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so this hexagon right over here the whole thing is filled in with this pink color so we'll say that this represents one whole the whole thing is filled in now what I want you to think about is which of these other hexagons have 2/3 filled in so our goal is to identify the hexagons that are two-thirds filled in so pause the video now so I assume you have give it a go at it you have tried to determine which of these are two-thirds filled and now let's work on this together so when you when you're ticking in terms of thirds and here we're talking in terms of 2/3 literally two-thirds what we think about is dividing things into three equal sections so let me see if I can draw a hexagon fairly well so let me draw the hexagons and I'm going to try to split it up into three equal sections whoops I'm going to try to split it up into three equal sections so this is the center of the hexagon right over here and so maybe that's one of the equal sections and then if I do one more line I've split it up into three equal sections one two three it's actually kind of neat the way that it's drawn it looks like a three-dimensional cube but that was not my intent my intent was to draw a hexagon so let me just so these each of these is a third actually I could write this that's one third that's one third and this is one third but we care about it's two thirds so two of these one thirds and so let me clean this up a little bit so I would fill in I would fill in one of the one thirds and then two of the one thirds and this right over here this hexagon that I've just drawn now has two thirds of it filled in now I know what you're thinking all right Sal that would have been pretty straightforward if these were divided into thirds but these are not divided into thirds each of these are divided into 1 2 3 4 5 6 equal pieces this is divided into sixths how do we figure out how many of the sixths should be filled in in order to have the same thing as 2/3 well I would tell you you don't worry too much we have to do is we can redraw this or we can we can do a little bit of work here to split this into instead of three equal sections we can split into six equal sections well how would we do that well we take each of those three equal sections and then split them into two equal sections so this one right over here I could split this into two equal sections this one right over here I could split it into two equal sections this one right over here I can split it into two equal sections so I had three equal sections before now each of them have been splitted to two so now I have six equal sections so now the way I've drawn it I'm dealing with sixths and how many sixths represent the same represent the same fraction as the two thirds did well I still have my shaded area I have one two three four sixths so four sixths is the same thing as two thirds or another way to think about it any of these that have four out of the six equal sections filled in that means that two-thirds of the sections are filled in or I could say that two-thirds of the hexagon is filled in so let's just look at these so this one we have one well let me do the color that has a little more contrast so we have one two three four out of the six is filled in four six are filled in that's the same thing as 2/3 so this one represents 2/3 this one only has two of the six filled in so it's not it's not for six which has to be 2/3 this is 2/6 we want 2/3 this one is one two three four four of the six are filled in so this is 2/3 so I will put a square around that one and this one has one two three four of the six filled in so this is four six which we've already figured out is the same thing as 2/3 and we're done