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- [Voiceover] So if this bar right over here represents one whole, so the whole thing is shaded in with the purple color, my question to you is, which of these other bars, and there might be more than one of them, represent 1/2? So our goal, our goal is to see 1/2. So once again, like always, pause the video and try it on your own. Okay, so you've tried it on your own, let's work through it. If we're thinking about halves, and we just have one of them, let me just try to draw another bar here, it would look something like this. I'll try to draw it pretty close to these other bars here. I would divide it into two equal sections, and I would only care or I would really fill in one of them, that would be 1/2 of this figure. Actually, these sections don't look quite equal, that looks a little bit off... It's pretty good, I think you get the idea, that my intent is to draw these to be equal. Then, this right over here would be 1/2. Now, none of these are divided into halves. This one over here is divided into fourths, this one over here is divided into one, two, three, four, five, so it's divided into fifths, this one over here is divided into one, two, three, four, five, six, so it's divided into sixths, this is divided into thirds. We're going to have to really relate 1/2 to other - to breaking up your whole into different amounts, not just breaking it up into two equal sections, breaking it up into four equal sections, five equal sections, six equal sections, and three equal sections. How do we do that? The easiest thing might be to just break this one up into four equal sections. You break this up into four equal sections, that's just taking each of these two and then breaking those up into two. That's one equal section, and another, let me use that blue color actually, 'cause that's my... That's an equal section over here, and this is an equal section, so this is the same thing as 1/2. Notice I didn't change how much I shaded in, I just divided it into more sections. So we see that 1/2 is the exact same thing as two out of four. Well, how many do we have right over here? We have one, two out of four, so this is one, two out of four, and this is one, two out of four, so 2/4 and 1/2 are the same, these two are equivalent. Now this might not be obvious, but if you took this block right over here, and if you were to move this one over, and so this one is painted and this one isn't, they would look the same, so maybe that would help to see that this also has 1/2 of the block filled in. So this one is definitely 1/2. Now let's think about fifths. So let me, well there's two ways I could do it. Let me draw fifths, and this right over here is 3/5, so might as well just write it down. This is 3/5, this is 3/6, and this is 1/3. Let me draw 3/5 right below this. Let me draw, I keep wanting to change the color around, I'm using a new art tool and color changing isn't coming as naturally as my old one. This right over here, let me divide it into fifths the best I can, so one, two, three, four, five, and we're going to assume that these are equal sections, I know my drawing isn't perfect, but if we have 3/5, where are we going to get to? We're going to get to one, two, three. One way to think about it, this, what I just drew, is just a rearrangement of this, I just took the three filled in sections and put them all to the left. So I have one, two, three, and when you look at it this way, it's clear that 3/5 is more than 1/2. If we were to try to put the 3/5 onto this one right here, it would get us about this far, so 3/5 would go all the way over there. So 3/5 is definitely not the same thing as 1/2. Now what about 3/6? Let's think about that a little bit. Can we take - let me draw another one of these things that I have to keep drawing over and over again. We already know that if I split this into two equal pieces, I shade in one of them, that's 1/2. This right over here is 1/2. Could I turn this into sixths? If I take each of these two and I split them into three equal pieces, then I'm going to have two times six pieces, so I'm going to have sixths. Let me do that, so I'm going to use my blue color, there you go, and then there you go, I took each of the two and I split them into three, and now I have six pieces. I haven't changed how much I shaded in, I have now - it was 1/2 of the entire bar, but now, when I think in terms of sixths, it's one, two, 3/6, 3/6 is the exact same thing as 1/2. We have one, two, 3/6, and once again, if you took these two and shifted them over here, you would get something that looks very much like that or like this. This right over here is the same thing as 1/2. Now what about 1/3? All right, I think you see where this is going. And always, you should just feel free to pause the video and try to work it out on your own, or frankly, if you get what's going on in the video, you don't have to watch it! (laughs) All right, so let's divide it into thirds, and we're talking about 1/3. We're talking about 1/3 right over here, and very clearly you see that 1/3 is less than 3/6, and 3/6 is the same thing as 1/2. 1/2 would take you about this far, would take you that far, 1/3 is less than that. So 1/3 is not equal to 1/2. Hopefully you found that fun.