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I think you've probably heard the word divide before where someone tells you to divide something up divide the money between you and your brother or between you and your buddy and it essentially means to cut up something so let me write down the word divide divided so if we had let's say that I have four quarters let me see do my best to draw the quarters if I have four quarters just like that no you know that's my rendition of George Washington on the quarters and let's say there's two of us and we're going to divide the quarters between us so this is me right here let me try my best to draw me so that's me right there oh let's see I have a lot of hair and then this is you right there do my best say you're bald but you have sideburns maybe that looks more let's see if you have a little bit of a beard I don't want to get too focused on the drawing and so that's you that's me and we're going to divide these four quarters between the two of us so notice we have four quarters four quarters and we're going to divide between the two of us there are two of us two of us and I want to stress the number two so we're gonna divide four quarters by two we're gonna divide it between the two of us and you've probably done something like this what happens well each of us are going to get two quarters so let me divide it we're gonna divide it into two essentially what I did do is I take the four quarters and I divide it into two equal groups two equal groups and that's what division is we cut up this group of quarters into two equal groups so when you divide four quarters into two groups so this was four quarters right there let me so that was four quarters and you want to divide it into two groups this is Group one group one right here and this is group two right here how many numbers are in each group or how many quarters are in each group well in each group I have one 2/4 I need to use a brighter color I have one 2/4 in each group 1/4 and 2/4 in each group so to write this out mathematically I think this is something that you've done probably as long as you've been splitting money between you and your siblings and your buddies actually let me scroll over a little bit so you can see my entire picture so what how do we write this mathematically we can write we can write that 4 / so this 4 we use the right colors so this 4 which is this 4 divided by the two groups so the two groups these are the two groups Group one and this is group two right here so divide it into two groups are into two collections 4 divided by 2 is equal to when you divide 4 by into two groups each group is gonna have two quarters in it it's gonna be equal to two and I just wanted to use this example because I want to show you that division is something that you've been using all along and another important I guess takeaway or thing to realize about this is on some level this is the opposite of multiplication if I said that I had two groups if I said that I had two groups of two quarters I would multiply the two groups times the two quarters each times the two quarters each and I would say I would then have four quarters so on some level these are saying the same thing but just to make it a little bit more concrete in our head let's do a couple of more examples let's do a bunch of more examples so let's write down what is 6 / I'll try to keep it nice and color-coded 6 divided by 3 what is that equal to let's just draw 6 objects they can be anything let's say I have six six bell peppers and I won't take too much trouble to draw them well that that's not what a bell pepper looks like but you get the idea so one two three four five six and I'm going to divide it by three in one way that we can think about that is that means I want to divide my six bell peppers into three equal groups of bell peppers you could kind of think of it if it's three people are going to share these bell peppers how many do each of them get so let's divide it into three groups so that's our six bell peppers I'm gonna divide it into three groups so the best way to divided into three groups is I can have one group right there two groups or the second group right there and then the third group and then each group each group will have exactly how many bell peppers they'll have one two one two one two bell pepper so six divided by three is equal is equal to two so the best way or one way to think about it is that you divided the six into three groups now you could view that acolyte lis different way although it's it's not completely different but it's a good way to think about it you could also think of it as six divided by three and once again let's say I have well let's say I have raspberries now easier to draw one two three four five six and here instead of draw instead of dividing it into three groups like we did here right this was one group two group three groups instead of dividing into three groups what I wanted to do is say well if I'm dividing six divided by three I want to divide it into groups of three not into three groups I want to divide it into groups of three so how many groups of three am I going to have well let me let me draw some groups of three so that is one group of three and that is two groups of three that is two groups of three right there so if I take six things and I divide them into groups of three I will end up with one two groups so that's another way to think about division and this is an interesting thing when you think about these two relations you'll see a relationship between six to by three and six divided by two let me do that right here what is six divided by six divided by two when you think of it in this context right here six divided by two when you do it like that let me draw one two three four five six when we think about six divided by two in terms of dividing it into two groups what we can end up is we could have one group like this and then one group like this and each group will have three elements I'll have three things in it so six divided by two is three or you could think of it the other way you could say that six divided by two is you're taking six objects one two three four five six and you're dividing it into groups of two where each group has two elements and that on some level is an easier thing to do if each group has two elements well that's one right there I could even they don't even have to be nicely ordered this could be one group right there and that could be the other group right there I don't have to draw them all stacked up these are just groups of two but how many groups do I have I have one two three I have three groups but notice something it's no coincidence that 6 divided by 3 is 2 6 divided by 3 is 2 and 6 divided by 2 is 3 let me write that down we get 6 divided by 3 is equal to 2 and 6 divided by 2 is equal to 3 and the reason why these you see this relation where you can kind of swap this 2 and this 3 is because 2 times 3 is equal to 6 if I have if I have let's say I have 2 groups of 3 let me draw two groups of three so that's one group of 3 and then here's another group of 3 right that's one group of 3 and that's another group of 3 so 2 groups of 3 is equal to 6 2 times 3 is equal to 6 or you could think of it the other way if I have 3 groups of 2 so that's one group of 2 right there other group of two right there and then I have a third group of two right there what is that equal to three groups of two three times two that's also equal to 6 so 2 times 3 is equal to 6 3 times 2 is equal to 6 we saw this in the multiplication video that the order doesn't matter but that's the reason why if you want to divide it if you want to go the other way if you have 6 things and you want to divide it into groups of 2 you get 3 if you have 6 and you want to divide it into groups of 3 you get 2 let's do a couple of more problems and I think it'll really make sense about what division is all about so let's do let's do 9 let's do an interesting one let's do 9 divided by 4 so if we think about 9/4 let me draw nine objects 1 2 3 4 5 6 7 8 9 now when you divide by 4 I'm gonna thin this and this for this problem to think about it into dividing it into groups of 4 so if I want to divide it into groups of 4 let me try doing that so here is one group of 4 I just picked any of them right like that that's one group of 4 then here's another group of 4 right there and then I have this leftover thing maybe we call it a remainder where I don't have I can't divide put this one into a group of 4 when I'm dividing by 4 I can only put I can only cut up the 9 into groups of 4 so the answer here and this is a new concept for you maybe 9 divided by 4 is going to be 2 groups right I have one group here another group here and then I have a remainder of 1 I have 1 left over that I wasn't able to do with remainder a remainder that says remainder 1 9 divided by 4 is 2 remainder 1 if I asked you what 12 divided by 4 is let me do 12 1 2 3 4 5 6 7 8 9 10 11 12 so let me write that down 12 divided by for so I want to dry it divide these 12 objects maybe they're apples or plums and divide them into groups of four so let me see if I can do that so this is one group of four just like that this is another group of four just like that and this is pretty straightforward then I have a third group of four just like that and there's nothing left over like I had before that I can exactly divide 12 objects into three groups of four right one two three groups of four so 12 divided by four is equal to is equal to three and we can do the exercise that we saw in the previous video what is 12 divided by three let me do a new color twelve divided by three now based on what we learned so far we say oh well that should just be 4 because 3 times 4 is 12 but let's prove it to ourselves so 1 2 3 4 5 6 7 8 9 10 11 12 let's divide it into groups of 3 and I'm gonna make them little strange-looking just so you say see that you don't always have to do it in 2 nice clean columns so that's a group of 3 right there 12 divided by 3 let's see here is a here's another group of 3 just like that and then maybe I'll take this group of 3 like that and then I'll take this group of 3 there's off see you see a much easier way of dividing it up than doing these weird l-shaped things but I want to show you doesn't matter you're just dividing it into groups of 3 and how many groups do we have we have one group and then we have our second group right here and then we have our third group right there and then we have let me do it in a new color and then we have our fourth group right there so we have exactly 4 groups and when I say there was an easier way to divide the easier way was obviously or maybe not obviously if I didn't wanted to divide these into groups of 3 I could have just done one two three four groups of 3 either of these I'm dividing the 12 objects in two packets of three you can imagine them that way let's do another one that maybe has a remainder let's see what is what is 14 divided by divided by five so let's draw 14 objects 14 objects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14 objects and I'm gonna divide it into groups of 5 so let me draw well the easiest thing is was one group right there two groups right there but then this last one I only have four left so I can't make another group of 5 so the answer here is I can make two groups of five and I'm gonna have a remainder are 4 remainder of 4 2 remainder 4 now what you get enough practice you don't you're not always gonna be wanting to draw these circles and dividing them up like that although that would not be incorrect so another way to think about this type of problem is to say well 14 divided by 5 how do I figure that out and actually another way of writing this and though no harm in showing you I could say 14 divided by 5 is the same thing as 14 divided by this sign right here divided by 5 and what you do is you say well let's see how many times does 5 go into 14 well let's see 5 times and you kind of do multiplication tables in your head 5 times 1 is equal to 5 5 times 2 is equal to 10 so that's still less than 14 so 5 goes at least 2 times 5 times 3 is equal to 15 well that's bigger than 14 so I have to go back here so 5 only goes 2 times so it goes 2 times 2 times 5 is 10 and then you subtract you say 14 minus 10 is 4 and that's the same remainder is right here well I could divide 5 into 14 exactly 2 times which would get us two groups of 5 which is essentially just 10 but we still have the 4 left over we still have the 4 left over just like that let me do a couple more just to really make sure you you get this stuff really really really really well so let's say that I have let me write it in that notation let's say I would do 8 divided by 2 and I could also write this as 8 so I want to know what that is that's a question mark I could also write this as 8 divided by 2 and the way I do either of these I would I'll draw the circles in the second but the way I do it without doing a second without drawing the circles I say well 2 times 1 is equal to 2 so that definitely goes into 8 but maybe I can think of a larger number that goes into that when I multiply it by 2 still goes into 8 two times 2 is equal to 4 that's still less than 8 so 2 times 3 is equal to 6 still less than 8 2 times 2 times something weird happens in my pen 2 times 4 is exactly equal to 8 so 2 goes into 8 4 times so I could say 2 goes into 8 4 times or 8 divided by 2 is equal to 4 now we can even draw our circles 1 2 3 4 5 6 7 8 I drew a messy on purpose and let's divide them into groups of 2 I have one group of 2 2 groups of 2 3 groups of two four groups of 2 so if I have 8 objects divide them into groups of 2 you have 4 groups so 8 divided by 2 is 4 8 divided by 2 is 4 hopefully you found that helpful