One thing that a real number line is very
useful for is talking about when one number
is greater than or less than another number.
These are what are known as "inequalities".
So we use this as a greater than symbol to
indicate one number is greater than another
number, and when it's reversed we would say
that symbol indicates one number is less than
another number. Now here's how this equates
with the number line. We would say that "p"
is greater than the number "q" if "p" is to
the right of "q" on a number line. So you
have your larger numbers on the right, and
any number to left of that would be smaller.
So if you have zero here, it doesn't matter
where p and q are, they can be in the negatives,
they can be in the positives, one can be in
the negative, one can be in the positive,
all that's irrelevant. But if you have one
number here and we'll call this q, and then
you have p to the right of it, then that indicates
that p is greater than q.
So if you have these really confusing inequalities
it is very simple, all you do is you plot
them on a number line. You just see which
one is farther to the right. And, so this
is helpful for when you have negatives compared
with other negatives, and positives compared
to negatives, and so on, and so forth. So
let's try a couple, we'll do a few here, and
we'll run through some examples. So let's
say we had seven, blank three; so is seven
greater than three, or less than three? We'll
obviously we're going to start easy, seven
is clearly greater than three, we know that.
But how would you show that, how would you
explain that to somebody? Well on a number
line if here's zero, and you have zero, one,
two, three, four, five, six, seven, here's
seven, and here's one, two, here's three,
well just look on a number line, seven is
farther to the right than three is, so again
seven is greater than three, because it's
farther to the right on the number line.
So let�s try to make the next few a little
bit more challenging. How about negative three,
blank six. So for this one here we have zero,
we have negative one, two, here's negative
three, here's one, two, three, four, five,
here's six, and again six is to the right
of negative three on a number line, so we
would say negative three is less than six,
or you can say six is greater than negative
three, it doesn't matter how you say it. The
inequality would face this way.
Alright a couple of more, how about zero blank,
negative four, zero blank, negative four,
here's zero, negative one, two, three, here's
negative four. Now, four is greater than zero,
but negative four is less than zero because
it�s to the left of zero on a number line.
Another way to say that is zero is greater
than negative four, because it�s to the
right of negative four on a number line.
Alright here's where it starts to get really
challenging. How about negative nine blank,
blank negative eleven. Now these really give
students a hard time because eleven is bigger
than nine, but does that mean that negative
eleven is larger than negative nine or less
than negative nine, it gets a little confusing
when they are both negatives. Very simply
just put them on a number line here's zero,
negative one, negative two, negative three,
negative four, five, six, seven, eight, here's
negative nine, here's negative ten, here's
negative eleven. So once you have these on
a number line it is immediately clear. Negative
nine is greater than negative eleven, because
it�s to the right of negative eleven on
the number line, it doesn't matter that they
are in the negatives its simply to the right,
which makes it immediately larger.
Alright, last one and we will be done. How
about we'll just chose some crazy decimal,
four point, five, eight, one, and we will
compare this with like Pi, or something like
that. Well Pi we know is roughly three point,
one, four, one, five, nine, etc... And on
a number line we would have zero, and here�s
one, two, here's three, here's four, here's
five.
So Pi would be roughly right about here, three
point, one, four, etc... And four point, five,
eight, one, it is tough to get an exact plotting
of that point because it is such a specific
decimal. But it is roughly between four and
five. And now I see it pretty clearly, this
point: four point, five, eight, one is to
the right of Pi on a number line. So that
means it�s greater than Pi.
