Changing an Improper Fraction to a Mixed Number

U02_L1_T2_we3 Changing an Improper Fraction to a Mixed Number

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 into 7.

so you divide 4 into 7

If we're dealing with fourths,
4 goes into 7 a

total of one time.

4 goes into 7 a total of one time

Let me do this in
another color.

A total of one time

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, you have one whole ,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 I'm gonna do it. 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?

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?

How many? How many?

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.