WEBVTT 00:00:00.536 --> 00:00:09.113 We've got 24 triangle things here, what I want to do in this video is to divide it into different numbers of groups. 00:00:09.113 --> 00:00:16.536 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, 00:00:16.536 --> 00:00:20.069 and think about how many do I end up with per group. 00:00:20.069 --> 00:00:24.446 So let's try that out... So I'm going to divide into 3 equal groups. 00:00:24.446 --> 00:00:36.278 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. 00:00:36.278 --> 00:00:43.937 So if I divide 24 into 3 equal groups... 1, 2, 3... How many are going to be in each group? 00:00:43.937 --> 00:00:52.402 Well we can count that! We have 1... 2... 3... 4... 5... 6... 7... 8... in each group. 00:00:52.402 --> 00:00:59.279 So we can say that 24 divided by 3 is equal to 8. 00:00:59.279 --> 00:01:02.946 Now you might say, "Hey! This is very similar to what we saw in multiplication!" 00:01:02.946 --> 00:01:10.612 In Multiplication, we said, "if we have 3 groups of 8 we can view that as 3 times 8 and get 24." 00:01:10.612 --> 00:01:12.403 And you are exactly right! 00:01:12.403 --> 00:01:32.003 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. 00:01:32.003 --> 00:01:39.946 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. 00:01:39.946 --> 00:01:45.203 Or you can say 3 equal groups of 8 is equal to 24. 00:01:45.203 --> 00:01:52.699 But there's even other ways of thinking about this. (So let me clear this up a little bit)... 00:01:54.159 --> 00:02:05.612 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! 00:02:05.612 --> 00:02:10.804 So let's think about what that looks like... so if we divide into groups of 3... 00:02:10.804 --> 00:02:20.803 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... 00:02:20.803 --> 00:02:28.869 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... 00:02:28.869 --> 00:02:35.696 So, this is another group of 3... and that's another group of 3. 00:02:35.696 --> 00:02:44.862 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. 00:02:44.862 --> 00:02:56.946 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. 00:02:56.946 --> 00:03:03.003 And one way of thinking about this... if you want to express the same thing in terms of multiplication... 00:03:03.003 --> 00:03:12.946 If you have 8 groups of 3, that is also going to be equal to 24. 00:03:12.946 --> 00:03:21.403 Whether you have 3 groups of 8 or 8 groups of 3... either way, you're going to have 24. 00:03:21.403 --> 00:03:25.697 Now... let's make things more interesting... 00:03:25.697 --> 00:03:28.202 What I want you to think about is: 00:03:28.202 --> 00:03:46.029 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. 00:03:46.029 --> 00:03:51.203 Well... I assume you have paused the video, and there's two ways to think about 24 divided by 12. 00:03:51.203 --> 00:03:58.804 You could say... let's divide 24 into groups of 12, and think about how many groups we have... So we can do that. 00:03:58.804 --> 00:04:12.779 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? 00:04:12.779 --> 00:04:18.868 Well, we have 2 groups of 12, so we could say 24 divided by 12 is 2. 00:04:18.868 --> 00:04:30.536 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." 00:04:30.536 --> 00:04:35.113 So if I want to divide into 12 groups... 12 equal groups... Well let's see... 00:04:35.113 --> 00:04:56.613 So this is 1 equal group... 2 equal groups... 3... 4... 5... 6... 7... 8... 9... 10... 11... 12. 00:04:56.613 --> 00:05:02.402 So once again, if you say "I'm going to divide 24 into 12 equal groups, how many do you have in each group?" 00:05:02.402 --> 00:05:09.138 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, 00:05:09.138 --> 00:05:15.736 or 24 divided into groups of 12, and how many groups would you have? And that's what we saw in the last example. 00:05:15.736 --> 00:05:18.337 So now let's make things even more interesting... 00:05:18.337 --> 00:05:22.946 I want you to think about a couple of things: 00:05:22.946 --> 00:05:31.279 What 24 divided by 6 is... 00:05:31.279 --> 00:05:41.469 And I also want you to figure out what 24 divided by 4 is. 00:05:41.469 --> 00:05:45.335 Once again, I encourage you to pause the video, draw out these triangles, and figure it out. 00:05:45.335 --> 00:05:49.030 What is 24 divided by 6, and 24 divided by 4? 00:05:49.030 --> 00:05:51.469 So let's tackle 24 divided by 6 first. 00:05:51.469 --> 00:05:57.736 So I'll view this as: let's try divide 24 into 6 equal groups. 00:05:59.519 --> 00:06:11.279 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... 00:06:11.279 --> 00:06:24.736 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? 00:06:24.736 --> 00:06:29.403 Well, it's pretty clear: you have 4 in each group. 00:06:29.403 --> 00:06:43.279 Another way we could have thought about that... is we could have said, "Let me divide 24 into groups of 6." 00:06:43.279 --> 00:06:48.403 So if you divide 24 into groups of 6... You could have viewed it as this: 00:06:48.403 --> 00:07:01.446 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. 00:07:01.446 --> 00:07:10.280 We have 4 groups of 6. 00:07:10.280 --> 00:07:20.737 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! 00:07:20.737 --> 00:07:24.779 I have 4 equal groups, and in each group I have 6. 00:07:27.809 --> 00:07:34.113 So notice: 24 divided by 6 is 4, and 24 divided by 4 is 6. 00:07:34.113 --> 00:07:38.113 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.