Topic D: Foundations
Current time:0:00Total duration:5:19
Brandon ate 5 slices of apple-- of pie. I'm just assuming it's apple pie. They didn't tell me that. Gabriela ate 3 slices. If there were originally 9 slices, what fraction of the pie was eaten? So let me see if I can draw this thing out. So let me draw the pie. I will draw the pie in a yellowish color. So let me try my best. So let's see how good I am at drawing a pie. So I'll just draw it from the top view as a circle. And there're 9 slices. I think it's a reasonable assumption to say that they're 9 equal slices. So we have 9 equal slices of pie. And I'll just make sure they're initially 9 equal slices. What fraction of the pie was eaten? So let's first divide this into 9 sections. So one way I could do that, I could divide it into 3 sections first, so it looks like a peace symbol. It actually looks more like the Mercedes emblem. So I'll draw it into 3 sections first. Then I'll do each of those into 3 sections, and I'll have 9. So let's see, I'll draw like that and like that. Keep in mind, I'm trying to make these as equal as possible. So bear with me if they don't look 100% equal, but I'm trying. I am trying my best. So 9 equal slices-- so that looks pretty respectable. So here's our pie that initially had 9 equal slices. Now, they tell us that Brandon ate 5 slices of pie. So Brandon eats-- he seems like a hungry young man-- so he eats 1, 2, 3, 4, 5. You could say that he ate 5/9 of the pie. But that's not it. That's not what they're asking. It's saying total, not just how much did Brandon eat, but how much was eaten total between Brandon and Gabriela. And they tell us Gabriela ate 3 slices. So she ate 1-- sounds like they didn't really eat dinner-- 1, 2, 3. So now let's answer their question. What fraction of the pie was eaten? Well, we know that there was a total of 9 equal slices of pie. What fraction was eaten? Well, as we see, 1, 2, 3, 4, 5, 6, 7, 8. 8/9 of the pie was eaten. So let's actually type that in. And then we will do it right over here. We'd say 8, and we use that little slash symbol on your computer like this. 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten. Let's do a couple more of these. Ishaan ate 2 slices of pizza. Omar ate 3 slices. If there were originally 8 slices, what fraction of the pie is remaining? So this is interesting. Actually, let me copy and paste this so that I can do it on my little notepad right over here. So let's do it right over-- trying to find some space. There you go. Let me put that in here. So the same thing, we have-- well, this is a pizza now, not a pie. And so pizza I will draw in brown. It has 8, and we can assume it's initially 8 equal slices. So it's actually a little bit easier to draw 8 equal slices, since 8 is an even number. So let's see. That is my best attempt at drawing a circle. And let's see, first I can divide the pizza into 2 slices, then I can divide it into 4 slices. And I'm going to try to make them look as equal as possible. And now I'm going to-- with two more cuts, I should be able to get 8 so-- and one more just like this. So there you have it, a pizza that has 8 equal slices. Now, they tell us Ishaan ate 2 slices of pizza. So he eats 1, 2 slices of pizza. Omar ate 3 slices. Omar ate 3. So he eats 1, 2, 1, 2, 3 slices of pizza. Now, you might immediately say, oh, OK, the answer to this must be 1, 2, 3, 4, 5. It must be that they ate 5 slices of pizza over a total of 8 slices of pizza. So they ate 5/8 of the pizza. You would be right in saying that they ate 5/8 of the pizza, because they ate 1, 2, 3, 4, 5 out of a total of 8 pieces. But that's not what this question is asking. They are asking, what fraction of the pizza is remaining? So what's left over after Ishaan and Omar had their go at the pizza? Well, what's remaining is 1, 2, 3 slices. So what's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining. So let's input that. So we could go right here. And we would say 3 over 8, 3/8, is remaining. So let's check our answer, and we got it right.