Equivalent fraction models

- 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 2/3 filled in. So, pause the video now. So, I assume you have given a go at it, you have tried to determine which of these are 2/3 filled in. Now let's work on this together. So, when you're thinking in terms of thirds, and here we're thinking in terms of 2/3, literally two thirds, what we think about is dividing things into three equal sections. Let me see if I can draw a hexagon fairly well. So, let me draw the hexagon. 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 split it up into three equal sections, one, two, three. It's actually kind of neat the way it's drawn. It looks like a three dimensional cube. But that was not my intent. My intent was to draw a hexagon. So 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 what we care about is two thirds, so two of these one thirds. And so, let me clean this up a little bit. So, 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 2/3 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 one, two "three, four, five, six 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." All we have to do, is we can redraw this or we can do a little bit of work here to split this into, instead of three equal sections, we can split it into six equal sections. Well, how would we do that? We take each of those three equal sections and then split them into two equal sections. So, this one right over here, I can split this into two equal sections. This one right over here, I can split into two equal sections. This one right over here, I can split into two equal sections. So, I had three equal sections before, now each of them have been split into two, so now I have six equal sections. So now, they way I've drawn it, I'm dealing with sixths. And how many sixths represent the same fraction as the 2/3 did? I still have my shaded area. I have one, two, three, four sixths. So, 4/6 is the same thing as 2/3. Or, another way to think about it, any of these that have four out of the six equal sections filled in, that means that 2/3 of the sections are filled in. Or I could say 2/3 of the hexagon is filled in. So, let's just look at these. This one, we have one, well let me do it in a color that has a little more contrast. So we have one, two, three, four out of the six is filled in. 4/6 are filled in, that's the same thing as 2/3. So, this one represents 2/3. This one only has two of the sixths filled in, so it's not 4/6, which has to be 2/3, this is 2/6. We want 2/3. This one is one, two, three, four. Four of the sixths 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 sixths filled in, so this is 4/6, which we've already figured out is the same thing as 2/3. And we're done.