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## Multiplying fractions and whole numbers

## Video transcript

Let's think a little
bit about what it means to multiply
2/3 times 6. One way to think about it
is to literally take six 2/3 and add them together. This is six 2/3 right 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 same 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 so I don't have to keep switching colors. This is going to be
the same thing as 3/3 plus 3/3 plus 3/3 plus 3/3. And each of these are
obviously a whole. 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 way to think
of it is as 2/3 of 6. So let's think about that. Let me draw a number line here. And I'm going to draw
the number line up to 6. So what I care about is the
section of the number line that goes to 6. So that looks pretty good. So this is 1, 2, 3, 4, 5, and 6. So if we want to
take 2/3 of 6, we can think of this whole
section of the number line between 0 and
6 as the whole. And then we want to
take 2/3 of that. So how do we do that? Well, we divide it into thirds,
to three equals sections. So that's one equal
section, two equal sections, and three equal sections. And we want two of those thirds. So we want 1/3 and 2/3. Now where does that get us? That gets us to 4. So we get, obviously,
to the same answer. We would be in a tough
situation if somehow we got two different answers. Either way, 2/3
times 6 or 6 times 2/3, either way, that is
going to be equal to 4. But there are two different
ways of viewing this. This first way is literally
viewing it as 2/3 six times. And this way is we're taking
a fraction of the number 6. We're going 2/3 of the way to
6, which would get us to 4.