Uploaded by MuchoMath on 03.08.2008

Transcript:

>> Professor Perez: Hey!

This is Professor Perez again!

We're going to continue our work with fractions on a number line.

Of course, we can't get started without our student of the semester,

and that's Charlie, he better be ready to go!

>> Charlie: Yeah!

>> Professor Perez: Uh-huh...you better be.

Okay, here we go, right there!

We're going to work with fractions on a number line.

Now with this video, we will be adding and subtracting fractions

with the same denominators, and we will also be adding whole numbers

and subtracting whole numbers from fractions and we will also deal

with fractions with different denominators.

How will we add and subtract that?

But we're going to do everything on a number line so we can visualize everything.

Okay. So here we go, Charlie, right there, There's our number line there.

Now here comes our first problem.

We have 1 third plus 2 thirds plus 4 thirds.

All right, we like it when all the denominators are the same because it's just basic arithmetic.

This problem is just saying, hey, you have 1 apple plus 2 more apples plus 4 more apples.

Now, Charlie, what's 1 apple plus 2 apples plus 4 more apples?

>> Charlie: 7 apples.

>> Professor Perez: 7 apples.

So what's 1 third plus 2 thirds plus 4 thirds?

>> Charlie: 7 thirds.

>> Professor Perez: It's 7 thirds.

Really all you have to do is 1 plus 2 plus 4.

And that's what we're going to show you here.

So here we go, Charlie.

All the denominators are the same, we're dealing with thirds.

We have 1 third plus 2 thirds, right?

Which is 3 thirds, and now we've got to add 4 thirds which gives us what, Charlie?

>> Charlie: 7 thirds.

>> Professor Perez: 7 thirds.

Okay. How do we show our work?

Well, we're dealing with thirds, so we write our fraction bar, 3 is our denominator,

and basically we just add 1 plus 2 plus 4, we just deal with those numerators.

And what's 1 plus 2 plus 4, Charlie?

>> Charlie: 7.

>> Professor Perez: 7, but in this case it's 7 thirds, there you go.

Very easy when the denominators are the same.

Okay, let's do another one here.

Let's do 2 thirds plus 7 thirds subtract 4 thirds.

Now, don't get scared!

Again, they're all thirds, so this problem is just basically 2 plus 7 subtract 4.

Charlie, what's 2 plus 7 subtract 4?

It's 5, so our answer should be 5 thirds.

So let's do it on the number line.

There we go, 2 thirds...plus 7 thirds is what, Charlie?

>> Charlie: 9 thirds.

>> Professor Perez: 9 thirds, take away 4 thirds gives you what?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds, that's it.

How do you show your work?

Well, they're all thirds, and so we put our fraction bar, 3 is our denominator,

and those numerators are 2 plus 7 subtract 4.

What's 2 plus 7 subtract 4, Charlie?

>> Charlie: 5.

>> Professor Perez: 5, and it's 5 thirds and that's it.

Very easy when the denominators are the same, right?

Okay, let's do halves now.

Here we have 5 halves subtract 3 halves Charlie.

Very simple.

What's 5 subtract 3?

>> Charlie: 2.

>> Professor Perez: 2.

So our answer should be 2 halves.

Well let's show our work here on the number line.

We go over to 5 halves, take away 3 halves, gives you how many halves, Charlie?

>> Charlie: 2 halves.

>> Professor Perez: 2 halves, and that's it.

How do we show our work?

Well, we have halves, our numerators are 5 and 3 and we're subtracting, that's our operation.

And what's 5 subtract 3, Charlie?

>> Charlie: 2.

>> Professor Perez: 2, and we have 2 halves.

Now, remember, 2 halves means 2 divided by 2, what is 2 divided by 2, Charlie?

>> Charlie: 1.

>> Professor Perez: 1, of course, there it is right there on the number lines, right?

And that's that.

Now I know what you're all saying, well what if the denominators aren't the same, Mr. Perez?

All right, let's deal with that now.

Well, suppose we have fractions and whole numbers?

Let's do that first.

Okay, here we have 3 halves subtract 1 plus 2.

Okay, now, how do we deal with this?

Remember, this video we're going to deal with number lines.

All right, so we want fractions that all have the same denominator.

In this case, we only have one fraction which is 3 halves so we want to write those whole numbers

as fractions with denominators of 2.

So here we go.

We have 3 halves, we're going to leave that one alone.

And we're going to subtract 1.

Now, the question is, how do you write 1 with a denominator of 2?

Well, look at our number line here, how many halves does it take to make up a 1, Charlie?

>> Charlie: 2.

>> Professor Perez: It's 2 halves, so 1 is 2 divided by 2,

that makes sense, what's 2 divided by 2, Charlie?

>> Charlie: 1.

>> Professor Perez: It's 1, right?

Remember, we want all our fractions to have the same denominator, so we write 1 as 2

over 2 because 2 divided by 2 is 1.

So now, we're going to add 2 to it.

Right? Now, how many halves does it take to make a 2, Charlie?

>> Charlie: 4.

>> Professor Perez: 4 of them, because 4 divided by 2 is 2.

You can look at the number line there.

So, 2 written as a fraction with a denominator of 2 is 4 over 2.

It makes sense because you can see 4 halves is the same as 2.

And now, all your denominators are the same, correct?

All right, Charlie, so what do we do?

Let's go to the number line and say 3 halves take away 2 halves...plus 4 halves is what,

Charlie?

>> Charlie: 5 halves.

>> Professor Perez: 5 halves, right?

How do we show our work?

Well, write our fraction bar, your denominators are 2 because we're dealing with halves,

and we write our numerators, 3 subtract 2 plus 4, right?

And 3 subtract 2 is what, Charlie?

>> Charlie: 1.

>> Professor Perez: Plus 4...is 5 and so our answer is 5 halves.

So there you go.

All right, finally, what if the fractions have different denominators?

Well, this is the case where you must find a common denominator,

the lowest common denominator.

Now we're going to work more in detail in the next video, part 3.

Right now we're going to visualize everything on the number line here.

Okay, so here we go, Charlie.

We have 3 halves subtract 2 thirds plus 5 sixths.

Now you see, all the denominators are different.

All right, you've got to make them the same.

So, we have a number line with halves, and we have a number line with thirds,

and we have a number line with sixths here on the bottom, right?

Now 6 is actually called the lowest common denominator because that 3 halves

and 2 thirds can be written as a fraction with a denominator of 6.

We will learn the technique in the next video,

here we're going to visualize on the number line.

So Charlie, here we go.

Look at the 3 halves.

Now, 3 halves is how many sixths?

>> Charlie: 9 sixths.

>> Professor Perez: It's 9 sixths, right?

And so 3 halves can be written as 9 sixths, right?

Just look at the number line.

Now, we're going to subtract 2 thirds,

but 2 thirds can be written as how many sixths, Charlie?

>> Charlie: 4 sixths.

>> Professor Perez: 4 sixths, you can see it right there.

Right? And the 5 sixths, we're going to leave that one alone, so we just add the 5 sixths.

Now, notice all the denominators are the same so it becomes a basic arithmetic problem, right?

So, here we go, Charlie, we have 9 sixths take away 4 sixths, is what Charlie?

>> Charlie: 5 sixths.

>> Professor Perez: 5 sixths, right?

And we add 5 sixths to that and what do we get?

>> Charlie: 10 sixths.

>> Professor Perez: 10 sixths.

All right, we'll show that again on a number line in a second.

Now realize here, denominators are the same so we'll write our fraction bar,

write our denominator, 6, our lowest common denominator is a 6, and now we just deal

with those numerators, 9 subtract 4 plus 5.

And so basically, once you get the denominators all the same, when you're adding or subtracting,

it's just basic arithmetic, it's just 9 subtract 4 plus 5.

So, here we go again on the number line, Charlie.

Basically we're doing 9, that's 9 sixths, take away 4, add 5.

And so our answer is what, Charlie?

>> Charlie: 10 sixths.

>> Professor Perez: 10 sixths.

Very nice there.

Now look at our number lines.

10 sixths can actually be written as a fraction with a denominator of 3, right?

Look over there.

10 sixths is the same as what fraction Charlie?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds.

Now, that's called reducing fractions.

Now, our answer is 5 thirds as a reduced fraction.

Now, that's fine if you have number lines in front of you, right?

Well what if you don't have number lines?

That's where you have to change the denominators using arithmetic.

And that's what we're going to cover in our next video, so I hope you all come back soon!

This is Professor Perez again!

We're going to continue our work with fractions on a number line.

Of course, we can't get started without our student of the semester,

and that's Charlie, he better be ready to go!

>> Charlie: Yeah!

>> Professor Perez: Uh-huh...you better be.

Okay, here we go, right there!

We're going to work with fractions on a number line.

Now with this video, we will be adding and subtracting fractions

with the same denominators, and we will also be adding whole numbers

and subtracting whole numbers from fractions and we will also deal

with fractions with different denominators.

How will we add and subtract that?

But we're going to do everything on a number line so we can visualize everything.

Okay. So here we go, Charlie, right there, There's our number line there.

Now here comes our first problem.

We have 1 third plus 2 thirds plus 4 thirds.

All right, we like it when all the denominators are the same because it's just basic arithmetic.

This problem is just saying, hey, you have 1 apple plus 2 more apples plus 4 more apples.

Now, Charlie, what's 1 apple plus 2 apples plus 4 more apples?

>> Charlie: 7 apples.

>> Professor Perez: 7 apples.

So what's 1 third plus 2 thirds plus 4 thirds?

>> Charlie: 7 thirds.

>> Professor Perez: It's 7 thirds.

Really all you have to do is 1 plus 2 plus 4.

And that's what we're going to show you here.

So here we go, Charlie.

All the denominators are the same, we're dealing with thirds.

We have 1 third plus 2 thirds, right?

Which is 3 thirds, and now we've got to add 4 thirds which gives us what, Charlie?

>> Charlie: 7 thirds.

>> Professor Perez: 7 thirds.

Okay. How do we show our work?

Well, we're dealing with thirds, so we write our fraction bar, 3 is our denominator,

and basically we just add 1 plus 2 plus 4, we just deal with those numerators.

And what's 1 plus 2 plus 4, Charlie?

>> Charlie: 7.

>> Professor Perez: 7, but in this case it's 7 thirds, there you go.

Very easy when the denominators are the same.

Okay, let's do another one here.

Let's do 2 thirds plus 7 thirds subtract 4 thirds.

Now, don't get scared!

Again, they're all thirds, so this problem is just basically 2 plus 7 subtract 4.

Charlie, what's 2 plus 7 subtract 4?

It's 5, so our answer should be 5 thirds.

So let's do it on the number line.

There we go, 2 thirds...plus 7 thirds is what, Charlie?

>> Charlie: 9 thirds.

>> Professor Perez: 9 thirds, take away 4 thirds gives you what?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds, that's it.

How do you show your work?

Well, they're all thirds, and so we put our fraction bar, 3 is our denominator,

and those numerators are 2 plus 7 subtract 4.

What's 2 plus 7 subtract 4, Charlie?

>> Charlie: 5.

>> Professor Perez: 5, and it's 5 thirds and that's it.

Very easy when the denominators are the same, right?

Okay, let's do halves now.

Here we have 5 halves subtract 3 halves Charlie.

Very simple.

What's 5 subtract 3?

>> Charlie: 2.

>> Professor Perez: 2.

So our answer should be 2 halves.

Well let's show our work here on the number line.

We go over to 5 halves, take away 3 halves, gives you how many halves, Charlie?

>> Charlie: 2 halves.

>> Professor Perez: 2 halves, and that's it.

How do we show our work?

Well, we have halves, our numerators are 5 and 3 and we're subtracting, that's our operation.

And what's 5 subtract 3, Charlie?

>> Charlie: 2.

>> Professor Perez: 2, and we have 2 halves.

Now, remember, 2 halves means 2 divided by 2, what is 2 divided by 2, Charlie?

>> Charlie: 1.

>> Professor Perez: 1, of course, there it is right there on the number lines, right?

And that's that.

Now I know what you're all saying, well what if the denominators aren't the same, Mr. Perez?

All right, let's deal with that now.

Well, suppose we have fractions and whole numbers?

Let's do that first.

Okay, here we have 3 halves subtract 1 plus 2.

Okay, now, how do we deal with this?

Remember, this video we're going to deal with number lines.

All right, so we want fractions that all have the same denominator.

In this case, we only have one fraction which is 3 halves so we want to write those whole numbers

as fractions with denominators of 2.

So here we go.

We have 3 halves, we're going to leave that one alone.

And we're going to subtract 1.

Now, the question is, how do you write 1 with a denominator of 2?

Well, look at our number line here, how many halves does it take to make up a 1, Charlie?

>> Charlie: 2.

>> Professor Perez: It's 2 halves, so 1 is 2 divided by 2,

that makes sense, what's 2 divided by 2, Charlie?

>> Charlie: 1.

>> Professor Perez: It's 1, right?

Remember, we want all our fractions to have the same denominator, so we write 1 as 2

over 2 because 2 divided by 2 is 1.

So now, we're going to add 2 to it.

Right? Now, how many halves does it take to make a 2, Charlie?

>> Charlie: 4.

>> Professor Perez: 4 of them, because 4 divided by 2 is 2.

You can look at the number line there.

So, 2 written as a fraction with a denominator of 2 is 4 over 2.

It makes sense because you can see 4 halves is the same as 2.

And now, all your denominators are the same, correct?

All right, Charlie, so what do we do?

Let's go to the number line and say 3 halves take away 2 halves...plus 4 halves is what,

Charlie?

>> Charlie: 5 halves.

>> Professor Perez: 5 halves, right?

How do we show our work?

Well, write our fraction bar, your denominators are 2 because we're dealing with halves,

and we write our numerators, 3 subtract 2 plus 4, right?

And 3 subtract 2 is what, Charlie?

>> Charlie: 1.

>> Professor Perez: Plus 4...is 5 and so our answer is 5 halves.

So there you go.

All right, finally, what if the fractions have different denominators?

Well, this is the case where you must find a common denominator,

the lowest common denominator.

Now we're going to work more in detail in the next video, part 3.

Right now we're going to visualize everything on the number line here.

Okay, so here we go, Charlie.

We have 3 halves subtract 2 thirds plus 5 sixths.

Now you see, all the denominators are different.

All right, you've got to make them the same.

So, we have a number line with halves, and we have a number line with thirds,

and we have a number line with sixths here on the bottom, right?

Now 6 is actually called the lowest common denominator because that 3 halves

and 2 thirds can be written as a fraction with a denominator of 6.

We will learn the technique in the next video,

here we're going to visualize on the number line.

So Charlie, here we go.

Look at the 3 halves.

Now, 3 halves is how many sixths?

>> Charlie: 9 sixths.

>> Professor Perez: It's 9 sixths, right?

And so 3 halves can be written as 9 sixths, right?

Just look at the number line.

Now, we're going to subtract 2 thirds,

but 2 thirds can be written as how many sixths, Charlie?

>> Charlie: 4 sixths.

>> Professor Perez: 4 sixths, you can see it right there.

Right? And the 5 sixths, we're going to leave that one alone, so we just add the 5 sixths.

Now, notice all the denominators are the same so it becomes a basic arithmetic problem, right?

So, here we go, Charlie, we have 9 sixths take away 4 sixths, is what Charlie?

>> Charlie: 5 sixths.

>> Professor Perez: 5 sixths, right?

And we add 5 sixths to that and what do we get?

>> Charlie: 10 sixths.

>> Professor Perez: 10 sixths.

All right, we'll show that again on a number line in a second.

Now realize here, denominators are the same so we'll write our fraction bar,

write our denominator, 6, our lowest common denominator is a 6, and now we just deal

with those numerators, 9 subtract 4 plus 5.

And so basically, once you get the denominators all the same, when you're adding or subtracting,

it's just basic arithmetic, it's just 9 subtract 4 plus 5.

So, here we go again on the number line, Charlie.

Basically we're doing 9, that's 9 sixths, take away 4, add 5.

And so our answer is what, Charlie?

>> Charlie: 10 sixths.

>> Professor Perez: 10 sixths.

Very nice there.

Now look at our number lines.

10 sixths can actually be written as a fraction with a denominator of 3, right?

Look over there.

10 sixths is the same as what fraction Charlie?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds.

Now, that's called reducing fractions.

Now, our answer is 5 thirds as a reduced fraction.

Now, that's fine if you have number lines in front of you, right?

Well what if you don't have number lines?

That's where you have to change the denominators using arithmetic.

And that's what we're going to cover in our next video, so I hope you all come back soon!