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## Topic B: Fractions as division

## Video transcript

In the previous video, splitting
this three-pack of soap with my wife, she cut it
right down the middle. So we each got half of all
three bars, or we got 3/2, or each of us got
3/2 bars of soap. Now, just to make
sure that we really understand what 3/2
is-- and remember, 3/2 is really the same
thing as 3 divided by 2. If someone says 3
divided by 2, you could say, hey, I'm going
to represent that as 3/2. Or someone says 3/2,
you could say, well, that's the same thing
as 3 divided by 2. But just to really
understand this number, let's actually think about
where we would plot it on a number line, as well. So let me draw a
number line here. I'm going to start that as 0. Let me draw a line,
as straight a line as I am capable of drawing. And let's say that this
right over here represents 1. So that would be 1 bar
of soap in this example. And let's say that this
right over here is 1/2 bar. This is 1/2 bar. And let's say that
this is 1 and 1/2 bars. And let's say that this right
over here is 2 bars of soap. So we have 3/2. So let's think about this. Remember, 3/2 is 3 times 1/2. Or, since we already
split this into halves, we just have to go
3 of these halves. So let's do that. So this is 1/2. This is 1/2. Now we're going to have 2/2. That takes us to 1. And we know that because
2/2 is equal to 1. And now let's do our third half. Our third half is
right over here. And so that is 3/2. And we see 3/2 is the exact
same thing as 1 and 1/2. Now, just to hit
that point home, we already saw that 3/2 is the
same thing as 3 divided by 2. If you were to divide 3 by
2, you would get-- well, 2 goes into 3 exactly one time. And then what would
you have left over? Well, you would
have 1/2 left over. So 3/2 is the same
thing as 1 and 1/2, which is exactly
what we saw here. You could view this as we
have 1 and 1/2 bars of soap. And this is where you would
plot it on the number line. 3/2 is halfway in
between 1 and 2.