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## Fractions and whole numbers

## Video transcript

So let's say that this
circle-looking thing represents a whole. We've already seen a
couple of situations. We said, hey, look,
we could divide this into two equal pieces. And if we shade in
one of them-- so one of these equal pieces--
that would be 1/2. And then if we shade in two
of them, this would be 2/2. So let me color that
in a little bit better. So this right over here, I've
divided into two equal pieces. And I'm shading in two
of these equal pieces. So what fraction of the
whole do I have shaded in? Well, we've seen
this multiple times. This is 2/2 of
the entire figure. And we see we've shaded
in the entire figure. So this is equal to 1 whole. And we could do that. We don't have to just split
it into two equal parts. We could split it into
three equal parts. So let's say we were to split
it into three equal parts-- let me do that, my best attempt
to draw three equal parts. Three equal parts looks
like a Mercedes symbol. And that's my best. I could draw a little
bit better job of that. Let me be clear that I'm
trying to make them equal. So that's three equal parts. And then if we were to
actually shade in the three equal parts-- so that
would be one of the three, so that's 1/3, 2/3, and 3/3. So once again, 3/3
is equal to 1 whole. Now, what if we were to do
something, on some level, even simpler? What if we just take our
whole and we divide it into only one equal section? Well, I've already done that. This is one equal
section right over here. And then I were to select
that one equal section-- so let me color it in. So I have one section, and
I'm going to shade it in. So what fraction of the whole
do I now have shaded in? Well, I had one equal
section to begin with. And I shaded in that
one equal section. So I have 1/1 of this shaded in. And this is also
clearly an entire whole. So this is also
equal to a whole. And I think you
see a pattern here. 2/2, 3/3, or 1/1-- these all
represent the exact same value. They all represent a whole. And you would also see this if
you were to draw a number line. So this is 0. This is 1. We could keep on going. Well, this is 1/1. If I were to say, well,
between 0 and 1, I just have 1, I divide it into one
equal chunk, well, that's just this whole
thing right over here. And if I were to move one
of those equal chunks, I would get to 1. If I divide it into two equal
chunks and if I make two jumps-- one, two jumps--
I still end up at 1. If I divide it into three
equal sections-- so let's say one, two, three
equal sections-- and I make three jumps-- one, two,
three-- I end up at 1 again. So 2/2, 3/3, 1/1,
or 1 over 1-- these all are different ways of
representing the number 1, or 1 whole.