Comparing fractions of different wholes
Sal compares fractions of different wholes.
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- Amir ate 2/3 of a piece of red licorice. So, let's draw a piece of red licorice over here and let's draw it into thirds, so, or split it into thirds. Three equal sections, as best as I can draw that, and he ate 2/3 of it, so that's 1/3 right over here and then, this is a second third, So, that's 2/3, what I shaded in. This is how much of that red licorice he would have eaten. Then, they tell us Nikko ate 2/3 of a longer, but equally thick, piece of red licorice. So, it's gonna be equally thick, but it's longer. So, I'm just gonna draw something that is longer. So, that's longer, but equally thick and he also ate 2/3 of this, but this is a longer piece and it's equally thick, so it's actually gonna be just a larger piece. It's gonna have more licorice in it. So, 2/3 of that, let me see if I can split this into thirds and this is 1/3, this is a second third. Well, 2/3 of a larger piece is going to be more than 2/3 of a smaller piece. This right over here, this amount that he ate, it has the same width, but it's longer than this right over here. So, Nikko, because this is a longer, but equally thick piece of red licorice, Nikko ate more red licorice. Nikko for sure. Let's do another one. My unicorn, that's interesting to have a unicorn. My unicorn, ate 2/6 of a pizza from Store A, alright. I ate 2/6 of a different pizza from Store B. Who ate more pizza? Well, it would depends. You know Store A's pizza might look like this. Store B's pizza might look like this. So, if this was the case, so if this is Store A and this is Store B, you eat 2/6 of this, let me divide this into sixths, so that's halves, and that would be, and then sixths. Woops, I don't wanna do eighths, I wanna do sixths. So, I wanna do something, so ah that's close enough. You get the idea. So 2/6 would be like this, one sixth, two sixths and 2/6 of this would be, would be like this. Let me do my best shot at drawing this. I'm trying to do six equal pieces, it's hard to hand draw, but this gets us close. 2/6 here would be that and that and if so, Store B's pizza is bigger than Store A's pizza, then I would have eaten more pizza than my unicorn. But, it might have been the other way around. Maybe Store B's pizza's like this and Store A's pizza's like this and if this was the case, my unicorn ate this 2/6 and the unicorn ate more. Or, maybe the pizzas were both this size, in which case, we would've eaten the same amount. So, just based on what they told us, we don't know how Store B's pizza compares to Store A's pizza. We don't know, We don't know whether I or my unicorn got more, got more pizza. Let's do one more of these, these are fun. It took Hiro 1/3 of an hour to run from his house to school. It took Fred 1/3 of an hour to run from his house to school. Who took more time running to school? Now, this is a good one, this is a good one, 'cause at first you might say, OK, ya know, Hiro might live here, that's Hiro's house. I'll put H for Hiro here. Maybe this is the school, I'll just try to draw larger, a larger building right here, this is the school. And, you might say, OK well maybe Fred's house, who knows where Fred's house is. Fred's house could be here. It could be there, it could be over here some place. It could be over here some place. We don't know where Fred's house is, we don't know if it's closer or further away than Hiro's house. So, you might be saying oh, we don't know. Well, remember, they're not saying who's house is closer or further away, or even who ran faster. They're telling us who took more time running to school and they directly tell us the amount of time they took. Hiro took 1/3 of an hour to run to school, from his house to school and Fred took exactly 1/3 of an hour. I don't know who ran faster or slower, or who went further distance or shorter distance, but I know that they both took the same amount of time. They both took 1/3 of an hour, so this is the same. They both took the same, same time. This questions a little bit like the famous brain teaser that some people might ask you, what weighs more, a pound of gold or a or, what would you rather have, or actually no. What would, I know which one you'd rather have. Which one weighs more, a pound of gold or a pound of cotton? And people are like oh, gold is heavier than cotton, maybe gold would make, but we're saying a pound of gold versus a pound of cotton. Well they're both a pound, they would weigh the same. That's kind of what we're doing in this question right over here.