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CCSS Math: 4.NF.B.3

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.