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CCSS.Math:

My wife and I have recently
purchased an assortment pack of soap, and we both want
to experience all 3 bars. And we are not willing to
share soap with each other. So we have a little
bit of a conundrum. How do we share
these 3 bars of soap so that we each get to
experience all of the smells? So this might be
a nice rose smell. This might be some
type of ivory smell. I don't even know if
that's a legitimate smell. This might be some
type of sandalwood, which is always very nice. And my wife has an idea. She says, look I'm going
to take these 3 bars, so we're starting
with 3 bars of soap. And I'm going to divide
it into 2 equal groups. And I said, how are
you going to do that? And she says, well, I'm
just going to take out some type of carving
saw or carving knife, or who knows what
it is, and I'm just going to cut it right down the
middle, so right down this. This is my wife cutting the soap
right over here with her saw. So she's cutting the
soap right over here. So she has divided the
soap into 2 equal groups. So she's taken 3 bars, and she's
divided into 2 equal groups. So the interesting question
here is, how many bars of soap do we each have now? And I encourage you
to pause the video and think about
that for a second. How many bars of soap
do we each have now? Well, let's just
visualize my share. Let's say I take this
bottom half right over here. So this is Sal's
share of the soap. Let me write this out. So this is Sal's share. My wife took this top half. Well, what do I have? Well, I have 1/2, I have another
1/2, and I have another 1/2 of a bar. So I have 3/2 bars of soap. Or you could say that I have
3 times 1/2 bars of soap. Notice, something very
interesting happened here. 3 divided by 2 is
equal to 3 times 1/2. And we could make it
even more interesting, because we know 2 is the
exact same thing as 2/1. So 3 divided by 2/1 is
equal to 3 times 1/2. Notice we went from a
division to a multiplication, and we took the reciprocal. And that makes complete sense. We have 3/2 bars now. But what's 3 times 1/2? Well, 3 times 1/2
is equal to 3/2. So just doing this little
simple, smelly soap example, we've got a very
interesting result. 3 divided by 2 is the
same thing as 3 times 1/2, which is the same thing as 3/2.