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# Division with area models

CCSS.Math:

## Video transcript

let's say that this rectangle this is a green rectangle right over here let's say it had an area of 268 square units whatever those units are you could imagine them being square centimeters or if you imagine this being a big field that you're looking at from space it could be square miles or something so I'm just going to write square units and let's say you knew the dimensions of one side of the field so let's say that you knew you knew that this let me just a color let's see let's say you knew that this side of the field right over here the length of this side of the field is 2 units 2 units and I haven't really drawn this to scale if I wanted to draw it to scale it would be like it would be like much shorter be like that but you would have trouble seeing the rectangle then but let's just assume it's 2 units so if you know the whole area is 268 square units and one side is 2 units what's the other side going to be what is the other side going to be what is what is let me pick another color what is this side what is this side of this rectangular of this rectangle this field whatever this might be what is the length of that side well if you multiply these two sides you get the area so if you start with the area if you start with 268 268 and you divide by the other side divided by the other side you're going to get the length of this side right over here so if we wanted to figure out the length of that side it would be 268 divided by 2 and you've already seen or we've already seen multiple ways to figure out what 268 divided by 2 is but the whole reason of me drawing this rectangle or this aerial view of this field or whatever you want to call it is so that we visualize it using area and so one way to do it is is to break up this 268 square unit area into areas that are easier to imagine dividing by 2 so here I have the city I have the same field but I've just broken it up so it's the same field this dimension right over here is still two units two units but I've broken it up this blue area is 200 let me do that in a in another color so this blue area is 200 units this yellow area is 60 units and this magenta area is 8 units now why is that useful well now each of these it's much easier to divide by 2 all I did is I took the 268 and I'd of Ni and I said well look this is the same thing as 200 plus 60 plus 60 plus 8 I just broke up the 268 into things that are easier to divide by 2 and now I can take those things and divide by 2 I could take each of them and divide by 2 so what is what is this what is this dimension going to be right over here actually we do that in a different color what is this dimension right over here going to be well 2 times that is going to be a hundred so this is going to be 100 and how did we get that well we got that by 200 divided by 2 200 divided by 2 is 100 what's 60 divided by 2 well 60 divided by 2 is going to be 30 so this part of the field is going to be 30 in that direction and 2 in this direction and once again not drawn by not drawn to scale and then finally what's this section going to be it's going to be it's going to be 8 divided by 2 which is 4 notice 100 times 2 is 230 times 2 is 64 times 2 is 8 and so this this whole length up here is going to be 100 plus 30 plus 4 or 134 and we've already seen other ways of coming up with this you say look 200s divided by 2 is 106 10s divided by 2 is 3 tens 8 ones divided by 2 is 4 ones and that's exactly what we just did over here but we visualized it using this kind of a rectangle breaking it up into chunks that are maybe easier to imagine dividing by two we broke it up into two hundreds to hundreds right over here we broke it up into six tens or 60 or 60 right over here and we broke it up into eight ones eight ones we broke up the area and then we took each of those areas and we divided it by two to find that part of the length and when you add them all together you get the entire you get the entire length now that's just one way to do it where you take each of the place values and you break up your field or your rectangle like that but you could do it other ways you don't always have to break it up that much for example let's say let's say that this let's say that this area is 856 square units square units and let's say that this dimension right over here is 8 is 8 units is 8 units so how could we break this up so it's easier to think about what the other dimension would be what the length is going to be and this length once again is going to be 850 6/8 856 divided by 8 is this length right over here well you could break it up into eight hundreds five tens and six ones but you might notice well five tens it's not so easy to divide that by eight but we can divide 56 by eight we know that 8 times 7 is 56 so what you could do is you could break this rectangle into the 856 square units you could break it up into 800 square units and then another 56 and another 56 square units so once again we broke it up into eight hundreds and then 56 ones and then 50 56 856 ones same area I just broke it up and now if you say look this is eight if you say if you say this here is 8 well what is going to be what is going to be this length what is this length up here going to be well it's going to be 800 divided by its going to be 800 divided by 8 so actually let me write it below it so 800 divided by 8 this length right over here is going to be is going to be 100 how did I get that I got 8 hundredths divided by 8 is 100 800 divided by 8 is 100 and then you have this other magenta part what is 56 divided by 8 well that's 7 56 divided by 8 this length right over here is going to be 7 so what's this entire length what's this entire length I was going to be 100 plus 7 which is equal to 107 so once again you could have said look 8 goes into 800 100 times 8 goes into 56 7 times 107 why did Sal draw these rectangles well just so that you can help something it's sometimes helpful to visualize this as a look you're trying this is an area problem if this is the total area if 856 is the total area and 8 is one of the dimensions well then 856 divided by 8 is going to be the other dimension and one way when you're breaking this up by place value breaking up the numbers into pieces that are easier to divide by 8 you could think of it as you're just breaking up that area and you're just trying to figure out parts of this length so that's 100 right over there and then this right over here is 7 so anyway hopefully this this broadens your visualization capabilities when you are dividing multiple when you're when you're doing division