>> Professor Perez: Hey!
This is Professor Perez again.
Today we're going to do subtraction.
Oh what fun!
And of course, we cannot have a class
without our student of the semester,
and that's Charlie, he better be ready to go!
Hey Charlie, you ready to go?
>> Charlie: Yeah?
>> Professor Perez: Uh-huh.
Hey, you know what?
I didn't get your last homework assignment.
What's up with that?
>> Charlie: Uh...uh...can I still turn it in?
>> Professor Perez: Sure!
You can still turn it in!
Next semester!
Uh-huh! This is college now,
you're in the big time, Charlie!
What, I suppose you're expecting me to
give you one of those take-home tests.
>> Charlie: Sure, why not?
>> Professor Perez: Yeah, you
can have a take-home test.
You can take home the test any
time you want...after I grade it!
That's right!
Uh-huh! ...tell me about take-home
tests...Anyway, let's get started.
We've got to do the first problem, right here.
6 subtract 5.
Okay, let's bring out a number line here.
Now, we're doing subtraction now, remember, when
we did addition, you move which way, Charlie?
>> Charlie: To the right.
>> Professor Perez: To the right.
Now we're doing subtraction
so we move which way, Charlie?
>> Charlie: To the left.
>> Professor Perez: To the left, that's right.
To the left.
>> Charlie: To the left.
>> Professor Perez: All right,
so, anyway, 6 subtract 5.
We start where, Charlie?
>> Charlie: 6.
>> Professor Perez: 6.
And we move which way?
>> Charlie: To the left.
>> Professor Perez: To the left,
5 times, so we end up at 1.
Very nice there, okay.
Let's do another problem here.
6 subtract 7, Charlie.
All right.
Now here we start at 6.
Now, is our answer going to be
positive or negative, Charlie?
>> Charlie: Negative!
>> Professor Perez: Negative, why?
>> Charlie: Because you're going to cross 0.
>> Professor Perez: Because we're going to
cross the 0, so, notice here if we start at 6
and we move 6 spaces to the left, right?
We're at 0.
Okay, now, remember, we start at 6 and
we're supposed to move a total of 7,
so if we move 6 we've got to
move how many more, Charlie?
>> Charlie: 1 more.
>> Professor Perez: 1 more, and
that gives us what, Charlie?
>> Charlie: Negative 1.
>> Professor Perez: Negative 1, very nice, okay.
So our answer is negative 1.
Now, 0 subtract 5.
Is this answer positive or negative?
>> Charlie: Negative.
>> Professor Perez: It's negative, because you
start at 0, and you move to the left, 5 times,
giving us our answer, negative 5.
Very nice, there.
Okay, so, let's do another one.
Negative 4 subtract 5.
Here we go.
Negative 4, we start right here.
And we move which way, Charlie?
>> Charlie: To the left.
>> Professor Perez: To the left,
5 times, and we end up where?
>> Charlie: Negative 9.
>> Professor Perez: Negative 9, very nice!
Okay, now, here we have 4 subtract 9.
So, now we start at where Charlie?
>> Charlie: 4.
>> Professor Perez: At 4.
And we move to the left...
>> Charlie: 9 times.
>> Professor Perez: 9 times, very nice.
Okay, now notice, we start at 4 and we
move 4 units to the left we end up at 0.
And we still have to move
how many more, Charlie?
>> Charlie: 5 more.
>> Professor Perez: 5 more.
And our answer is?
>> Charlie: Negative 5.
>> Professor Perez: Negative 5.
Now you notice here we started at the
4 and we moved a total of 9 units,
which gives us negative 5, there's your answer.
Okay, now, watch this, Charlie.
9 subtract 4...what's 9 subtract 4, Charlie?
>> Charlie: 5.
>> Professor Perez: That would be 5.
Very nice.
Okay, Now notice those two results at the end.
This is a Kung-Fu Math technique, because
when someone asks you, what's 4 subtract 9,
a person with good Kung-Fu says, hey, 9
subtract 4 is 5, so 4 subtract 9 is negative 5.
That's right.
So, we'll talk more about that
technique later on in the semester.
Anyway, let's move on to our
next problem here, Charlie.
This is a word problem...now don't get scared.
We're going to first do it on the number
line and then we're going to take a look
at the problem in an equation form.
Okay? So, here we go.
What number do you subtract from 5
to get to this negative 2, Charlie?
Okay? Well, watch.
If we're at 5, what number do I subtract from
5, or in other words, how far do I have to move
to the left to get to the negative 2?
Well first, if we move 5 units to
the left, we're at this 0, right?
We're trying to get to that negative 2,
so we still have to move 2 more units,
and there we are at the negative 2.
So we moved a total of how many
units to the left, Charlie?
>> Charlie: 7.
>> Professor Perez: 7.
So, what number do you subtract
from 5 to get negative 2?
The answer is what, Charlie?
>> Charlie: 7.
>> Professor Perez: 7, that's true.
So notice, 5 subtract 7 is that negative 2.
Now, here is the same problem in equations form.
This is what you'll be asked
in Beginning Algebra.
5 subtract x equals negative 2.
That equation is simply asking you, what number
do you subtract from 5 to get negative 2?
And we just did it on a number line and
the unknown number is represented by x,
which is called the variable, and the
variable x is equal to what, Charlie?
>> Charlie: 7.
>> Professor Perez: 7.
That's because 5 subtract 7 is negative 2.
We'll be doing those problems later in the
semester...you know, that's when you add numbers
or subtract numbers to both sides of an
equation, don't worry about that right now,
right now we're focusing on the number
line, to do these simple problems.
Okay, now here we go.
What number do you subtract from a
negative 3 to get negative 8, Charlie?
Negative 3 is right here and we want
to get to this negative 8, right?
Okay, and so, what number?
We start at negative 3, what
number do we subtract, we mean,
how many units to the left do we have to move?
>> Charlie: 5.
>> Professor Perez: 5, that's right.
And so, what number do you subtract from
negative 3 to get to this negative 8?
>> Charlie: 5.
>> Professor Perez: 5, that's right.
That's your answer.
So, we'll note that negative 3
subtract 5 is equal to negative 8.
There it is on the number line.
Now, in the equation form, it's
negative 3 subtract x equals negative 8.
x is called the variable, it
represents the unknown number.
That equation is basically
asking you, what number, x,
do you subtract from negative
3 to get negative 8.
And so, we just found out that
the answer's 5, so the answer,
the solution to that equation is x equals
5, because that is the unknown number.
There we go!
So, that's our introduction to subtraction.
So, we're going to keep working,
develop some more subtraction techniques
and then combine those with addition
and we're going to have lots of fun!
Anyway, remember, this is college, Charlie!
You're in the big time, I
don't take late assignments!
Anyway, we'll see you all again soon!
 
