Multiplying fractions and whole numbers (video) | Khan Academy

Video transcript

Let ‘s think a little bit about what it means to multiply 2/3 times 6. One direction to think about it is to literally take six 2/3 and add them together. This is six 2/3 correct over here. And if we wanted to actually compute this, this would be equal to — well, we ‘re going to take these six 2 ‘s and add them together. So we could view it as 2 times 6 over 3. 2 times 6 over 3, which is the like thing, of course, as 2, 4, 6, 8, 10, 12, 12/3. And what is 12/3 equal to ? Well, we could rewrite 12 as — so this is equal to — we could rewrite 12 as 3 plus 3 plus 3 plus 3 over the yellow 3. Let me do it like this therefore I do n’t have to keep switch colors. This is going to be the lapp thing as 3/3 plus 3/3 plus 3/3 plus 3/3. And each of these are obviously a wholly. Each of these equal 1. That ‘s 1 and that ‘s 1, so this is going to be equal to 4. So that ‘s one way to conceptualize 2/3 times 6. Another means to think of it is as 2/3 of 6. So let ‘s think about that. Let me draw a number line hera. And I ‘m going to draw the numeral channel up to 6. So what I care about is the section of the phone number line that goes to 6. then that looks pretty thoroughly. So this is 1, 2, 3, 4, 5, and 6. thus if we want to take 2/3 of 6, we can think of this whole section of the act line between 0 and 6 as the whole. And then we want to take 2/3 of that. So how bash we do that ? well, we divide it into thirds, to three equals sections. So that ‘s one equal department, two equal sections, and three equal sections. And we want two of those thirds. So we want 1/3 and 2/3. immediately where does that get us ? That gets us to 4. So we get, obviously, to the same solution. We would be in a sturdy position if somehow we got two different answers. Either way, 2/3 times 6 or 6 times 2/3, either manner, that is going to be equal to 4. But there are two different ways of viewing this. This first direction is literally viewing it as 2/3 six times. And this way is we ‘re taking a divide of the number 6. We ‘re going 2/3 of the way to 6, which would get us to 4.

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