>>Hi this is Julie Harland
and I'm your math gal.
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What is absolute value?
The absolute value
of a number is its distance
to zero on the number line.
And the symbol used
to denote absolute value is 2
vertical bars around a number.
Alright so if I write this,
see this 2 vertical bars
around the number negative 4,
we read this the absolute
value of negative 4.
And then this is what it
means, you have a number line.
And let's see, here's zero, 1,
2, 3, 4, that's
where negative 4 would be,
right?
So what we're looking
for is its distance to zero
so how many spaces is that?
It's basically 1, 2, 3,
4 spaces so then we say the
absolute value
of negative 4 is just the
number 4 because it's 4 spaces
from zero.
So one thing you might note is
absolute value cannot
be negative.
[silence]
It can never be negative
because we're talking
about distance
and it doesn't make sense
to talk about a
negative distance.
So here's four problems
for you to try.
See if you could figure
out the absolute value
of these four numbers.
Alright so what's the
first one?
This would be the absolute
value of negative 2.
How far is negative 2 to zero
on the number line?
It's 2 spaces from zero.
Absolute value of 3,
how far away is 3 from zero?
Three spaces.
Now you could think how far
away is 3 from zero
or how far is it
to zero from 3?
It's the same thing.
Absolute value
of negative 1/2,
alright well that's only a
half space away from zero
or half space to zero.
And 5.6, the absolute value
of 5.6, that's just 5.6
spaces away.
So that's really all there is
to it.
Let's do one more.
What about the absolute value
of zero itself?
Well if you look at that,
here's zero, right?
Alright so how far away is
zero from zero
or how far do I have to go?
No place at all so that
as well is just zero.
So notice in all
of these answers none
of them are negative
but you can have the answer
of zero.
Alright so it's not
that they're all positive,
it's just that none
of them can be negative.
So that's it.
That's all there is
to the absolute value
of a number.
If you're trying
to simplify an absolute value
and there's an expression
inside the absolute value then
first you need
to simplify inside
and then determine what the
absolute value is.
So let's look at this example,
we've got the absolute value
of 5 minus 2.
Before we you the absolute
value you first have
to just write
down what the 5 minus 2 is.
So I still write the absolute
value symbols down
but 5 minus 2 is 3.
And now I say what's the
absolute value of 3?
That would be 3.
Here's another example,
we've got the absolute value
of something
that just isn't a single
number so what you're going
to have to do is determine
first of all what
that number is.
You have to simplify it.
So in this case it's
multiplication so I have
to do 3 times 7 which is 21.
And now I take the absolute
value of 21
so you don't figure
out what the absolute value is
until you get a single number
inside of there.
And so this is just the basics
of absolute value
and it can get a lot more
complicated than this
but we're just getting
down to what does it mean.