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

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