WEBVTT

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We've got 24 triangle
things right over here.

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And what I want to
do in this video

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is to divide it into
different numbers of groups.

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So the first thing
I want to do is

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I want to divide this 24
triangle things into 3 groups

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and think about how many
do I end up per group.

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So let's try that out.

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So I'm going to divide
it into 3 equal groups.

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So that is one equal
group right over there.

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Then I have another equal
group right over here.

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And then I have a third
equal group right over here.

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So if I divide 24 into 3 equal
groups-- 1, 2, 3-- how many

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are going to be in each group?

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Well, we can count that.

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We have 1, 2, 3, 4, 5,
6, 7, 8 in each group.

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So we could say that 24
divided by 3 is equal to 8.

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Now, you might say,
hey, this is very

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similar to what we
saw in multiplication.

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In multiplication, we said
if we have 3 groups of 8,

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we could view that as
3 times 8 and get 24.

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And you are exactly right.

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Let me do those same colors--
we could also write that 3

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times 8-- so if I
have 3 groups of 8,

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that that is going
to be equal to 24.

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So when we started in this
video, we had 24 things.

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We want to divide it
into 3 equal groups.

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We got 8 in each group, or you
could say 3 equal groups of 8

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is equal to 24.

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But there's even other ways
of thinking about this.

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So let me clear this
up a little bit.

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So let me clear that.

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So in the first example, I
divided 24 into 3 equal groups.

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But you could also
view 24 divided by 3

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as dividing 24 into groups of 3.

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So let's think about
what that looks like.

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So if we divide it
into groups of 3,

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then, for example,
this is a group of 3.

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That is a group of 3.

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This is a group of 3.

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You might see where
this is going.

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That's a group of 3.

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That is another group of 3.

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And we're going to think
about how many groups of 3

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we're actually going to get.

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So this is another group of 3.

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And that's another group of 3.

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So how many groups
of 3 did we get?

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Let's see, we have 1, 2, 3,
4, 5, 6, 7, 8 groups of 3.

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So another way of
viewing 24 divided by 3

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is divide 24 into groups of 3.

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And then you will
have 8 groups of 3.

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And one way of
thinking about this--

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if you want to express
the same thing in terms

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of multiplication--
is if you have

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8 groups of 3, that is also
going to be equal to 24.

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Whether you have 3 groups
of 8 or 8 groups of 3,

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either way, you're
going to have 24.

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Now, let's make things
more interesting.

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What I want you to think about
is, based on what we just saw,

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what is 24 divided by 12?

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And I encourage you
to pause the video,

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draw out 24 triangles
like this, and try

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to figure out what
24 divided by 12 is.

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Well, I assume you've
paused the video.

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And there's two ways to
think about 24 divided by 12.

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You could say, well, let's
divide 24 into groups of 12

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and think about how
many groups we have.

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So we could do that.

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So let's see.

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This is one group of
12 right over here.

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That's one group of 12, and then
here is another group of 12.

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So how many groups
of 12 do we have?

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Well, we have 2 groups of 12.

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So we could say 24
divided by 12 is 2.

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But another just as reasonable
way of doing this is you

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could have said,
well, let me divide 24

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into 12 groups instead
of groups of 12.

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So if I want to divide
it into 12 groups,

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12 equal groups--
well, let's see.

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This is 1 equal group,
2 equal groups--

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actually let me do it this way.

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Well, let me do this-- 2 equal
groups, 3 4, 5, 6, 7, 8, 9, 10,

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11, 12.

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So once again, if you say, oh,
I'm going to divide 24 into 12

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equal groups, how many do
you have in each group?

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Well, you have 2.

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So once again, 24
could be viewed

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as 24 divided into
12 equal groups.

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And how many do you
have in each group?

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Or 24 divided into groups of
12, and how many groups would

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you have?

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And that's what we saw
in the last example.

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So now, let's make things
even more interesting.

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What I want you to think
about-- a couple of things.

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I want you think about
what 24 divided by 6 is.

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And I also want you to figure
out what 24 divided by--

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let me use that
same color-- 4 is.

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And once again, I encourage
you to pause the video,

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draw these triangles,
and figure it out.

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What is 24 divided by
6 and 24 divided by 4?

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So let's tackle 24
divided by 6 first.

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And let's try to divide
24 into 6 equal groups.

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So let's see.

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This could be 1 equal group,
2 equal groups-- in fact,

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each group here is a group of 4.

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And we have 6 rows.

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So 3 equal groups, 4, 5, and 6.

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And so if you divide
24 into 6 equal groups,

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how many do you
have in each group?

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Well, it's pretty
clear you have 4.

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You have 4 In each group.

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Another way we
could have thought

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about that is we
could have said,

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let me divide 24
into groups of 6.

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So if you divided
24 into groups of 6,

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you could have
viewed it like this.

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So that's 1 group
of 6 right there.

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That's another group
of 6 right over here.

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That's another group of 6.

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And I think you see how
many groups of 6 we have.

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How many groups of 6 do we have?

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We have 4.

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We have 4 groups of 6.

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Well, now let's think about
what 24 divided by 4 is.

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Well, if I view 24 divided by
4 as taking 24 and dividing it

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into 4 equal groups,
I've just drawn that.

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I have 4 equal groups, and
in each group I have 6.

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So notice 24 divided by 6 is 4.

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24 divided by 4 is 6.

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And that's because I could
view this as 4 groups of 6

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or say that 4 times
6 is equal to 24.

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Or you could just as
equivalently say that 6 times 4

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is 24.

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You could equivalently say
that 6 times 4 is equal to 24.