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## Multiplying unit fractions and whole numbers

## Video transcript

Let's think about how or
what 1/2 times 5 represents. So one way to think about it is
that this could be five 1/2's added together. So you could view this
as 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2, which is the
same thing as 1 plus 1 plus 1 plus 1 plus 1, over 2,
which is equal to 5/2. The other way to
think about this is that you start with 5 things. So let's say, that's 1 thing. Let me copy and paste that
so they all look the same. So then let me paste it. So that's 2 things. That's 3 things. That's 4 things. And that's 5 things. So the other way to think about
it is you start with 5 things, and you take 1/2 of them. So what would be 1/2 of this? Well, let's see. You have 5 things, so you
would get-- 5 divided by 2 would be 2 and 1/2. So you would get this far. Let me make it like this. So you would get this one. You would get this one. And you would get this one. Now, is this the
same thing as 5/2? Well, what happens if we
divide each of these wholes into halves? So let's do that. So if we just multiplied-- so
we just divide each of these into 2. So instead of having 5
wholes, we now have 10 halves. How many of those halves
have we filled in? Well, we have filled
in 1, 2, 3, 4, 5. So this is also equal to 5/2. So far we just did it
thinking about what multiplication actually means. But if you said, well,
how did I compute this? Well, the way you
could think about it, and multiplying
fractions is actually straightforward from
that point of view, is as long as you can express
both of them as fractions, and 5 we already know is
the same thing as 5 ones, so this we can just
multiply times 5/1. So now that I've expressed
both of them as fractions, I can just multiply
the numerator. So 1 times 5 over 2 times 1. And what's that
going to be equal to? Well, 1 times 5 is 5. 2 times 1 is 2. So once again, we get 5/2.