Comparing fractions of different wholes
I want to make a quick clarification based on the last video. In the last video, we compared fractions. For example, we compared 4/7 to 3/7. And we saw, clearly, 4/7 is a larger fraction of the whole than 3/7 was. But you might say, hey, but what if my whole was bigger? What if I took 3/7 of this big thing here? Then 3/7 would look like this. So it would be 1, 2, 3/7. And so this 3/7-- this looks like I have filled in more than I would have over here for the 4/7. So doesn't it matter which whole you're taking the fraction of? And the answer is yes. It does matter. And when you compare fractions, you assume that you're taking fractions of the same whole. So you can only make this comparison right over here. So it has to be-- let me make this very clear. It has to be the same. It has to be the same whole that you're making the comparison. You can't compare 4/7 of a mouse to 3/7 of an elephant. Those are two different things. You cannot make that comparison. You could compare 4/7 of a mouse to 3/7 of that same mouse, or a mouse the same size. Then you could make the same comparison. When we talk about fractions as just pure numbers, then we automatically go to the number line. The whole that we talk about when we're on the number line is the section of our number line between 0 and 1. So if this is 0 and then this is 1 here, when we talk about fractions as just pure numbers, we're not saying 4/7 of a mouse or 4/7 of an elephant. We're just talking about a number on the number line. And so we would split this into sevenths. Let me see if I could do that. Let me draw-- so that's 1/7, 2/7, 3/7, 4, 5, 6, and that's 7/7 right over there, or 1. So this is 7/7, or 1. And this right over here is 1/7, 2/7, 3/7, 4/7, 5/7, and 6/7. And so when you look at the number line here, it's clear that 3/7, which is three jumps from 0, three jumps of a seventh each-- 1, 2, 3-- 3/7 puts you right there, while 4/7 is a larger number. It's to the right of 3/7. You have to make four jumps-- 1, 2, 3, 4-- four jumps of a seventh to get right over there. So you can make this comparison as long as you're looking at the fraction of the same whole. Here, the same whole is the region of our number line between 0 and 1. In the previous video, the same whole was this yellow bar. You can't compare 4/7 of this yellow bar to 3/7 of this much larger blue bar.