Introduction to Order of Operations Part 1


Uploaded by MuchoMath on 12.07.2008

Transcript:
>> Professor Perez: Hey!
This is Professor Perez again.
Today, we're going to do an introduction to the Order of Operations.
Of course, we can't get started 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: All right, we're doing Order of Operations today, an introduction!
Okay, here we go, Order of Operations, right here, Charlie.
Now, there are four parts...FOUR...to Order of Operations.
First part has to do with parenthesis.
First, perform the operations within the parenthesis.
So here's our example.
6 subtract the quantity 4 subtract 1.
The 4 subtract 1 is in parenthesis so we have to do that first, Charlie.
Now watch.
What's 4 subtract 1?
>> Charlie: 3.
>> Professor Perez: 3.
Then we bring down our 6 subtract 3.
Now notice we have a 3 in the parenthesis.
That 3 is positive, therefore,
we don't necessarily need those parenthesis around that positive 3.
We're going to talk more about this when we start dealing
with subtracting negative numbers and adding negative numbers.
So, we don't necessarily need that 3 in parenthesis so we'll bring it down.
6 subtract 3.
Now what's 6 subtract 3, Charlie?
>> Charlie: 3.
>> Professor Perez: 3, very nice!
And that's our answer there.
All right, let's do another one!
8 subtract the quantity 4 plus 1.
Now, Charlie, we have 4 plus 1 in parenthesis.
What is 4 plus 1?
>> Charlie: 5.
>> Professor Perez: 5.
That's right.
>> Charlie:
>> Professor Perez:
>> Charlie:
>> Professor Perez:
>> Charlie:
>> Professor Perez: And it's 8 subtract 5.
Again, we have a positive 5 in the parenthesis.
We don't necessarily need it.
So we have 8 subtract 5.
What is it, Charlie?
>> Charlie: 3.
>> Professor Perez: It's 3, the same as the one before.
Our answer is 3.
Very nice!
But notice, we're doing the parenthesis first!
Okay, now, here's another problem here, another expression with two parentheses.
Now, the parentheses have to be done first before you move on.
The first set of parenthesis, 4 subtract 7, is what, Charlie?
>> Charlie: Negative 2...3.
>> Professor Perez: Negative 3 in parenthesis, okay.
And the next one, what's 5 plus 1?
>> Charlie: 6.
>> Professor Perez: That's 6, and don't forget we have a subtraction between those two.
Now, negative 3 is in parenthesis but because it's the leading term of this expression,
we don't need those parentheses around that negative 3,
and we can just write it as negative 3 subtract 6.
Now, the 6 was positive in the parenthesis.
So, if this is giving you problems, ask your tutor, your facilitator, your parents,
your brother or sister, and work at this.
But we'll talk more about these parentheses when you can take them off, when we get to adding
and subtracting negative numbers, which is coming up pretty soon.
Now, negative 3 subtract 6, Charlie, think of the number line.
Think of the number line.
Negative 3, we subtract, which way do we move, Charlie?
>> Charlie: To the left!
>> Professor Perez: To the left, that's right, so negative 3 subtract 6 would be what, Charlie?
>> Charlie: Negative 9.
>> Professor Perez: Negative 9, very nice there!
So, we should have our subtraction techniques down by now.
Okay, now, we've done parenthesis.
So, now we're moving to the next one which is the second step,
the second thing to look for is exponents, okay?
Simplify any numbers that exponents.
Okay, so here's our example, 6 subtract 3 squared.
Now, a lot of people want to do 6 subtract 3 first.
Well, if you do that, you'll be coming back next semester to repeat the class.
Remember, Order of Operations, you have to do parenthesis first.
Well we don't have any parenthesis.
We have to do the exponent.
Now, that is 6 subtract 3 squared, that is not a negative 3 up there, not the way it's written.
It's 6 subtract 3 squared, so do the exponents, what's 3 squared, Charlie?
>> Charlie: 9.
>> Professor Perez: 9.
And so we have 6 subtract 9, and now a subtraction, 6 subtract 9 is a what, Charlie?
>> Charlie: Negative 3.
>> Professor Perez: Negative 3, very nice, okay.
Now, here's a problem with parenthesis.
Parenthesis first.
Now in this problem, with those parenthesis over there, you have to do the 6 subtract 3.
What's 6 subtract 3, Charlie?
>> Charlie: 3.
>> Professor Perez: It is 3.
And so it's 3 squared.
And, do we need the parenthesis around that 3, Charlie?
>> Charlie: No.
>> Professor Perez: It's a positive 3, we don't necessarily need it.
So 3 squared is what, Charlie?
>> Charlie: 9.
>> Professor Perez: It's 9, that's right.
It's 6 if you want to repeat this class!
Remember, 3 squared means 3 times 3 which is 9.
Go back and review that exponent video if you're having problems.
7 plus 2 squared, here's another problem.
Exponents first!
Charlie, what's 2 squared?
>> Charlie: 4.
>> Professor Perez: It's 4, that's right.
7 plus 4 is 11, there we go.
There's our answer.
Now, let's go to our third one.
So we have parenthesis, we have exponents, now we're going to the next, the third one,
which is perform multiplication and division
in order working left to right, very important here.
And so here's an example.
6 divided by 3 times 2.
Now, a common error is to do the 3 times 2 first,
but Order of Operations says you do multiplication and division all
at the same time working left to right, whichever one comes first.
Now, since the division is first here, we do the division, 6 divided by 3 is 2,
bring down our times 2, and now we can do multiplication.
2 times 2 is 4.
Be very careful with this.
Let's do another one.
This is 6 times 3 divided by 2.
Remember, Order of Operations does not say do multiplication before division.
It doesn't say that.
It says do multiplication and division at the same time,
whichever comes first working left to right.
Now this problem, 6 times 3 divided by 2.
Which comes first, Charlie, the multiplication or division?
>> Charlie: Multiplication.
>> Professor Perez: The multiplication.
So we do 6 times 3 which is 18 divided by 2.
What's 18 divided by 2, Charlie?
>> Charlie: 9.
>> Professor Perez: 9.
You better know that by now.
And that is our answer there.
All right.
Now let's step it up a bit.
Let's do this problem over here.
Now, what do we have to do first, Charlie?
>> Charlie: Parenthesis.
>> Professor Perez: Parenthesis, that's right.
5 plus 3 is 8.
We'll bring down our work.
Now, again, we don't necessarily need that parenthesis around the 8.
Now, we have 8 divided by 2 squared times 2.
What do we have to do next?
>> Charlie: Exponent.
>> Professor Perez: The exponent, the 2 squared.
Now, what's 2 squared, Charlie?
>> Charlie: 4.
>> Professor Perez: 4, okay, so we'll do that first, and we'll bring down our work.
8 divided by 4 times 2.
Now, division and multiplication, Charlie.
We do them at the same time working left to right,
so we've got to do...we have to do division first.
8 divided by 4 is 2.
2 times 2, right?
Is 4. And that is our answer there.
Very nice there, Charlie.
All right, let's go to our last one now.
We have parenthesis, exponents, multiplication, division,
and the last part is addition and subtraction.
The fourth part is to perform addition and subtraction
in order working left to right, whatever comes first.
So, 6 subtract 3 plus 2, you cannot add the 3 plus 2 first.
It doesn't say do addition before subtraction.
It says do whatever comes first working left to right.
So you must do the 6 subtract 3 which is 3, and then add the 2.
And Charlie, what's 3 plus 2?
>> Charlie: 5.
>> Professor Perez: That's 5, very nice.
And so here's another one.
6 plus 3 subtract 2, Charlie.
Be careful with this.
Which do we do first?
>> Charlie: Addition.
>> Professor Perez: The addition because it comes first working left to right.
And 6 plus 3 is what, Charlie?
>> Charlie: 9.
>> Professor Perez: 9, subtract 2, that's right.
What's 9 subtract 2?
>> Charlie: 7.
>> Professor Perez: 7, very nice.
Now, step it up a bit.
5 plus 3 in parenthesis, subtract 2 squared plus 4.
Parenthesis first, which is 8, and now, bring down our work.
What's next, Charlie?
We've done our parenthesis, do we have exponents?
>> Charlie: Exponents!
>> Professor Perez: Yes, so we've got to do the 2 squared which is a 4, right?
And we bring down our work.
8 subtract 4 plus 4.
Now, addition, subtraction, which one comes first?
>> Charlie: Subtraction.
>> Professor Perez: Subtraction, so we do 8 subtract 4, which is what, Charlie?
>> Charlie: 4.
>> Professor Perez: 4.
4 plus 4 is 8.
Very nice there, Charlie!
So, that's our Order of Operations.
Now, let's do a couple of problems.
And remember, parenthesis, exponents, multiplication and division is done
at the same time working left to right, addition and subtraction done
at the same time working left to right.
So, here we go, we're going to step it up.
Here's our problem, we have parenthesis, we've got to do those first, Charlie, right?
And so that's 8, bring down your work, okay?
Now, no more parentheses.
Do we have exponents, Charlie?
>> Charlie: Yes.
>> Professor Perez: Yes, the 2 squared, so we'll do that first.
4. Right? Bring down our 8 subtract 4 and bring down the rest of our work.
Now, no more exponents.
So we're looking at our multiplications and divisions Charlie.
Okay, do we have multiplications and divisions?
>> Charlie: Yes.
>> Professor Perez: Okay, now working left to right, which one comes first?
>> Charlie: The division.
>> Professor Perez: The division, so we have to do that operation first.
And that's not a negative 4, it's 4 divided by 4.
It's 8 subtract 4 divided by 4 times 3.
So we have to do the 4 divided by 4 first.
What's 4 divided by 4, Charlie?
>> Charlie: 1.
>> Professor Perez: That's 1, that's the easy one.
And bring down your work.
8 subtract 1 times 3.
Very nice!
Now, do we have any multiplications and divisions, Charlie?
>> Charlie: Yeah.
>> Professor Perez: Yes, we have a subtraction and a multiplication.
Which one do we do first?
>> Charlie: Multiplication.
>> Professor Perez: The multiplication, that's right.
And so, 1 times 3 is what, Charlie?
>> Charlie: 3.
>> Professor Perez: It is 3.
Now remember, that's not a negative 1.
It's 8 subtract 1 times 3, that's how it's written.
1 times 3 is 3, and finally 8 subtract 3 is what Charlie?
>> Charlie: 5.
>> Professor Perez: 5.
There you go, that's our answer!
Phew! That was a tough one, right?
All right.
Let's do another tough one!
That's right!
Here we have 4 squared subtract 2 cubed divided by 4 times 3.
Now don't get scared!
Okay, Charlie, do we have any parenthesis?
>> Charlie: No.
>> Professor Perez: No we don't.
Do we have exponents?
>> Charlie: Yes.
>> Professor Perez: Yes we do!
So let's do our exponents first.
Now what's 4 squared, Charlie, remember, 4 squared means 4 times 4, right?
And so what is it?
>> Charlie: 16.
>> Professor Perez: 16.
Now, we have a 2 cubed, it's not a negative 2, that's a subtraction symbol.
It's 2 cubed, now, 2 cubed means 2 times 2 times 2, which is what, Charlie?
>> Charlie: 8.
>> Professor Perez: Which is 8, that's right.
Now, bring down our work.
We have a subtraction between those two, and bring down our divided by 4 times 3.
All right, now here we go, Charlie.
Do we have any divisions or multiplications?
>> Charlie: Yes.
>> Professor Perez: Yes, we do.
Now which one comes first?
>> Charlie: Division.
>> Professor Perez: The division, so we have to do that first.
So we have 16 subtract 8 divided by 4 times 3.
We've got to do the 8 divided by 4 first.
And what's 8 divided by 4, Charlie?
>> Charlie: 2.
>> Professor Perez: 2, right?
Okay, bring down your work.
16 subtract 2 times 3.
All right.
Now, what do we do first?
We've got a subtraction and a multiplication Charlie.
>> Charlie: Multiplication.
>> Professor Perez: You have to do the multiplication first, right?
All right, now here we go.
Now, it's just 2 times 3, right?
What's 2 times 3, Charlie?
>> Charlie: 6.
>> Professor Perez: 6, right?
And we have 16 subtract 6 which is 10.
Phew! Very nice there!
Now all these expressions that we've worked on, we've been dealing with positive numbers.
Remember, the negative numbers are coming.
I know you're thinking, well what happens when you're subtracting a negative number,
adding a negative number, you know, it's easy to get confused
in all this stuff, but we've got to work in steps.
These problems here, they're all positive numbers,
and we're just working through them, okay?
So practice and then we'll move on.
So, we'll see you all again soon!