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Write 5 and 1/4 as an[br]improper fraction.

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An improper fraction is just[br]a pure fraction where the

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numerator is greater than[br]the denominator.

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This right here, it's[br]not a pure fraction.

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We have a whole number mixed[br]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[br]1/4 represents, and let me

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rewrite it.

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So if we're talking about 5 and[br]1/4, and you can literally

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think of this as 5 and 1/4 or 5[br]plus 1/4, that's what 5 and

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1/4 represents.

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So let's think about 5.

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Five is 5 wholes, or if you're[br]thinking of pie, we could draw

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literally five pies.

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Let me just cut up the pies[br]from the get go into four

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pieces since we're dealing[br]with fourths.

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So let me just cut up the[br]pies right over here.

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So that's one pie right[br]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[br]have three pies, and then I

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have four pies, and then[br]I have five pies.

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So this is what the[br]5 represents.

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5 literally represents--[br]so let me

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circle all of this together.

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That is the 5 part[br]right there.

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That is what 5 literally[br]represents.

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It represents five whole pies.

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Now, I have cut up the pies into[br]four pieces, so you can

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imagine each piece represents[br]a fourth.

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Now, how many pieces do I[br]have in these five pies?

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Well, I have four[br]pieces per pie.

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Let me just right it here.

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4 pieces per pie times 5 pies[br]is equal to 20 pieces.

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Or another way to think of it,[br]since each piece is a fourth,

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this is also equal to 20 times[br]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[br]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[br]same thing twice.

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So that's what the five[br]pies represent.

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20/4 or 20 pieces, where[br]each piece is 1/4.

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Now, the 1/4 right here[br]represents literally one more

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fourth of a pie or one more[br]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[br]one of these pieces, right?

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This is one of the[br]four pieces.

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The denominator tells[br]us how many pieces.

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The 1 tells us how many of those[br]pieces we're dealing

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with, so it's just this[br]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,[br]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[br]the same thing as 5 plus 1/4,

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which is the same thing as--[br]we just saw that five whole

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pies is the same[br]thing as 20/4.

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And to see that these are the[br]same thing, you literally just

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divide 4 into 20.

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You get 5, and nothing[br]is left over.

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So 5 is the same thing as 20/4,[br]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[br]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[br]it, this 5 is-- so this

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right here is 20[br]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,[br]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,[br]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[br]one piece plus one piece, so

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total we're going to[br]have 21 pieces.

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So we have 21 pieces, where each[br]piece is 1/4, so we could

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say we have 21 times 1/4 or[br]21 fourths pieces of pie.

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However you want to[br]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[br]an improper fraction.

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Now, I've gone through great[br]pains to give you the

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intuition of what 5 and 1/4[br]means, but there is a fairly

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straightforward process for[br]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,[br]to convert it into an improper

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fraction, you're going to keep[br]the same denominator, so

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you're going to have[br]the over 4 there.

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But your numerator is going to[br]be your numerator of the

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fraction part before.

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So it's going to be 1 plus your[br]whole number times your

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denominator.

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So 1 plus-- or actually, let[br]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[br]I want to color code it.

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4 times 5, and then to that,[br]I add this numerator.

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So I literally do 4 times 5 plus[br]1, which is-- so this is

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equal to 4 times 5 is 20, plus[br]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[br]a fast way to do it.

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We're literally doing the exact[br]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[br]the same thing as 20 fourths,

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so you take 5, and I figure that[br]out, 5 times 4, and then

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I have one more fourth there, so[br]4 times 5 plus 1 gives 21.

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