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We've got 24 triangle things here, what I want to do in this video is to divide it into different numbers of groups.

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So the first thing I want to do is I want to divide this 24 triangle things, I want to divide it into 3 groups,

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

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So let's try that out... So I'm going to divide into 3 equal groups.

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So that is one equal group right over there... Then I have another equal group right over here... 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 are going to be in each group?

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Well we can count that! We have 1... 2... 3... 4... 5... 6... 7... 8... in each group.

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

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Now you might say, "Hey! This is very similar to what we saw in multiplication!"

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In Multiplication, we said, "if we have 3 groups of 8 we can view that as 3 times 8 and get 24."

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And you are exactly right!

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We could also write that 3 times 8, so if we have 3 groups of 8, then that is going to be equal to 24.

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So we started in this video, we had 24 things, we want to divide it into 3 equal groups, we got 8 in each group.

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Or you can say 3 equal groups of 8 is equal to 24.

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But there's even other ways of thinking about this. (So let me clear this up a little bit)...

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So in the first example, I've divided 24 into 3 equal groups... but you can also view 24 divided by 3 as dividing 24 into groups of 3!

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So let's think about what that looks like... so if we divide into groups of 3...

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Then for example, this is a group of 3. That is a group of 3. This is a group of 3. You might see where this is going...

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That's a group of 3... That is another group of 3... We're going to think about how many groups of 3 we're actually going to get...

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So, this is another group of 3... and that's another group of 3.

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So... how many groups of 3 did we get? Well 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 is divide 24 into groups of 3, and then you will have 8 groups of 3.

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And one way of thinking about this... if you want to express the same thing in terms of multiplication...

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If you have 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... 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:

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What is 24 divided by 12? And I encourage you to pause the video, draw out 24 triangles like this, and try to figure out what 24 divided by 12 is.

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Well... I assume you have paused the video, and there's two ways to think about 24 divided by 12.

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You could say... let's divide 24 into groups of 12, and think about how many groups we have... So we can do that.

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So let's see... this is... 1 group of 12 right over here. And then here is another group of 12. So... How many groups of 12 do we have?

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Well, we have 2 groups of 12, so we could say 24 divided by 12 is 2.

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But another, just as reasonable, way of doing this.... You could have said, "Well... let me divide 24 into 12 groups, instead of groups of 12."

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So if I want to divide into 12 groups... 12 equal groups... Well let's see...

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So this is 1 equal group... 2 equal groups... 3... 4... 5... 6... 7... 8... 9... 10... 11... 12.

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So once again, if you say "I'm going to divide 24 into 12 equal groups, how many do you have in each group?"

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Well you have 2. So once again 24 can be viewed as 24 divided into 12 equal groups 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 you have? 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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I want you to think about a couple of things:

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What 24 divided by 6 is...

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And I also want you to figure out what 24 divided by 4 is.

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Once again, I encourage you to pause the video, draw out 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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So I'll view this as: let's try divide 24 into 6 equal groups.

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So let's see... this could be 1 equal group... 2 equal groups... in fact each group here is a group of 4, and we have 6 rows...

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So 3 equal groups, 4... 5... and 6. So if you divide 24 into 6 equal groups, how many do you have in each group?

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Well, it's pretty clear: you have 4 in each group.

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Another way we could have thought about that... is we could have said, "Let me divide 24 into groups of 6."

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So if you divide 24 into groups of 6... You could have viewed it as this:

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So that's is 1 group of 6 right there... That's another group of 6 right over here... That's another group of 6... and I think you can see how many groups of 6 we have.

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We have 4 groups of 6.

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Well, now let's think what 24 divided by 4 is. Well, if I view 24 divided by 4 as taking 24 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, and 24 divided by 4 is 6.

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And that's because I can view this as 4 groups of 6 (4 times 6 is equal to 24). Or you can just as equivalently say that 6 times 4 is 24.