Intro to fractions

What we're going to talk about in this video is the idea of a fraction. And we'll see there's many ways to think about a fraction. But first, we'll think about the most fundamental. So let's say that I have this square. And we can consider this a whole. So let me write that down. This is a whole. It is a complete square. Now, what I'm going to do is divide this into 4 equal parts. So with one cut like that, I've divided it into 2 equal parts, and then with another cut like this, I could divide it into 4 equal parts. So there are 4 equal parts. And now what I'm going to do is I'm going to select one of those equal parts, so let's say this part right over here. I am going to select that. So the question is, what fraction of the whole is the part that I have shaded in red? Well, it is 1 out of the 4 equal parts, right? I've shaded in 1 out of 1, 2, 3, 4 equal parts. So we write this as this fraction. This piece represents 1/4 of the whole. And there's two ways that you can think about this. You could view this as 1 of the 4 equal parts, or you could view this as a whole divided by 4 would get you exactly this much. Now let's do another one. And this time, let's think about how we could represent 1 over 8, so 1 over 8. Well, we could divide this whole, in this case, the whole is this rectangle-looking thing. We could divide the whole into 8 equal parts. So let's do that. So here I've divided into 2 equal parts. That looks pretty good. And now I can divide each of those into 2 equal parts to get me 4 equal parts. And then if I were to divide each of those into 2 equal parts, I will have 8 equal parts. And it's not exact. Obviously, I've drawn it by hand, but hopefully this gets you a sense. So now I have 8 equal parts. And now I'm going to select exactly one of them. And that'll represent 1/8. And I could select any one of these, but I'll just do this one to show you it does not have to be necessarily the first one. So once again, this square right over here that I'm shading in red represents 1/8 of the whole. Now, let's look at a few more examples where I've shaded them in ahead of time. And what I want you to do right now is pause the video, and either in your head or a piece of paper write down if you consider this purple thing, the whole, what fraction does this red part represent? If you consider this blue part the whole, what fraction does this red part represent? If you view this yellow triangle as a whole, what fraction does this red part represent? And so I encourage you to pause the video now. Well, let's look at each of these. So in this case, for this rectangle, we have 3 equal parts, and we've shaded in one of them. So this red rectangle right over here represents 1/3 of the whole. Now, Over here, in this kind of pie-looking thing, this circle-looking thing, we have 1, 2, 3, 4, 5 equal parts. And we have shaded in 1 of those 5 equal parts. So this little slice of the pie, this represents 1/5. This right over here is 1/5 of the entire pie. Now, this one's interesting. You might be tempted to say, well, I've got 5 parts, and then I've shaded in 1. That must represent 1/4. But remember, it needs to be 4 equal parts. And it's pretty clear looking at this that this part right over here is not equal in size to this part right over here or this part right over here. These are not 4 equal parts. So we cannot say that this is 1/4 of the triangle. So you cannot say that.