Topic B: Unit fractions and their relation to the whole
I have a square here divided into one, two, three, four, five, six, seven, eight, nine equal sections. And we've already seen that if we were to shade in one of these sections, if we were to select one of these sections, let's say the middle one right over here, this is one out of the nine equal sections. So if someone said, what fraction of the whole does this purple square represent? Well, you would say, well, that represents 1/9 of the whole. This thing right over here represents 1/9. Now what would happen if we shaded in more than that? So let's say we shaded in this one and this one, let me shade it in a little bit better. And this one and this one right over here. Now what fraction of the whole have we shaded in? Well, each of these, we've already seen, each of these represent 1/9. So that's 1/9, that's 1/9. When I say 1/9, I could also say a ninth. So this is 1/9 or a ninth, so each of these represents a ninth. But how many of these ninths do we have shaded in? Well we have one, two, three, four shaded in. So now we have a total of 4/9 shaded it. 4 of the 9 equal sections are shaded in. So 4/9 of the whole is shaded in. Now let's make things a little bit more interesting. Let's shade in. So here I have five equal sections. Let me write this down. I have five equal sections. And let me shade in five of them. So one, two, three, four, five. We already know that each of these sections, each of these situated in sections represent 1/5. So 1/5, another way of saying that is a fifth, is 1/5. But now how much do I have shaded in? Well I have five out of the five equal sections shaded, or I have 5/5 shaded in. And you might be saying, wait, wait, if I gave five out of the five equal sections shaded in, if I have 5/5 shaded in, I've got the whole thing shaded in. And you would be absolutely right. 5/5 is equal to the whole. Now what I want you to do is pause this video and write down on a piece of paper or at least think in your head, what fraction of each of these wholes is shaded in? So let's go to this first one. We have one, two, three, four, five, six equal sections. And we see that one, two, three, four are shaded in. So 4/6 of this figure is shaded in. Let's go over here. We have one, two, three, four, five equal sections. And one, two, three, four are shaded in. So here, 4/5 of this circle is shaded in. Now in this figure, I have two equal sections and both of them are shaded in. And this we would say two halves of this figure are shaded in. And once again, if two halves are shaded in, that means everything is shaded in, that this represents a whole. Now this one right over here it might be tempting to say, I have one, two, three, four sections and one, two, three have been shaded in so maybe the red represents 3/4 of the figure. But remember, the sections have to be equal sections. And this red section is way bigger. It actually looks like it's bigger than the other three combined. So you do not have four equal sections here. So at least based on how it's drawn, you can't say that 3/4 is actually filled in.