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# The idea of division

## Video transcript

we've got 24 triangle things right over here what I want to do in this video is to divide it into different numbers of groups 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 and think about how many do I end up per group so let's try that out so I'm going to divide into 3 equal groups 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 so if I divide 24 into three equal groups one two three how many are going to be in each group well we can count that we have 1 2 3 4 5 6 7 8 in each group so we could say that 24 divided by 3 is equal to 8 now you might say hey this is very similar to what we saw in multiplication and multiplication we said if we have 3 groups of 8 we could view that as 3 times 8 and get 24 and you are exactly right we could also write 3 let me do this that's those same colors we could also write that 3 times 8 so if I have 3 groups of 8 3 groups of 8 that that is going to be equal to that is going to be equal to 24 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 or you can say 3 equal groups of 8 is equal to 24 but there's even other ways of thinking about this so let me clear this up a little bit so let me clear that we could also view so in the first example I view 25 divided 24 into 3 equal groups but you could also view 24 divided by 3 as dividing 24 into groups of 3 so let's think about what that looks like so if we divide it into groups of 3 then for example this is a group of three that is a group of three this is a group of three you might see where this is going that's a group of three that is another group of three we're going to think about how many groups of three we're actually going to get so this is another group of three and that's another group of three so how many groups of three did we get well see we have one two three four five six seven eight groups of three so another way of viewing twenty eight so the other way of viewing 24 divided by three is divide 24 into groups of three and then you will have eight groups of three and one way of thinking about this if you want to express the same the same thing in terms of multiplication is if you have eight groups of three if you have eight groups of three that is also going to be equal to 24 whether you have four group that whether you have three groups of eight or eight groups of three either way you're going to have 24 now let's make things more interesting what I want you to think about is what is based on what we just saw what is 24 what is 24 divided by 12 and I encourage you to pause the video draw out 24 triangles like this and try to and try to figure out what 24 divided by 12 is well I assume you've paused the video and there's two ways to think about 24 divided by 12 you could say well let's divide 24 into groups of 12 and think about how many groups we have so we could do that so let's see this is this is one group of 12 right over here that's one group of 12 and then here is another group of 12 it's another group of 12 so how many groups of 12 do we have well we have two groups of 12 so we could say 24 divided by 12 is 2 but another just is reasonable way of doing this is you could have said you could have said well let me divide 24 into 12 groups instead of groups of 12 so if I want to divide it into 12 groups 12 equal groups well let's see this is one equal group two equal groups actually let me do it this way well let me do this yet two equal groups 3 4 5 6 7 8 9 10 11 12 so once again if you say well I want to divide 24 into 12 equal groups how many do you have in each group well you have two so once again 24 could be viewed as 24 divided into twelve equal groups and how many you have in each group or 24 divided into groups of 12 and how many groups would you have and that's what we saw in the last example so now let's make things even more interesting what I want you to think about a couple of things I want you to think about what 24 what 24 divided by let's say divided by 6 is and I also want you to figure out what 24 what 24 divided by use the same color divided by 4 is divided by 4 is and once again I encourage you to pause the video draw these triangles and figure it out what is 24 divided by 6 and 24 divided by 4 so let's tackle 24 divided by 6 versus and I'll view this as let's try to group let's try to divide 24 into 6 equal groups 6 equal groups so let's see this could be one equal group 1 equal group 2 equal groups in fact each group here is a group of 4 and we have 6 rows so 3 equal group there are 3 equal groups 4 5 & 6 and so if you divide 24 into 6 equal groups how many do you have in each group well it's pretty clear you have 4 you have 4 in each group another way we could have thought about that another way we could have thought about that is we could have said we could have said what is how let me divide 24 two groups of six so if you divided 24 into groups of six you could have viewed it like this so that's one group of six that's one group of six right there that's another group of six right over here it's another group of six and I think you see how many groups of six we have how many groups of six we have we have four we have four groups of six four groups of six well now let's think about what 24 divided by four is well if I divide if I think if I view 24 divided by four is they're taking 24 and dividing it into four equal groups I've just drawn that I have four equal groups and in each group I have six in each group I have six so notice 24 divided by 6 is 4 24 divided by 4 is 6 and that's because I could view this as four groups of six or say that 4 times 4 times 6 4 times 6 is equal to 24 is equal to 24 or you could just as equivalent Li say that 6 times 4 is 24 you can equivalently say that 6 times 4 is equal to 24