Uploaded by MuchoMath on 23.06.2008

Transcript:

>> Professor Perez: Hey!

This is Professor Perez again.

Today, we're going to work on some properties of addition.

And of course, we cannot have a class without our student of the semester, and that's Charlie.

He better be ready to go!

Charlie! Wake up over there!

What do you think you're doing?

You've got your piece of paper?

And a pencil?

What, are you tired?

>> Charlie: Yeah, I've been working.

I've got a lot of things going on in my life!

>> Professor Perez: Nobody wants to hear your story!

And by the way, how many of you out there are working and are tired too?

Yeah, you're not the only one, Charlie!

Anyway, let's get to work!

Yeah, you better be ready Charlie, here we go!

Our first problem is right there.

2 plus 3, Charlie.

So, how do we do 2 plus 3 on a number line, Charlie?

>> Charlie: Start at 2, move right 3.

>> Professor Perez: Okay, we start at 2 and we move to the right 3 times.

And that gives us 5.

Very nice, there Charlie, okay.

Now, watch what happens here Charlie, we're going to switch the order

on 2 plus 3 and make it 3 plus 2.

Now, if we're doing 3 plus 2, we start at 3 and we move

to the right 2 times which again, gives us 5.

And so, Charlie, 2 plus 3 and 3 plus 2 both give us the same answer, correct?

>> Charlie: Yes.

>> Professor Perez: All right.

Now, that is showing us that hey!

If you're adding two numbers together, and you switch the order, you get the same result.

And that is what's called the Commutative Property for Addition.

Right there Charlie, so, the Commutative Property for Addition says

that a plus b is the same as what, Charlie?

>> Charlie: b plus a!

>> Professor Perez: b plus a. Now, that could be of some use to us when we add negative numbers.

Now, adding negative numbers is a whole separate video which comes up later in the series.

But right now, what we're going to do is we're going to take this sum 7 plus a negative 3

and we're going to apply the Commutative Property which changes is to what, Charlie?

>> Charlie: Negative 3 plus 7.

>> Professor Perez: Negative 3 plus 7.

And so, in our problem, we're going to start at negative 3

and we've got to move, how far Charlie?

>> Charlie: 7 times!

>> Professor Perez: 7 times.

Now, here we go.

We're going to work in steps.

We first go to the zero.

We move 3 times, right?

And then we take a break.

Phew! Okay, now, how many more do we have to go, Charlie?

>> Charlie: 4 more!

>> Professor Perez: 4 more, and so that puts us at 4 so negative 3 plus 7 is 4.

Okay? And so, what we've just shown here, okay, is that 7 plus a negative 3, remember, is 4.

And when we get to subtraction which is coming

up very soon 7 plus a negative 3 is the same as 7 subtract 3.

Now that's adding negative numbers.

Again, that will come up soon after we get through subtraction, okay?

Well, anyway, let's go on here.

Let's look at...uh...this sum right here.

2 plus 3 plus 4, Charlie.

Okay, let's just move...work this problem working left to right.

So we start at 2 and we move to the right 3 times which gives us what, Charlie?

>> Charlie: 5.

>> Professor Perez: 5.

Okay. And now to the 5 we have to add the 4 and so we end up at where?

>> Charlie: 9.

>> Professor Perez: 9.

So that is our answer there.

Okay? So 2 plus 3 plus 4 is 9.

Now watch this.

Let's put parenthesis.

Now, the parenthesis is our first order of operations and order

of operations is coming up soon too!

So, don't get scared!

Okay? So, let's simplify the parenthesis first.

The parenthesis says do this sum first.

Now, what's 2 plus 3, Charlie?

>> Charlie: 5.

>> Professor Perez: That's 5.

Very nice.

And to the 5 we have to add the 4.

Correct? Okay, so let's add the 4 now.

And we end up at 9.

Correct? Okay, it's the same as our first answer there.

Now, watch this, Charlie!

Here's a sum again.

It's 2 plus the quantity, 3 plus 4.

So the parenthesis is telling you do this first.

Add the 3 and the 4 first.

So Charlie, what's 3 plus 4?

>> Charlie: 7.

>> Professor Perez: 7.

Very nice.

And to the 7 we have to add that 7 to the 2.

So we have 2 plus 7.

And now let's do 2 plus 7.

What do we get, Charlie?

>> Charlie: 9.

>> Professor Perez: 9.

Very nice.

And notice here, those two sums there with the parenthesis give the same result.

Okay? Now that is called the Associative Property for Addition.

Now what the Associative Property of Addition states Charlie, is this.

If you have the quantity a plus b in parenthesis here saying you have to add a plus b first

and then add the c, you will get the same result if you were

to add the quantity b plus c first...so the parenthesis is saying

over here add the b plus c first and then add it to the a and you will get the same result.

Okay? So basically, the Associative and Commutative Properties...it's a tongue twister!

When you put those together, you could basically show that whenever you have numbers

that are all being added together, you could add the numbers in any order.

Only if they are all being added together.

Now, that could be of some use to us, and we'll see that in our next video, okay?

Now, let's look at 2 plus 3 plus 4.

We can arrange these in any order we want because they're all being added together.

And so, Charlie, give us another arrangement!

>> Charlie: 4 plus 2 plus 3.

>> Professor Perez: 4 plus 2 plus 3, okay!

So let's do 4 plus 2 plus 3.

4 plus 2 is what, Charlie?

>> Charlie: 6.

>> Professor Perez: 6.

Plus 3 more is?

>> Charlie: 9.

>> Professor Perez: 9.

Again, we get 9.

So, try it out!

You can arrange the 2 plus 3 plus 4, put the numbers in any order you want,

and you're always going to get 9.

Okay? And so, we'll come back very soon in our next video

and we'll show you some techniques called Kung-Fu Addition!

That's what some students call it anyway.

And we're going to do some of these techniques

and show how it could make your life a little bit easier when you're adding numbers together.

Anyway, we'll see you all again soon!

This is Professor Perez again.

Today, we're going to work on some properties of addition.

And of course, we cannot have a class without our student of the semester, and that's Charlie.

He better be ready to go!

Charlie! Wake up over there!

What do you think you're doing?

You've got your piece of paper?

And a pencil?

What, are you tired?

>> Charlie: Yeah, I've been working.

I've got a lot of things going on in my life!

>> Professor Perez: Nobody wants to hear your story!

And by the way, how many of you out there are working and are tired too?

Yeah, you're not the only one, Charlie!

Anyway, let's get to work!

Yeah, you better be ready Charlie, here we go!

Our first problem is right there.

2 plus 3, Charlie.

So, how do we do 2 plus 3 on a number line, Charlie?

>> Charlie: Start at 2, move right 3.

>> Professor Perez: Okay, we start at 2 and we move to the right 3 times.

And that gives us 5.

Very nice, there Charlie, okay.

Now, watch what happens here Charlie, we're going to switch the order

on 2 plus 3 and make it 3 plus 2.

Now, if we're doing 3 plus 2, we start at 3 and we move

to the right 2 times which again, gives us 5.

And so, Charlie, 2 plus 3 and 3 plus 2 both give us the same answer, correct?

>> Charlie: Yes.

>> Professor Perez: All right.

Now, that is showing us that hey!

If you're adding two numbers together, and you switch the order, you get the same result.

And that is what's called the Commutative Property for Addition.

Right there Charlie, so, the Commutative Property for Addition says

that a plus b is the same as what, Charlie?

>> Charlie: b plus a!

>> Professor Perez: b plus a. Now, that could be of some use to us when we add negative numbers.

Now, adding negative numbers is a whole separate video which comes up later in the series.

But right now, what we're going to do is we're going to take this sum 7 plus a negative 3

and we're going to apply the Commutative Property which changes is to what, Charlie?

>> Charlie: Negative 3 plus 7.

>> Professor Perez: Negative 3 plus 7.

And so, in our problem, we're going to start at negative 3

and we've got to move, how far Charlie?

>> Charlie: 7 times!

>> Professor Perez: 7 times.

Now, here we go.

We're going to work in steps.

We first go to the zero.

We move 3 times, right?

And then we take a break.

Phew! Okay, now, how many more do we have to go, Charlie?

>> Charlie: 4 more!

>> Professor Perez: 4 more, and so that puts us at 4 so negative 3 plus 7 is 4.

Okay? And so, what we've just shown here, okay, is that 7 plus a negative 3, remember, is 4.

And when we get to subtraction which is coming

up very soon 7 plus a negative 3 is the same as 7 subtract 3.

Now that's adding negative numbers.

Again, that will come up soon after we get through subtraction, okay?

Well, anyway, let's go on here.

Let's look at...uh...this sum right here.

2 plus 3 plus 4, Charlie.

Okay, let's just move...work this problem working left to right.

So we start at 2 and we move to the right 3 times which gives us what, Charlie?

>> Charlie: 5.

>> Professor Perez: 5.

Okay. And now to the 5 we have to add the 4 and so we end up at where?

>> Charlie: 9.

>> Professor Perez: 9.

So that is our answer there.

Okay? So 2 plus 3 plus 4 is 9.

Now watch this.

Let's put parenthesis.

Now, the parenthesis is our first order of operations and order

of operations is coming up soon too!

So, don't get scared!

Okay? So, let's simplify the parenthesis first.

The parenthesis says do this sum first.

Now, what's 2 plus 3, Charlie?

>> Charlie: 5.

>> Professor Perez: That's 5.

Very nice.

And to the 5 we have to add the 4.

Correct? Okay, so let's add the 4 now.

And we end up at 9.

Correct? Okay, it's the same as our first answer there.

Now, watch this, Charlie!

Here's a sum again.

It's 2 plus the quantity, 3 plus 4.

So the parenthesis is telling you do this first.

Add the 3 and the 4 first.

So Charlie, what's 3 plus 4?

>> Charlie: 7.

>> Professor Perez: 7.

Very nice.

And to the 7 we have to add that 7 to the 2.

So we have 2 plus 7.

And now let's do 2 plus 7.

What do we get, Charlie?

>> Charlie: 9.

>> Professor Perez: 9.

Very nice.

And notice here, those two sums there with the parenthesis give the same result.

Okay? Now that is called the Associative Property for Addition.

Now what the Associative Property of Addition states Charlie, is this.

If you have the quantity a plus b in parenthesis here saying you have to add a plus b first

and then add the c, you will get the same result if you were

to add the quantity b plus c first...so the parenthesis is saying

over here add the b plus c first and then add it to the a and you will get the same result.

Okay? So basically, the Associative and Commutative Properties...it's a tongue twister!

When you put those together, you could basically show that whenever you have numbers

that are all being added together, you could add the numbers in any order.

Only if they are all being added together.

Now, that could be of some use to us, and we'll see that in our next video, okay?

Now, let's look at 2 plus 3 plus 4.

We can arrange these in any order we want because they're all being added together.

And so, Charlie, give us another arrangement!

>> Charlie: 4 plus 2 plus 3.

>> Professor Perez: 4 plus 2 plus 3, okay!

So let's do 4 plus 2 plus 3.

4 plus 2 is what, Charlie?

>> Charlie: 6.

>> Professor Perez: 6.

Plus 3 more is?

>> Charlie: 9.

>> Professor Perez: 9.

Again, we get 9.

So, try it out!

You can arrange the 2 plus 3 plus 4, put the numbers in any order you want,

and you're always going to get 9.

Okay? And so, we'll come back very soon in our next video

and we'll show you some techniques called Kung-Fu Addition!

That's what some students call it anyway.

And we're going to do some of these techniques

and show how it could make your life a little bit easier when you're adding numbers together.

Anyway, we'll see you all again soon!