Uploaded by MuchoMath on 02.08.2008

Transcript:

>> Professor Perez: Hey!

This is Professor Perez from Saddleback College.

Today's the day we're going to do fractions!

Oh! Charlie, he's really excited.

He says he can hardly wait, so here's the day.

Let's see if he's ready to go!

Charlie, what are you doing over there?

Wake up! We're doing fractions today!

Get out a piece of paper and a pencil and get ready to go!

All right, Charlie, so, here we go, right here.

We're going to put a number line up.

Now, we were doing addition and subtraction on a number line, and today, we're going to work

with adding and subtracting fractions on a number line of course.

So, here we go.

There's a number line there, let's bring a number line right below it,

Charlie, pay attention.

Now, here's 0, right?

Okay. What we're going to do, is we're going to take 1 and we're going to divide it by 2, okay?

Don't get scared!

Here we go.

If we take 1 and basically divide it by 2, break it up into 2 pieces, we have 1 divided by 2.

And there's our fraction.

Now we normally say that fraction as "1 half" which means 1 divided by 2, right?

Now, the 1 on top is a numerator and then we have the fraction bar,

and the 2 on the bottom is called the denominator.

Now, pay attention to denominators because when you're adding or subtracting fractions,

the denominators have to be the same.

Now, we'll talk more about that very soon.

Okay, here's 1 half.

Now, let me ask you something, Charlie.

If that's 1 half, and over here we have another half, right?

How many halves does it take to make up a 1?

>> Charlie: 2 of them.

>> Professor Perez: 2 of them, of course.

Now, let's show this on a number line.

Here we go, Charlie, 1 half...there we go.

That's 1 half.

And if we add another half to this, right?

What's 1 half plus another half, Charlie?

>> Charlie: 2 halves.

>> Professor Perez: 2 halves which is the same as 1.

Of course!

Because 2 divided by 2 is 1.

So, 1 half plus another half is two halves.

It's like saying if you have 1 apple and somebody gives you another apple,

how many apples do you have, Charlie?

>> Charlie: 2 apples!

>> Professor Perez: 2 apples, that's right.

1 apple plus another apple is 2 apples.

1 half plus another half is 2 halves.

That's it!

Okay, Charlie, so, let's continue on.

Let's add another half.

So, how many halves do we have now?

>> Charlie: 3 halves.

>> Professor Perez: 3 halves, that's right.

Now, as a mixed number notation, some of you I know have heard of,

here we go...we have 1 and another half.

That's the same as 3 halves.

We'll talk about mixed numbers a little bit in this lecture, because this is an introduction.

We'll talk later on in the semester, more in detail, about mixed numbers.

Okay, here we go, Charlie, we have 3 halves which is the same as 1 and 1 half.

If we add another half, how many halves do we have, Charlie?

>> Charlie: 4 halves.

>> Professor Perez: 4 halves, there you go.

And 4 halves is the same as what, Charlie?

>> Charlie: 2.

>> Professor Perez: 2 because 4 divided by 2 is 2, that's right.

All right, let's continue on.

Let's add another half.

How many halves do we have now?

>> Charlie: 5 halves.

>> Professor Perez: 5 halves, very good.

As a mixed number, it's what?

>> Charlie: 2 and a half!

>> Professor Perez: 2 and another half, there you go.

Now, let's add 1 more half, and how many halves do we have, Charlie?

>> Charlie: 6 halves.

>> Professor Perez: 6 halves, that's right.

And 6 halves is the same as 3, very nice!

Okay, let's talk a little bit about that mixed number.

Here we have 3 halves, Charlie.

Remember? That's 1 half plus another half, plus another half, that's 3 halves.

1 half plus 1 half plus 1 half is 3 halves.

It's like 1 apple plus another apple plus another apple is 3 apples,

except we have halves.

All right, Charlie, now, in the mixed number notation, it's 1 and 1 half, right?

1 and 1 half is the same as 3 halves.

Now, how do you change a mixed number into the improper fraction?

3 halves is said to be an improper fraction because it's a fraction

that represents a number bigger than 1, okay?

All right, Charlie, now, what are you supposed to do to change a mixed number

to the improper fraction, Charlie?

>> Charlie: Put a fraction bar with a 2 on the bottom.

>> Professor Perez: Yeah, we bring a fraction bar and we put a denominator of 2

because we're dealing with halves, right?

All right, now what are you supposed to do?

>> Charlie: 2 times 1.

>> Professor Perez: 2 times 1.

Now what is 2 times 1, Charlie?

>> Charlie: 2.

>> Professor Perez: 2.

Now why do you do this?

Most people are just told, hey, just multiply this and add that.

That's what we're going to talk about.

What you're actually doing here, is when you take 2 times 1, it's 2.

Well that 2 times 1 is telling you that you have 2 halves that make up a 1.

See? 2 halves make up the 1, so when you do 2 times 1, it's telling you 2 halves make up a 1.

And then what are you supposed to do, Charlie?

>> Charlie: Add 1.

>> Professor Perez: Add another 1, right?

Because, what you have here, is you have 2 halves plus the other half, right?

So 2 times 1 is 2, plus the 1 up there.

The 1 half which gives you how many halves, Charlie?

>> Charlie: 3 halves!

>> Professor Perez: 3 halves.

So there's your introduction to changing a mixed number to an improper fraction.

We'll talk more about that later in the semester.

All right, let's go back to our fractions though.

Okay, here we go Charlie.

Some number lines...this time we're going to take a 1

and we're going to break it up into 3 pieces.

Which means we're going to take 1 and divide it by 3.

And so here we have 1 divided by 3, which we say as "1 third".

Okay Charlie.

Now, how many thirds, Charlie, does it take to make up a 1?

>> Charlie: 3 of them.

>> Professor Perez: 3 of them of course!

So let's do our addition on the number line with fractions.

So here we go.

1 third...1 third Charlie, plus another third is how many thirds?

>> Charlie: 2 thirds.

>> Professor Perez: 2 thirds of course!

It's like 1 apple plus another apple is 2 apples, except we're dealing with thirds.

So 1 third plus another third is 2 thirds.

Let's add another third Charlie, what do we get?

>> Charlie: 3 thirds!

>> Professor Perez: 3 thirds, very nice.

And 3 thirds is the same as...

>> Charlie: 1.

>> Professor Perez: 1, very nice there, Charlie.

Let's continue on.

Add another third, how many thirds do we have?

>> Charlie: 4 thirds.

>> Professor Perez: 4 thirds, that's right.

Which is 1 and 1 third.

You can see it right there.

If we add another third, that is how many thirds, Charlie?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds which is the same as 1 and 2 thirds in the mixed number notation.

Now, add another third.

How many thirds do we have, Charlie?

>> Charlie: 6 thirds.

>> Professor Perez: 6 thirds, that's right.

Which is the same as...

>> Charlie: 2.

>> Professor Perez: 2, because 6 divided by 3 is 2.

There you go.

All right, Charlie, here we go.

Add another third.

What do we have?

>> Charlie: 7 thirds.

>> Professor Perez: 7 thirds which is the same as 2 and...

>> Charlie: 1 third.

>> Professor Perez: 1 third, very nice.

If we add another third, how many thirds are there?

>> Charlie: 8 thirds.

>> Professor Perez: 8 thirds, and that's 2 and 2 thirds, and finally another third gives us...

>> Charlie: 9 thirds.

>> Professor Perez: 9 thirds which is the same as 3.

So, if you have all thirds, just add them up!

All right, so let's do some problems.

Here we have 2 thirds plus 3 thirds, Charlie.

Now don't get scared!

It's like saying, hey, what's 2 plus 3, Charlie?

>> Charlie: 5.

>> Professor Perez: 5, that's right.

If you have 2 apples and somebody gives you 3 more apples,

how many apples do you have, Charlie?

>> Charlie: 5 apples.

>> Professor Perez: 5 apples, that's right.

So Charlie, what is 2 thirds plus 3 more thirds?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds!

That's right!

Now if we show this on a number line, here we go,

2 thirds plus 3 more thirds is how many thirds, Charlie?

>> Charlie: 5 thirds!

>> Professor Perez: 5 thirds, there it is!

So, as long as your denominators are the same, basic arithmetic.

Just plus 2 thirds plus 3 thirds is 5 thirds.

Now how do you show this if you're going to write down your work?

Well, since we're dealing with thirds, we write a fraction bar,

bring our 3 down in the denominator because we're dealing with thirds.

And all you have to do is add the numerators, it's just 2 plus 3.

And Charlie, what's 2 plus 3?

>> Charlie: 5.

>> Professor Perez: 5, but it's 5 what?

>> Charlie: Thirds.

>> Professor Perez: 5 thirds and that's it!

There's your answer.

So you see, as long as the denominators are the same, it's very easy.

Very soon we'll get to the problems where the denominators are not the same,

we'll have to find the common denominator, or preferably the lowest common denominator.

That's coming up soon!

But let's do one more problem here, Charlie.

Here we have 8 thirds subtract 4 thirds.

Now don't get scared!

It's like if you have 8 apples and somebody takes 4 of your apples away,

Charlie, how many apples do you have?

>> Charlie: 4 apples.

>> Professor Perez: 4 apples, so 8 thirds take away 4 thirds is what, Charlie?

>> Charlie: 4 thirds.

>> Professor Perez: 4 thirds, it's that easy!

So go over here.

We'll take 8 thirds and now subtract, means we're going to move to the left,

but we're going to subtract 4 thirds and what do we end up at, Charlie?

>> Charlie: 4 thirds.

>> Professor Perez: 4 thirds of course.

And so to show our work, hey, we draw our fraction bar, we have thirds,

and we take our numerators, 8 subtract 4.

What's 8 subtract 4, ?

>> Charlie: 4.

>> Professor Perez: 4, but it's 4 thirds.

And there you go!

That's part 1 of our introduction to fractions, so, we'll come back for part 2 very soon!

So take a break, relax, and we'll come back and do more fractions!

This is Professor Perez from Saddleback College.

Today's the day we're going to do fractions!

Oh! Charlie, he's really excited.

He says he can hardly wait, so here's the day.

Let's see if he's ready to go!

Charlie, what are you doing over there?

Wake up! We're doing fractions today!

Get out a piece of paper and a pencil and get ready to go!

All right, Charlie, so, here we go, right here.

We're going to put a number line up.

Now, we were doing addition and subtraction on a number line, and today, we're going to work

with adding and subtracting fractions on a number line of course.

So, here we go.

There's a number line there, let's bring a number line right below it,

Charlie, pay attention.

Now, here's 0, right?

Okay. What we're going to do, is we're going to take 1 and we're going to divide it by 2, okay?

Don't get scared!

Here we go.

If we take 1 and basically divide it by 2, break it up into 2 pieces, we have 1 divided by 2.

And there's our fraction.

Now we normally say that fraction as "1 half" which means 1 divided by 2, right?

Now, the 1 on top is a numerator and then we have the fraction bar,

and the 2 on the bottom is called the denominator.

Now, pay attention to denominators because when you're adding or subtracting fractions,

the denominators have to be the same.

Now, we'll talk more about that very soon.

Okay, here's 1 half.

Now, let me ask you something, Charlie.

If that's 1 half, and over here we have another half, right?

How many halves does it take to make up a 1?

>> Charlie: 2 of them.

>> Professor Perez: 2 of them, of course.

Now, let's show this on a number line.

Here we go, Charlie, 1 half...there we go.

That's 1 half.

And if we add another half to this, right?

What's 1 half plus another half, Charlie?

>> Charlie: 2 halves.

>> Professor Perez: 2 halves which is the same as 1.

Of course!

Because 2 divided by 2 is 1.

So, 1 half plus another half is two halves.

It's like saying if you have 1 apple and somebody gives you another apple,

how many apples do you have, Charlie?

>> Charlie: 2 apples!

>> Professor Perez: 2 apples, that's right.

1 apple plus another apple is 2 apples.

1 half plus another half is 2 halves.

That's it!

Okay, Charlie, so, let's continue on.

Let's add another half.

So, how many halves do we have now?

>> Charlie: 3 halves.

>> Professor Perez: 3 halves, that's right.

Now, as a mixed number notation, some of you I know have heard of,

here we go...we have 1 and another half.

That's the same as 3 halves.

We'll talk about mixed numbers a little bit in this lecture, because this is an introduction.

We'll talk later on in the semester, more in detail, about mixed numbers.

Okay, here we go, Charlie, we have 3 halves which is the same as 1 and 1 half.

If we add another half, how many halves do we have, Charlie?

>> Charlie: 4 halves.

>> Professor Perez: 4 halves, there you go.

And 4 halves is the same as what, Charlie?

>> Charlie: 2.

>> Professor Perez: 2 because 4 divided by 2 is 2, that's right.

All right, let's continue on.

Let's add another half.

How many halves do we have now?

>> Charlie: 5 halves.

>> Professor Perez: 5 halves, very good.

As a mixed number, it's what?

>> Charlie: 2 and a half!

>> Professor Perez: 2 and another half, there you go.

Now, let's add 1 more half, and how many halves do we have, Charlie?

>> Charlie: 6 halves.

>> Professor Perez: 6 halves, that's right.

And 6 halves is the same as 3, very nice!

Okay, let's talk a little bit about that mixed number.

Here we have 3 halves, Charlie.

Remember? That's 1 half plus another half, plus another half, that's 3 halves.

1 half plus 1 half plus 1 half is 3 halves.

It's like 1 apple plus another apple plus another apple is 3 apples,

except we have halves.

All right, Charlie, now, in the mixed number notation, it's 1 and 1 half, right?

1 and 1 half is the same as 3 halves.

Now, how do you change a mixed number into the improper fraction?

3 halves is said to be an improper fraction because it's a fraction

that represents a number bigger than 1, okay?

All right, Charlie, now, what are you supposed to do to change a mixed number

to the improper fraction, Charlie?

>> Charlie: Put a fraction bar with a 2 on the bottom.

>> Professor Perez: Yeah, we bring a fraction bar and we put a denominator of 2

because we're dealing with halves, right?

All right, now what are you supposed to do?

>> Charlie: 2 times 1.

>> Professor Perez: 2 times 1.

Now what is 2 times 1, Charlie?

>> Charlie: 2.

>> Professor Perez: 2.

Now why do you do this?

Most people are just told, hey, just multiply this and add that.

That's what we're going to talk about.

What you're actually doing here, is when you take 2 times 1, it's 2.

Well that 2 times 1 is telling you that you have 2 halves that make up a 1.

See? 2 halves make up the 1, so when you do 2 times 1, it's telling you 2 halves make up a 1.

And then what are you supposed to do, Charlie?

>> Charlie: Add 1.

>> Professor Perez: Add another 1, right?

Because, what you have here, is you have 2 halves plus the other half, right?

So 2 times 1 is 2, plus the 1 up there.

The 1 half which gives you how many halves, Charlie?

>> Charlie: 3 halves!

>> Professor Perez: 3 halves.

So there's your introduction to changing a mixed number to an improper fraction.

We'll talk more about that later in the semester.

All right, let's go back to our fractions though.

Okay, here we go Charlie.

Some number lines...this time we're going to take a 1

and we're going to break it up into 3 pieces.

Which means we're going to take 1 and divide it by 3.

And so here we have 1 divided by 3, which we say as "1 third".

Okay Charlie.

Now, how many thirds, Charlie, does it take to make up a 1?

>> Charlie: 3 of them.

>> Professor Perez: 3 of them of course!

So let's do our addition on the number line with fractions.

So here we go.

1 third...1 third Charlie, plus another third is how many thirds?

>> Charlie: 2 thirds.

>> Professor Perez: 2 thirds of course!

It's like 1 apple plus another apple is 2 apples, except we're dealing with thirds.

So 1 third plus another third is 2 thirds.

Let's add another third Charlie, what do we get?

>> Charlie: 3 thirds!

>> Professor Perez: 3 thirds, very nice.

And 3 thirds is the same as...

>> Charlie: 1.

>> Professor Perez: 1, very nice there, Charlie.

Let's continue on.

Add another third, how many thirds do we have?

>> Charlie: 4 thirds.

>> Professor Perez: 4 thirds, that's right.

Which is 1 and 1 third.

You can see it right there.

If we add another third, that is how many thirds, Charlie?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds which is the same as 1 and 2 thirds in the mixed number notation.

Now, add another third.

How many thirds do we have, Charlie?

>> Charlie: 6 thirds.

>> Professor Perez: 6 thirds, that's right.

Which is the same as...

>> Charlie: 2.

>> Professor Perez: 2, because 6 divided by 3 is 2.

There you go.

All right, Charlie, here we go.

Add another third.

What do we have?

>> Charlie: 7 thirds.

>> Professor Perez: 7 thirds which is the same as 2 and...

>> Charlie: 1 third.

>> Professor Perez: 1 third, very nice.

If we add another third, how many thirds are there?

>> Charlie: 8 thirds.

>> Professor Perez: 8 thirds, and that's 2 and 2 thirds, and finally another third gives us...

>> Charlie: 9 thirds.

>> Professor Perez: 9 thirds which is the same as 3.

So, if you have all thirds, just add them up!

All right, so let's do some problems.

Here we have 2 thirds plus 3 thirds, Charlie.

Now don't get scared!

It's like saying, hey, what's 2 plus 3, Charlie?

>> Charlie: 5.

>> Professor Perez: 5, that's right.

If you have 2 apples and somebody gives you 3 more apples,

how many apples do you have, Charlie?

>> Charlie: 5 apples.

>> Professor Perez: 5 apples, that's right.

So Charlie, what is 2 thirds plus 3 more thirds?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds!

That's right!

Now if we show this on a number line, here we go,

2 thirds plus 3 more thirds is how many thirds, Charlie?

>> Charlie: 5 thirds!

>> Professor Perez: 5 thirds, there it is!

So, as long as your denominators are the same, basic arithmetic.

Just plus 2 thirds plus 3 thirds is 5 thirds.

Now how do you show this if you're going to write down your work?

Well, since we're dealing with thirds, we write a fraction bar,

bring our 3 down in the denominator because we're dealing with thirds.

And all you have to do is add the numerators, it's just 2 plus 3.

And Charlie, what's 2 plus 3?

>> Charlie: 5.

>> Professor Perez: 5, but it's 5 what?

>> Charlie: Thirds.

>> Professor Perez: 5 thirds and that's it!

There's your answer.

So you see, as long as the denominators are the same, it's very easy.

Very soon we'll get to the problems where the denominators are not the same,

we'll have to find the common denominator, or preferably the lowest common denominator.

That's coming up soon!

But let's do one more problem here, Charlie.

Here we have 8 thirds subtract 4 thirds.

Now don't get scared!

It's like if you have 8 apples and somebody takes 4 of your apples away,

Charlie, how many apples do you have?

>> Charlie: 4 apples.

>> Professor Perez: 4 apples, so 8 thirds take away 4 thirds is what, Charlie?

>> Charlie: 4 thirds.

>> Professor Perez: 4 thirds, it's that easy!

So go over here.

We'll take 8 thirds and now subtract, means we're going to move to the left,

but we're going to subtract 4 thirds and what do we end up at, Charlie?

>> Charlie: 4 thirds.

>> Professor Perez: 4 thirds of course.

And so to show our work, hey, we draw our fraction bar, we have thirds,

and we take our numerators, 8 subtract 4.

What's 8 subtract 4, ?

>> Charlie: 4.

>> Professor Perez: 4, but it's 4 thirds.

And there you go!

That's part 1 of our introduction to fractions, so, we'll come back for part 2 very soon!

So take a break, relax, and we'll come back and do more fractions!