## Changing a Mixed Number to an Improper Fraction

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Write 5 and 1/4 as an
improper fraction.
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An improper fraction is just
a pure fraction where the
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numerator is greater than
the denominator.
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This right here, it's
not a pure fraction.
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We have a whole number mixed
with a fraction, so we call
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this a mixed number.
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So let's think about what 5 and
1/4 represents, and let me
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rewrite it.
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So if we're talking about 5 and
1/4, and you can literally
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think of this as 5 and 1/4 or 5
plus 1/4, that's what 5 and
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1/4 represents.
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Five is 5 wholes, or if you're
thinking of pie, we could draw
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literally five pies.
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Let me just cut up the pies
from the get go into four
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pieces since we're dealing
with fourths.
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So let me just cut up the
pies right over here.
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So that's one pie right
over there.
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Let me copy and paste this.
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Copy and paste.
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So I have two pies, and then I
have three pies, and then I
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have four pies, and then
I have five pies.
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So this is what the
5 represents.
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5 literally represents--
so let me
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circle all of this together.
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That is the 5 part
right there.
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That is what 5 literally
represents.
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It represents five whole pies.
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Now, I have cut up the pies into
four pieces, so you can
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imagine each piece represents
a fourth.
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Now, how many pieces do I
have in these five pies?
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Well, I have four
pieces per pie.
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Let me just right it here.
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4 pieces per pie times 5 pies
is equal to 20 pieces.
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Or another way to think of it,
since each piece is a fourth,
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this is also equal to 20 times
1/4, or you could just write
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this as being equal to 20/4.
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So we have 5 whole pies is
equal to 20 fourths.
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Let me write it like that.
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20 fourths.
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Or we could write it as 20/4.
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I've kind of done the
same thing twice.
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So that's what the five
pies represent.
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20/4 or 20 pieces, where
each piece is 1/4.
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Now, the 1/4 right here
represents literally one more
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fourth of a pie or one more
piece of a pie, so let me draw
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another pie here.
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So that is another pie.
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Cut it into four pieces.
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But this 1/4 only represents
one of these pieces, right?
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This is one of the
four pieces.
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The denominator tells
us how many pieces.
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The 1 tells us how many of those
pieces we're dealing
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with, so it's just this
one piece over here.
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That right there is the 1/4.
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Now, if we write 5 and 1/4,
we just saw that the 5
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right here is 20/4.
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So we could rewrite this.
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Let me write it like this.
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5 and 1/4 can be rewritten as
the same thing as 5 plus 1/4,
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which is the same thing as--
we just saw that five whole
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pies is the same
thing as 20/4.
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And to see that these are the
same thing, you literally just
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divide 4 into 20.
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You get 5, and nothing
is left over.
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So 5 is the same thing as 20/4,
and then this plus 1/4
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is the same thing as plus 1/4.
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So if I have 20 fourths and I
add one more fourth to it, how
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many fourths do I have?
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Well, I have 21.
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I have 21 fourths.
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Or another way of thinking about
it, this 5 is-- so this
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right here is 20
pieces of pie.
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You can even count it.
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17,
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18, 19, 20.
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But a quicker way is to say,
well, we have five pies.
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Each of them have four pieces.
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5 times 4 is 20.
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This 1/4 right here represents
one piece plus one piece, so
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total we're going to
have 21 pieces.
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So we have 21 pieces, where each
piece is 1/4, so we could
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say we have 21 times 1/4 or
21 fourths pieces of pie.
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However you want to
think of it, but
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we've solved the problem.
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We're at an improper fraction.
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We've written 5 and 1/4 as
an improper fraction.
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Now, I've gone through great
pains to give you the
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intuition of what 5 and 1/4
means, but there is a fairly
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straightforward process for
getting straight to the
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improper fraction.
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Let me color code it.
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So if you have 5 and 1 over 4,
to convert it into an improper
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fraction, you're going to keep
the same denominator, so
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you're going to have
the over 4 there.
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But your numerator is going to
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fraction part before.
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So it's going to be 1 plus your
whole number times your
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denominator.
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So 1 plus-- or actually, let
me do it the way I tend to
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think of it.
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What I do is I take 4 times 5.
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So let me write that down and
I want to color code it.
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4 times 5, and then to that,
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So I literally do 4 times 5 plus
1, which is-- so this is
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equal to 4 times 5 is 20, plus
1 is 21, and then that's over
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4, so it's 21/4.
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And all of this is kind of
a fast way to do it.
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We're literally doing the exact
same thing that we did
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here in kind of a slower way.
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We're saying, OK, 5 wholes is
the same thing as 20 fourths,
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so you take 5, and I figure that
out, 5 times 4, and then
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I have one more fourth there, so
4 times 5 plus 1 gives 21.
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Title:
Changing a Mixed Number to an Improper Fraction
Description:

U02_L1_T2_we2 Changing a Mixed Number to an Improper Fraction

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Video Language:
English
Duration:
06:43
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