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Equivalent fraction and whole number multiplication problems

Sal relates mixed numbers to whole number/fraction multiplication problem. Created by Sal Khan.

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Video transcript

So we have here, it says 2 times 4/3 is equal to 8 times blank. And what I encourage you to do is pause the video right now and try to think about what should go in this blank. So I'm assuming you've given your try. Now, let's think through this. So 2 times 4/3, we can literally view that as the same thing as-- if we rewrite the 4/3, this is the same thing as 2 times-- instead of writing 4/3 like this, I'm literally going to write it as four 1/3's. And I know it sounds like I just said the same thing over again. But I'm literally going to write 1/3 four times-- 1/3 plus 1/3 plus 1/3 plus 1/3. If you call each of these 1/3, you literally have four of them. This is four 1/3's. 2 times 4/3 is the same thing as 2 times, literally, four 1/3's. Now, what would this be? Well, this is going to be equal to-- let me just copy and paste this-- is going to be this two times. So copy, and then let me paste it. So that's one group of those 1/3's, of those four 1/3's, or one group of one of these four 1/3's. And then, we'll have another one. And then, we'll have another one. And we're going to add them together. That's literally 2 times 4/3. So let's add these together. Now what do we have? Well, we have a bunch of 1/3's. And we need to count them up. We have one, two, three, four, five, six , seven, eight 1/3's. This is literally equal to-- and we could, just to make it clear what I've just done, we could ignore the parentheses and just add up all of these things together. So that might make it a little bit clearer. So let me do that just to make it clear that I literally take-- I've taken eight 1/3's and I'm adding them together, which is the exact same thing as 8/3. So let me clear that, and let me clear that, let me clear that. And so this is literally, or this is clearly, or hopefully clearly, equal to 8 times 1/3. I have 8 1/3's there. So going back to the original question, what is this equal to? 2 times 4/3 is the same thing as 8 times 1/3. And we've already seen that 8 times 1/3, well, that's literally 8/3. So we could also write it like this-- 8 over 3. Let me do that 3 in that other color-- 8 over 3.