Let's take a look back at the number line
and the thing I want you to notice on this
number line is there are great big gaps 
between the whole numbers.
And the things is, those points on the number
line, they're numbers, too.
What should we call them?
Let's look at this point.
It's somewhere between one and two.
What should we call it?
Well, look here.
If I split each of my units into three equal
parts, I get these little line segments
that are shorter than one unit each.
And I call these short pieces because I split
my unit into three equal parts, I call them
the thirds.
So, this point, this first one that I've marked,
this is called one-third.
Two-thirds.
Three-thirds.
Right?
One copy of a third.
Two copies of a third.
Three copies of a third.
Four copies of a third.
Five copies of a third.
Six.
Seven.
Eight.
I could keep going like this.
Of course, if I stay at zero, that's no copies
of a third.
What do I call this point, then?
I call this point, five-thirds.
Now, not every point on the number line between
one and two, between zero and one, between
two and three.
Not every line on the number line can be labeled
with a fraction but many of them can.
All right, when we write this symbol, five-thirds,
as we said, this symbol represents this point
on the number line.
How have we written this?
We've written this using two numerals with
a fraction bar between them.
The five is called the numerator.
And the numerator tells us how many of these
fractional pieces we have.
Think the numerator enumerates.
It tells us how many.
The denominator, the three in this case, tells
us how many pieces we've split each unit into.
The denominator tells us what kind of fraction
we're dealing with.
Think the denominator names.
Denominator like, what denomination of currency
is that?
Right?
What kind?
How many parts has each unit been split into?
All right, what do we notice about these fractions?
The first thing to notice is how to draw them
on a number line.
So, let's suppose I asked you to plot three-fifths
and seven-fourths on the same number line.
What would you do?
Well, first you would draw a number line and
mark the units.
Before we can figure out what fractions are we
need to know what the whole units are.
So, here I'll mark again
zero, one, and two.
Three-fifths.
The denominator is five.
That tells me I want to split each unit into
five equal parts.
So, one, two, three, four, five.
Notice, to get five parts I had to make four cuts.
One, two, three, four, five.
And my artwork is terrible but these are all
the same.
Same over here.
One, two, three, four cuts to get five parts.
One, two, three - ah, it doesn't go all the
way up to three so I can't make all of the fifths.
And so the fifths are zero-fifths, one-fifth,
two-fifths, and three-fifths.
This point here is three-fifths.
To plot seven-fourths, I'll need to divide
my number line into four equal parts.
One, two, three cuts to make four parts.
One, two, three cuts.
And then one, two and I can't go all the way
to three.
So, I'll have zero-fourths, one-fourth, two-fourths,
three-fourths, four-fourths, five-fourths,
six-fourths, seven-fourths.
Ah! Here we go.
This point is seven-fourths.
Notice again, we needed to put in the units
first and then split them up.
I'm going to have you try one of these now.
Just plotting two fractions on the same number line.
Plot three-halves and three-fourths on the
same number line.
Pause the video and try this now.
All right.
Well, we'll draw a number line and start by
marking the units.
Zero.
One.
Two.
Hopefully that's enough.
To plot three-halves, we're going to have
to divide each unit into two equal parts.
And then we'll mark zero-halves, one-half,
two-halves, three-halves.
There we go.
This point is three-halves.
To mark three-fourths?
Well, fourths we want to divide each unit
into four equal parts.
And then we'll have zero-fourths, one-fourth,
two-fourths, three-fourths.
Here it is.
Here is three-fourths on our number line.
Now, there's something I want you to notice
about how we say fractions.
First we say the name of the numerator.
And we say the name of the denominator but
as what's called an ordinal number.
So, second, third, fourth.
Not, two, three, four.
There are a couple of denominators with special names.
Denominator two is always, half or halves
never second.
Denominator four can be read as quarter or
as fourth and you'll hear me do both.
It's also important to be aware of denominators
one and zero.
We cannot have zero as a denominator.
Why?
Well, each unit already has one part.
There's no way that by cutting it up I can
get rid of that.
Whenever I cut up a unit, I get more parts,
not less.
So, I'm not allowed to have zero in my denominator,
it just doesn't work.
What about one?
Denominator one just means, well, that's the
whole unit.
So, zero is zero wholes.
One is one whole.
Two is two wholes.
Three is three wholes.
And that's how we understand denominator one
and even how we read it.
If we see numerator two, denominator one we'll
say, two wholes.
