There are many different
ways to represent fractions.
Today I'm going to be showing
you how to represent them
using a number line, a
circle, and fraction bars.
Let's first look at a number line.
Let's take the fraction 3/4
and represent that on a number line.
You can see that I've started
by drawing my number line,
and I'm zooming in on this
segment between zero and one.
Now, you might be
thinking why zero and one?
Well, I know that 3/4
is less than a whole.
So I can think of, in this case,
because my denominator is fourths,
4/4 is going to be my one.
Zero is going to be my 0/4.
So in order to put this
fraction on the number line,
I'm going to need to
segment my number line
into four equal parts.
You can see that I went ahead
and not only split it
into four equal parts,
so one, two, three, four,
but I've also gone
ahead and labeled those.
So again, I have 0/4, or
zero copy of a fourth.
I have 1/4, or one copy of a fourth,
two copies of a fourth here for 2/4,
here's one copy, two, so two copies,
three copies of a fourth here, so 3/4,
and then four copies of a
fourth to give me a whole.
I'm going to go ahead and put
this fraction on the number line.
Again, I can see that I have
one, two, three copies of 1/4,
which gives me 3/4.
I can use a number line to
represent that fraction.
Let's look at how we can use a circle
to represent that same fraction.
We can use a circle to represent
our same fraction of 3/4.
For this, just like we
did with the number line,
we're going to need to break our circle
into four equally sized pieces.
Now, if you're thinking why four,
this is what our denominator is.
Notice that I've also labeled each piece
with its correct name.
So this piece right here is 1/4,
this is another fourth,
this is another fourth,
and this is the last fourth.
Again, you can see that
there are one, two, three,
four copies of a fourth in the whole
since I've determined
the whole is this circle.
So if I'm going to shade in 3/4,
I just need to shade three copies of 1/4.
That's how we would use a
circle to represent that.
Now, there's one caveat with circles.
And that is if you have an
odd-numbered denominator,
for instance, 3/7, 2/5, 4/9,
all of these don't work well with circles.
Why is that?
'Cause it's really
difficult to cut a circle
into seven equally sized pieces.
It can be done.
It's super tricky though.
So if we're going to have
an odd-numbered denominator,
we want to use our third representation,
which is fraction bars.
Let's take our same fraction of 3/4
and now use a fraction
bar to represent it.
Again, I'm going to cut it
into four equally sized pieces.
You will also notice that
I've named each piece 1/4.
So again, I have four
copies of 1/4 in the whole.
If I need to shade in the fraction 3/4,
that means I need three
copies of a fourth.
Fraction bars actually are
not usually our default.
When we think of drawing a fraction,
we always think of pizzas
and pies and circles.
Fraction bars are actually a lot easier.
Let me show you how easy it would be
to shade in the fraction 3/7.
Now, if I'm thinking about
shading 3/7 on a circle,
that's really tricky to be able
to cut that circle into sevenths.
So let's go ahead and do it
here with our fraction bar.
I can find my center
and then know that I need
to probably scoot over a little bit
because I'm going to need to break one
side of that into fourths
and the other side into thirds.
Again, this isn't perfect,
but this is a lot easier
to show our representation
than if we were trying
to do this with a circle.
You can see that I'm going to go ahead
and label each name of each piece.
And let's just double-check.
Because we're operating in
sevenths, if this is my whole,
I should have seven copies of a seventh.
One, two, three, four, five, six, seven,
I'm good to go.
I need to shade in three
copies of a seventh,
and that's what 3/7 would look like.
One last thing, if you're
comparing fractions,
it's super important that you make sure
that your units are both the same size.
So if I was trying to
compare, say, 3/7 and 3/4,
I would want to make sure that
my units were the same length.
Notice that when I
break this into fourths,
I can see that my pieces of
1/4 are definitely larger
than my pieces of 1/7.
When I shade in 3/4,
I can easily see that it's more than 3/7.
So that's just a little side
note when you're comparing
two fractions using any representation.
I hope you found this video
helpful and you now have
a better idea on how to
represent your fractions
using a number line,
circle, and fraction bars.
