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Write 7/4 as a mixed number.
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So right now it's an
improper fraction.
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7 is larger than 4.
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Let's write it is
a mixed number.
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So first I'm just going
to show you a fairly
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straightforward way of doing
it and then we're going to
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think a little bit about
what it actually means.
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So to figure out what 7/4
represents as a mixed number,
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let me write it in
different colors.
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So this is going to be equal
to-- the easiest way I do it
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is you say, well, you
divide 4 into 7.
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so you divide 4 into 7
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If we're dealing with fourths,
4 goes into 7 a
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total of one time.
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4 goes into 7 a total of one time
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Let me do this in
another color.
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A total of one time
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1 times 4 is 4.
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And then what is
our remainder?
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7 minus 4 is 3.
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So if we wanted to write this
in plain-- well, let me just
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do the problem, and then
we'll think about what
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it means in a second.
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So you see that 4 goes into 7
one time, so you have one
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whole here, you have one whole ,and then how much
do you have left over?
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Well, you have 3 left
over, and that comes
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from right over there.
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That is the remainder when
you divide 4 into 7.
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3 left over, but it's 3 of
your 4, or 3/4 left over.
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So that's the way we just
converted it from an improper
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fraction to a mixed number.
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Now, it might seem
a little bit like
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voodoo what I just did.
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I divided 4 into 7, it goes
one time, and then the
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remainder is 3, so
I got 1 and 3/4.
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But why does that make sense?
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Why does that actually
makes sense?
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So let's draw fourths.
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Let's draw literally 7 fourths
and maybe it'll become clear.
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So let's do a little
square as a fourth.
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So I'm gonna do it. Say I have a square
like that, and that is 1/4.
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Now, let's think about what
seven of those mean, so let me
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copy and paste that.
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Copy and then paste it.
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So here I have 2 one-fourths,
or you could see I have 2/4.
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Now I have 3 one-fourths.
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Now, I have 4 one-fourths.
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Now this is a whole, right?
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I have 4 one-fourths.
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This is a whole.
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So let me start on
another whole.
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So now I have 5.
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Now I have 6 one-fourths, and
now I have 7 one-fourths.
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Now, what does this look like?
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So all I did is I rewrote
7/4, or 7 one-fourths.
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I just kind of drew
it for you.
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Now, what does this represent?
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Well, I have 4 fourths
here, so this is 4/4.
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This right here is 3/4.
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Notice, 7/4 is 4/4 with
3/4 left over.
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So let me write it this way.
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7/4 is 4/4 with 3/4 left over.
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Now what is 4/4?
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What is 4/4?
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4/4 is one whole.
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So you have one whole with
3/4 left over, so you end
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up with 1 and 3/4.
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So that is the 3/4 part and
that is your one whole.
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Hopefully that makes sense and
hopefully you understand why
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it connects.
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Because you say, well, how
many wholes do you have?
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When you're dividing the 4 into
the 7 and getting the
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one, you're essentially saying
how many wholes?
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How many? How many?
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So the number of wholes, or you
can imagine, the number of
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whole pies.
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And then how many pieces
do we have left over?
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Well, we have 3 pieces and each
piece is 1/4, so we have
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3/4 left over.
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So we have one whole pie and
three pieces, which are each a
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fourth left over.