then I have a third[br]equal group right over here.

0:00:36.340,0:00:42.280
So if I divide 24 into 3 equal[br]groups-- 1, 2, 3-- how many

0:00:42.280,0:00:43.890
are going to be in each group?

0:00:43.890,0:00:44.970
Well, we can count that.

0:00:44.970,0:00:52.500
We have 1, 2, 3, 4, 5,[br]6, 7, 8 in each group.

0:00:52.500,0:00:59.239
So we could say that 24[br]divided by 3 is equal to 8.

0:00:59.239,0:01:00.780
Now, you might say,[br]hey, this is very

0:01:00.780,0:01:02.488
similar to what we[br]saw in multiplication.

0:01:02.488,0:01:06.830
In multiplication, we said[br]if we have 3 groups of 8,

0:01:06.830,0:01:10.720
we could view that as[br]3 times 8 and get 24.

0:01:10.720,0:01:12.035
And you are exactly right.

0:01:12.035,0:01:14.670


0:01:14.670,0:01:18.940
Let me do those same colors--[br]we could also write that 3

0:01:18.940,0:01:25.620
times 8-- so if I[br]have 3 groups of 8,

0:01:25.620,0:01:32.040
that that is going[br]to be equal to 24.

0:01:32.040,0:01:34.580
So when we started in this[br]video, we had 24 things.

0:01:34.580,0:01:37.440
We want to divide it[br]into 3 equal groups.

0:01:37.440,0:01:42.780
We got 8 in each group, or you[br]could say 3 equal groups of 8

0:01:42.780,0:01:45.160
is equal to 24.

0:01:45.160,0:01:47.620
But there's even other ways[br]of thinking about this.

0:01:47.620,0:01:49.840
So let me clear this[br]up a little bit.

0:01:49.840,0:01:51.390
So let me clear that.

0:01:51.390,0:01:54.450


0:01:54.450,0:01:59.460
So in the first example, I[br]divided 24 into 3 equal groups.

0:01:59.460,0:02:02.730
But you could also[br]view 24 divided by 3

0:02:02.730,0:02:05.500
as dividing 24 into groups of 3.

0:02:05.500,0:02:07.890
So let's think about[br]what that looks like.

0:02:07.890,0:02:10.680
So if we divide it[br]into groups of 3,

0:02:10.680,0:02:15.270
then, for example,[br]this is a group of 3.

0:02:15.270,0:02:17.860
That is a group of 3.

0:02:17.860,0:02:19.494
This is a group of 3.

0:02:19.494,0:02:20.910
You might see where[br]this is going.

0:02:20.910,0:02:23.050
That's a group of 3.

0:02:23.050,0:02:25.430
That is another group of 3.

0:02:25.430,0:02:27.570
And we're going to think[br]about how many groups of 3

0:02:27.570,0:02:29.190
we're actually going to get.

0:02:29.190,0:02:32.780
So this is another group of 3.

0:02:32.780,0:02:35.750
And that's another group of 3.

0:02:35.750,0:02:38.490
So how many groups[br]of 3 did we get?

0:02:38.490,0:02:45.120
Let's see, we have 1, 2, 3,[br]4, 5, 6, 7, 8 groups of 3.

0:02:45.120,0:02:50.580
So another way of[br]viewing 24 divided by 3

0:02:50.580,0:02:54.450
is divide 24 into groups of 3.

0:02:54.450,0:02:57.120
And then you will[br]have 8 groups of 3.

0:02:57.120,0:02:58.620
And one way of[br]thinking about this--

0:02:58.620,0:03:01.900
if you want to express[br]the same thing in terms

0:03:01.900,0:03:03.550
of multiplication--[br]is if you have

0:03:03.550,0:03:13.070
8 groups of 3, that is also[br]going to be equal to 24.

0:03:13.070,0:03:18.140
Whether you have 3 groups[br]of 8 or 8 groups of 3,

0:03:18.140,0:03:21.820
either way, you're[br]going to have 24.

0:03:21.820,0:03:25.830
Now, let's make things[br]more interesting.

0:03:25.830,0:03:30.650
What I want you to think about[br]is, based on what we just saw,

0:03:30.650,0:03:37.640
what is 24 divided by 12?

0:03:37.640,0:03:39.330
And I encourage you[br]to pause the video,

0:03:39.330,0:03:42.050
draw out 24 triangles[br]like this, and try

0:03:42.050,0:03:46.460
to figure out what[br]24 divided by 12 is.

0:03:46.460,0:03:48.170
Well, I assume you've[br]paused the video.

0:03:48.170,0:03:51.260
And there's two ways to[br]think about 24 divided by 12.

0:03:51.260,0:03:55.860
You could say, well, let's[br]divide 24 into groups of 12

0:03:55.860,0:03:57.720
and think about how[br]many groups we have.

0:03:57.720,0:03:58.660
So we could do that.

0:03:58.660,0:03:59.201
So let's see.

0:03:59.201,0:04:04.530
This is one group of[br]12 right over here.

0:04:04.530,0:04:10.000
That's one group of 12, and then[br]here is another group of 12.

0:04:10.000,0:04:13.080
So how many groups[br]of 12 do we have?

0:04:13.080,0:04:14.780
Well, we have 2 groups of 12.

0:04:14.780,0:04:19.120
So we could say 24[br]divided by 12 is 2.

0:04:19.120,0:04:23.010
But another just as reasonable[br]way of doing this is you

0:04:23.010,0:04:27.190
could have said,[br]well, let me divide 24

0:04:27.190,0:04:30.460
into 12 groups instead[br]of groups of 12.

0:04:30.460,0:04:32.240
So if I want to divide[br]it into 12 groups,

0:04:32.240,0:04:34.530
12 equal groups--[br]well, let's see.

0:04:34.530,0:04:38.749
This is 1 equal group,[br]2 equal groups--

0:04:38.749,0:04:40.040
actually let me do it this way.

0:04:40.040,0:04:54.600
Well, let me do this-- 2 equal[br]groups, 3 4, 5, 6, 7, 8, 9, 10,

0:04:54.600,0:04:56.840
11, 12.

0:04:56.840,0:04:59.910
So once again, if you say, oh,[br]I'm going to divide 24 into 12

0:04:59.910,0:05:02.480
equal groups, how many do[br]you have in each group?

0:05:02.480,0:05:03.620
Well, you have 2.

0:05:03.620,0:05:05.100
So once again, 24[br]could be viewed

0:05:05.100,0:05:07.585
as 24 divided into[br]12 equal groups.

0:05:07.585,0:05:09.210
And how many do you[br]have in each group?

0:05:09.210,0:05:12.860
Or 24 divided into groups of[br]12, and how many groups would

0:05:12.860,0:05:13.420
you have?

0:05:13.420,0:05:16.020
And that's what we saw[br]in the last example.

0:05:16.020,0:05:18.940
So now, let's make things[br]even more interesting.

0:05:18.940,0:05:21.840
What I want you to think[br]about-- a couple of things.

0:05:21.840,0:05:31.100
I want you think about[br]what 24 divided by 6 is.

0:05:31.100,0:05:36.215
And I also want you to figure[br]out what 24 divided by--

0:05:36.215,0:05:41.070
let me use that[br]same color-- 4 is.

0:05:41.070,0:05:43.450
And once again, I encourage[br]you to pause the video,

0:05:43.450,0:05:45.170
draw these triangles,[br]and figure it out.

0:05:45.170,0:05:49.210
What is 24 divided by[br]6 and 24 divided by 4?

0:05:49.210,0:05:51.360
So let's tackle 24[br]divided by 6 first.

0:05:51.360,0:05:59.239
And let's try to divide[br]24 into 6 equal groups.

0:05:59.239,0:05:59.780
So let's see.

0:05:59.780,0:06:05.310
This could be 1 equal group,[br]2 equal groups-- in fact,

0:06:05.310,0:06:09.490
each group here is a group of 4.

0:06:09.490,0:06:11.300
And we have 6 rows.

0:06:11.300,0:06:19.190
So 3 equal groups, 4, 5, and 6.

0:06:19.190,0:06:23.150
And so if you divide[br]24 into 6 equal groups,

0:06:23.150,0:06:24.690
how many do you[br]have in each group?

0:06:24.690,0:06:27.780
Well, it's pretty[br]clear you have 4.

0:06:27.780,0:06:29.406
You have 4 In each group.

0:06:29.406,0:06:30.780
Another way we[br]could have thought

0:06:30.780,0:06:39.710
about that is we[br]could have said,

0:06:39.710,0:06:43.220
let me divide 24[br]into groups of 6.

0:06:43.220,0:06:45.860
So if you divided[br]24 into groups of 6,

0:06:45.860,0:06:49.000
you could have[br]viewed it like this.

0:06:49.000,0:06:53.490
So that's 1 group[br]of 6 right there.

0:06:53.490,0:06:57.090
That's another group[br]of 6 right over here.

0:06:57.090,0:06:58.475
That's another group of 6.

0:06:58.475,0:07:01.480
And I think you see how[br]many groups of 6 we have.

0:07:01.480,0:07:03.056
How many groups of 6 do we have?

0:07:03.056,0:07:04.484
We have 4.

0:07:04.484,0:07:10.120
We have 4 groups of 6.

0:07:10.120,0:07:13.370
Well, now let's think about[br]what 24 divided by 4 is.

0:07:13.370,0:07:18.400
Well, if I view 24 divided by[br]4 as taking 24 and dividing it

0:07:18.400,0:07:20.780
into 4 equal groups,[br]I've just drawn that.

0:07:20.780,0:07:23.965
I have 4 equal groups, and[br]in each group I have 6.

0:07:23.965,0:07:27.740


0:07:27.740,0:07:30.453
So notice 24 divided by 6 is 4.

0:07:30.453,0:07:33.900
24 divided by 4 is 6.

0:07:33.900,0:07:38.100
And that's because I could[br]view this as 4 groups of 6

0:07:38.100,0:07:44.140
or say that 4 times[br]6 is equal to 24.

0:07:44.140,0:07:47.140


0:07:47.140,0:07:50.890
Or you could just as[br]equivalently say that 6 times 4

0:07:50.890,0:07:52.570
is 24.

0:07:52.570,0:08:00.198
You could equivalently say[br]that 6 times 4 is equal to 24.

0:08:00.198,0:08:00.698