>> Professor Perez: Hey!
This is Professor Perez.
Today we are going to be
working on Absolute Value.
Of course, we've got to get Charlie
out, he better be ready to go!
Hey, Charlie, you ready to go?
>> Charlie: Yeah!
>> Professor Perez: All right,
here we go, right there!
Absolute value.
Absolute values actually represent distance.
That's why they're always positive.
That's true!
So, absolute value represents a distance.
Now, here we go.
The absolute value of negative 3.
Notice, the symbol for absolute value is
these two bars around that negative 3.
Well, the absolute value of negative
3 represents the distance, Charlie,
between 0 and negative 3 on the number line.
So, Charlie, if somebody asks
you how far is it from here
to the grocery store, what are you going to say?
>> Charlie: 5 miles?
>> Professor Perez: Yeah,
it would be about 5 miles.
You're not going to tell them
it's negative 5 miles, right?
Distances are always positive, that's why
absolute values are always positive, right?
Okay, now, if we look at the
number line here, Charlie,
how far apart are negative
3 and 0 on the number line?
What's the distance between them?
>> Charlie: 3.
>> Professor Perez: It is 3,
and that would be your answer.
So, let's do this one, the absolute value of 3.
How far apart is 3 and 0 on
the number line, Charlie?
>> Charlie: 3.
>> Professor Perez: 3 units, it's right there.
So the absolute value of 3 is 3.
There you go!
How about the absolute value
of negative 10, Charlie?
Negative 10 is over here, and 0 is over there.
How far apart are they?
>> Charlie: 10.
>> Professor Perez: 10.
So the absolute value of negative 10 is 10.
There you go!
All right, how about the absolute
value of negative 3 plus 5.
Well, before you do the absolute value,
you've got to simplify what's inside.
We'll do the operation that's inside.
In this case, it's an addition problem.
Charlie, what's negative 3 plus 5?
>> Charlie: 2.
>> Professor Perez: It's 2.
Now, we have the absolute value of 2.
What is the absolute value of 2, Charlie?
>> Charlie: 2.
>> Professor Perez: It's 2 because
the distance between 0 and 2 is 2.
That's it.
Now, over there.
Absolute value of negative 3 subtract 5.
Again, do the operations that are
inside the absolute value first.
Now, Charlie, what's a negative 3 subtract 5.
Charlie?
>> Charlie: Negative 8.
>> Professor Perez: Negative 8, and so now,
what is the absolute value of negative 8?
>> Charlie: 8.
>> Professor Perez: It's 8, there you go!
All right, now, let's move on.
We're going to move on to another
concept called the opposite.
And this is where students tend to
get confused because you're going
to hear me say opposite and negative.
We're so used to using, saying
negative when it comes to an opposite,
but opposites actually has something to
do with distance, you'll see right now.
Now, here we're asked, what
is the opposite of 3?
Well, the opposite of 3 is negative 3.
What does that mean?
Well, both 3 and negative 3 each are a
distance of 3 from 0 on the number line.
Watch. Here's a number line here, 3 is
over there, it's a distance of 3 from 0.
Negative 3 is over here, a distance of 3.
So negative 3 and 3 are called
opposites of each other.
Just like 4 and negative 4 would
be opposites of each other.
5 and negative 5 would be
opposites of each other.
Now, so here's a question here.
What is the opposite of 5?
Well, if we think of a number line, 5 is over
there, what is the opposite of 5, Charlie?
>> Charlie: Negative 5.
>> Professor Perez: It's this negative 5.
Remember, 5 is a distance
of 5 from 0 on that side.
On this side, negative 5
is a distance of 5 from 0.
So, they are opposites of each other.
And somebody asks you, Charlie, what is the
opposite of negative 5, what would you say?
Opposite of negative 5 is what?
>> Charlie: 5.
>> Professor Perez: Is 5.
It's very simple when they
ask you this in words, right?
What's the opposite 5?
Negative 5.
What's the opposite of negative 5, Charlie?
>> Charlie: 5.
>> Professor Perez: 5.
Well, how do you ask this
question using math symbols?
That's where it gets tricky, so, play
close attention, Charlie, here we go.
Right here.
We have a negative, or an opposite.
I want to read it as an opposite.
That is the opposite of 5.
That's what that statement is asking you.
What is the opposite of 5, Charlie?
>> Charlie: Negative 5.
>> Professor Perez: Negative 5, that's right.
We will soon find out the opposite,
taking the opposite of a number is just
like multiplying a number by negative 1.
We'll talk about multiplication with
negative numbers in the next video.
All right, so the opposite
of 5 is negative 5, right?
Okay, Charlie, now, what's
the opposite of negative 5?
>> Charlie: 5.
>> Professor Perez: It's a
positive 5, that's right.
The opposite of a negative number, right?
The opposite of a negative
number will always be positive.
That's sometimes called the
double negative rule.
Really, we can think of it as the basis
of why the negative times a
negative is a positive, okay?
We'll get to that in the next video.
Anyway, opposite of 5 is a negative 5.
Opposite of negative is a positive 5.
Okay, let's do some problems now.
Charlie, what's the opposite of 3?
>> Charlie: Negative 3.
>> Professor Perez: Negative 3.
And that's it.
What's the opposite of negative 3?
>> Charlie: Positive 3.
>> Professor Perez: That's 3.
Okay, you can think of this
as a double negative rule.
Negative times a negative
is a positive, that works.
All right, be careful with this one.
This is the opposite of the absolute value of 3.
The first thing you have to do, is you've
got to evaluate the absolute value.
You've got to take that absolute value.
Remember, Order of Operations never
talked about absolute value, did it?
Order of Operations was parenthesis, exponents,
multiplication and division done working left
to right, and then additions and subtractions
done in order working left to right.
That was the Order of Operations.
Now, what is the absolute value of 3, Charlie?
>> Charlie: 3.
>> Professor Perez: It's 3.
So notice, all we've done is we've
evaluated the absolute value of 3.
Don't forget, we've got that opposite or
negative sign, you've got to bring that down.
And now the question becomes
just like this first one.
That's asking you, what is the opposite of 3?
It is negative 3, and there you go.
Let's do this on over here.
Now, pay close attention to this, Charlie.
That is the opposite of the
absolute value of negative 3.
That's different from this question up here.
This question is saying what's the opposite
of negative 3, it's positive 3, right?
That's asking you what's the opposite
of the absolute value of negative 3.
Well, what is the absolute
value of negative 3, Charlie?
>> Charlie: 3.
>> Professor Perez: It's 3, okay.
And don't forget, bring down
your negative sign, or opposite.
And now it becomes, what's the opposite of 3.
It's a negative 3.
So be very careful and think
about the difference
between that absolute value problem
at the end and this one here.
This is a double negative rule, that's not
a double negative, that's a absolute value,
it's the opposite of the absolute value
which gives you a negative number.
Tricky, right?
All right, phew!
Let's move on.
Let's do some problems here.
Now, opposite of the difference of 7 subtract 5.
Well, Order of Operations, do the parenthesis
first, what's 7 subtract 5, Charlie?
>> Charlie: 2.
>> Professor Perez: 2, bring down your
negative and what's the opposite of 2,
or what's the negative of 2, you can
say it that way, it's negative 2.
There you go.
Now, here, we have a difference, with a
negative sign outside, or an opposite.
What's 5 subtract 9, Charlie?
>> Charlie: Negative 4.
>> Professor Perez: Negative 4.
That's done in the parenthesis, so bring
down your opposite or your negative sign.
And what's the opposite of negative 4?
>> Charlie: 4.
>> Professor Perez: It's positive 4.
Or double negative, however
you want to think of it.
The answer is 4.
Now, let's go to the next one.
A little tricky here.
We have an absolute value over there.
What's the...now in the absolute
value we have a difference,
what's negative 3 subtract 2, Charlie?
>> Charlie: Negative 5.
>> Professor Perez: That's a negative 5.
Right? Okay, so the absolute
value of negative 5.
Don't forget to bring down
your opposite or negative sign,
and don't forget you've got
to subtract 3 at the end.
Now, next step.
You've got to do that absolute value first.
What's the absolute value
of negative 5, Charlie?
>> Charlie: 5.
>> Professor Perez: 5, bring down
your negative sign, okay, subtract 3,
and now, what's the opposite of 5?
>> Charlie: Negative 5.
>> Professor Perez: Negative
5, and then we subtract 3,
and so negative 5 subtract 3 is what, Charlie?
>> Charlie: Negative 8.
>> Professor Perez: Negative 8.
Very nice there, Charlie!
So, we're going to stop right there.
Now I know this opposite, the
negative, and you get all confused,
but you have to work it out,
everybody thinks differently.
Now, get some help with your tutor, with
your facilitator, your teacher, your parents,
your children, and try to get this
straightened out because now we're going to move
on to multiplying and dividing negative numbers.
And after that, everybody's
favorite subject, fractions!
>> Charlie: Uggghhhh...
>> Professor Perez: Anyway,
we'll see you all again soon!
 
