Uploaded by MuchoMath on 01.03.2009

Transcript:

>> Professor Perez: Hey!

This is Professor Perez from Saddleback College.

Today, we're going to work on complex fractions!

And of course, we cannot get started without our student of the semester, and that's Charlie.

He better be ready to go!

Hey Charlie, you ready to go?

We're doing your favorite subject!

>> Charlie: What?

>> Professor Perez: Complex fractions!

Yeah, he like those!

Charlie's a complex person.

>> Charlie: What?

>> Professor Perez: Never mind, Charlie.

Let's get started, right there!

Now, first we're going to do a review.

Here, we are dividing with fractions.

Now, what do we do when we divide with fractions, Charlie?

>> Charlie: Multiply by the reciprocal.

>> Professor Perez: That's right.

So, here we go.

Notice, it's times 4 over 1.

The 2 thirds does not change.

Okay, now, how do we multiply fractions, Charlie?

>> Charlie: Straight across the top and straight across the bottom!

>> Professor Perez: Straight across the top and straight across the bottom!

Very nice!

And so, what's our answer, Charlie?

>> Charlie: 8 thirds.

>> Professor Perez: 8 thirds.

Very nice.

Now, here's the same problem.

But now, it's being presented as a complex fraction.

Don't get scared.

Okay, Charlie, now, we're going

to use our clearing fractions technique, or Kung-Fu fractions.

In order to do that, we need the lowest common denominator from both the fraction

from the top and the fraction on the bottom.

So, what's the LCD, Charlie?

>> Charlie: 12.

>> Professor Perez: Very nice.

Now, what we're going to do, is multiply both the top and the bottom by the LCD,

and here goes our Kung-Fu fraction technique, Charlie.

Okay, 3 goes into 12?

>> Charlie: 4.

>> Professor Perez: And 4 times 2?

>> Charlie: 8.

>> Professor Perez: Very nice there, Charlie.

And 4 goes into 12?

>> Charlie: 3.

>> Professor Perez: And 3 times 1?

>> Charlie: 3.

>> Professor Perez: Is 3.

Very nice and notice, the two answers are exactly the same.

Now, I know some of you are saying, well, I'm always going to do it that way.

Yeah, you will on these, but don't worry, they're going to get more complicated.

That's right.

And by the way, these are non-calculator problems so, all of you calculator kids

out there, put those calculators away, okay?

All right, let's do another one.

Here we go, Charlie.

Now, look at the two fractions, what is the lowest common denominator?

>> Charlie: 21.

>> Professor Perez: Very nice there, Charlie.

So, we're going to multiply both the top and the bottom by 21,

and let's do our Kung-Fu fraction technique, Charlie.

7 goes into 21...

>> Charlie: 3.

>> Professor Perez: And 3 times 3?

>> Charlie: 9.

>> Professor Perez: Is 9, that's right.

Yes, that's a negative 3.

My mistake.

3 times negative 3 is a negative 9.

There you go, Charlie.

Now, I got distracted, be quiet!

>> Charlie: What?

>> Professor Perez: All right, Charlie.

21 goes into 21?

>> Charlie: 1 time.

>> Professor Perez: And 1 times 5?

>> Charlie: 5.

>> Professor Perez: Very nice there, Charlie.

Our answer is negative 9 over 5.

Or, remember, we can put the negative in front and say it's negative 9 fifths, same answer.

Okay, now, that was a good warm up.

Let's get to the more complicated problems.

That's right.

These are called the attitude adjustment problems, for him!

All right, Charlie, don't get scared, here we go, right there.

That's right.

Now, just relax.

Use the force!

All you've got to do is find the lowest common denominator for all of your fractions.

Remember, don't just look at the top and don't just look at the bottom.

You have to look at all of them.

Okay, Charlie, what's the lowest common denominator?

>> Charlie: 12.

>> Professor Perez: That's right.

>> Charlie: Uh-huh!

>> Professor Perez: Now, we have to multiply top and bottom by that 12.

And now, we have to use the distributive property, Charlie.

That's right.

Just like this up here.

There you go.

And there you go there.

And then we come to the bottom, and there you go there, and there you go there!

That's right.

Okay! Now, let's do our Kung-Fu fraction technique, Charlie.

6 goes into 12...

>> Charlie: 2 times.

>> Professor Perez: And 2 times 11?

>> Charlie: 22.

>> Professor Perez: Very nice there.

Bring down your subtraction.

3 goes into 12...

>> Charlie: 4 times.

>> Professor Perez: And 4 times 2?

>> Charlie: 8.

>> Professor Perez: Very nice there Charlie.

Okay, 4 goes into 12?

>> Charlie: 3.

>> Professor Perez: And 3 times 3?

>> Charlie: 9.

>> Professor Perez: Very nice.

Bring down your addition.

And now, 2 goes into 12...

>> Charlie: 6 times.

>> Professor Perez: And 6 times 3?

>> Charlie: 18.

>> Professor Perez: 18.

Very nice there!

Now, what's 22 subtract 8, Charlie?

>> Charlie: 14.

>> Professor Perez: And 9 plus 18?

>> Charlie: 27.

>> Professor Perez: 27.

Very nice.

That's some Kung-Fu right there!

There you go!

That was so much fun, let's do another one!

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

Don't get scared!

Okay, Charlie.

Notice we have a whole number there, but don't worry about that.

Just look at the fractions, there's one on top, two on the bottom,

and what is the lowest common denominator for all three of those fractions?

>> Charlie: 20.

>> Professor Perez: Very nice there, Charlie.

So now, we're going to multiply both top and the bottom by that 20.

And we're going to do what, Charlie?

>> Charlie: Distribute.

>> Professor Perez: That's right, distribute.

There we go, and we'll do another one, and we come to the bottom and bring it home

with that one, and there's another one for you.

Anyway, now, let's do our clearing fraction, or Kung-Fu fraction technique, Charlie.

4 goes into 20...

>> Charlie: 5 times.

>> Professor Perez: And 5 times 5?

>> Charlie: 25.

>> Professor Perez: Very nice.

Bring down your subtraction.

Now, don't forget, every term has to be multiplied by 20.

So, you have to do 20 times 2 which is what, Charlie?

>> Charlie: 40.

>> Professor Perez: Very nice.

Now, 5 goes into 20...and 4 times 6?

>> Charlie: 24.

>> Professor Perez: Very nice.

And 2 goes into 20?

>> Charlie: 10 times.

>> Professor Perez: And 10 times 3?

>> Charlie: 30.

>> Professor Perez: Is 30.

Very nice.

Now, let's check your arithmetic.

25 subtract 40, Charlie.

>> Charlie: Negative 15.

>> Professor Perez: That's right.

And 24 plus 30?

>> Charlie: 54.

>> Professor Perez: 54.

Very nice there, Charlie.

Now, Charlie, are these numbers divisible by 3?

Oh, okay, let me review something for you.

Remember, and this is for you too, if you sum up the digits to any number

and that sum is divisible by 3, it means the number is divisible by 3.

Watch. 1 plus 5 is 6, and 6 is divisible by 3 which means 15 is divisible by 3.

54, 5 plus 4 is 9, and since that sum, 9, is divisible by 3, 54 is divisible by 3.

That works for any number.

Okay, Charlie, we'll put the negative in front, what's 15 divided by 3?

>> Charlie: 5.

>> Professor Perez: And 54 divided by 3?

Work that one out.

Don't get scared, don't get distracted, Charlie.

>> Charlie: Shhh!

>> Professor Perez: All right, Charlie, time's up.

What did you get?

>> Charlie: 18.

>> Professor Perez: 18.

So our answer is negative 5 over 18.

Don't forget to box your answer, and that's it for today.

So, phew! We'll see you all again soon!

This is Professor Perez from Saddleback College.

Today, we're going to work on complex fractions!

And of course, we cannot get started without our student of the semester, and that's Charlie.

He better be ready to go!

Hey Charlie, you ready to go?

We're doing your favorite subject!

>> Charlie: What?

>> Professor Perez: Complex fractions!

Yeah, he like those!

Charlie's a complex person.

>> Charlie: What?

>> Professor Perez: Never mind, Charlie.

Let's get started, right there!

Now, first we're going to do a review.

Here, we are dividing with fractions.

Now, what do we do when we divide with fractions, Charlie?

>> Charlie: Multiply by the reciprocal.

>> Professor Perez: That's right.

So, here we go.

Notice, it's times 4 over 1.

The 2 thirds does not change.

Okay, now, how do we multiply fractions, Charlie?

>> Charlie: Straight across the top and straight across the bottom!

>> Professor Perez: Straight across the top and straight across the bottom!

Very nice!

And so, what's our answer, Charlie?

>> Charlie: 8 thirds.

>> Professor Perez: 8 thirds.

Very nice.

Now, here's the same problem.

But now, it's being presented as a complex fraction.

Don't get scared.

Okay, Charlie, now, we're going

to use our clearing fractions technique, or Kung-Fu fractions.

In order to do that, we need the lowest common denominator from both the fraction

from the top and the fraction on the bottom.

So, what's the LCD, Charlie?

>> Charlie: 12.

>> Professor Perez: Very nice.

Now, what we're going to do, is multiply both the top and the bottom by the LCD,

and here goes our Kung-Fu fraction technique, Charlie.

Okay, 3 goes into 12?

>> Charlie: 4.

>> Professor Perez: And 4 times 2?

>> Charlie: 8.

>> Professor Perez: Very nice there, Charlie.

And 4 goes into 12?

>> Charlie: 3.

>> Professor Perez: And 3 times 1?

>> Charlie: 3.

>> Professor Perez: Is 3.

Very nice and notice, the two answers are exactly the same.

Now, I know some of you are saying, well, I'm always going to do it that way.

Yeah, you will on these, but don't worry, they're going to get more complicated.

That's right.

And by the way, these are non-calculator problems so, all of you calculator kids

out there, put those calculators away, okay?

All right, let's do another one.

Here we go, Charlie.

Now, look at the two fractions, what is the lowest common denominator?

>> Charlie: 21.

>> Professor Perez: Very nice there, Charlie.

So, we're going to multiply both the top and the bottom by 21,

and let's do our Kung-Fu fraction technique, Charlie.

7 goes into 21...

>> Charlie: 3.

>> Professor Perez: And 3 times 3?

>> Charlie: 9.

>> Professor Perez: Is 9, that's right.

Yes, that's a negative 3.

My mistake.

3 times negative 3 is a negative 9.

There you go, Charlie.

Now, I got distracted, be quiet!

>> Charlie: What?

>> Professor Perez: All right, Charlie.

21 goes into 21?

>> Charlie: 1 time.

>> Professor Perez: And 1 times 5?

>> Charlie: 5.

>> Professor Perez: Very nice there, Charlie.

Our answer is negative 9 over 5.

Or, remember, we can put the negative in front and say it's negative 9 fifths, same answer.

Okay, now, that was a good warm up.

Let's get to the more complicated problems.

That's right.

These are called the attitude adjustment problems, for him!

All right, Charlie, don't get scared, here we go, right there.

That's right.

Now, just relax.

Use the force!

All you've got to do is find the lowest common denominator for all of your fractions.

Remember, don't just look at the top and don't just look at the bottom.

You have to look at all of them.

Okay, Charlie, what's the lowest common denominator?

>> Charlie: 12.

>> Professor Perez: That's right.

>> Charlie: Uh-huh!

>> Professor Perez: Now, we have to multiply top and bottom by that 12.

And now, we have to use the distributive property, Charlie.

That's right.

Just like this up here.

There you go.

And there you go there.

And then we come to the bottom, and there you go there, and there you go there!

That's right.

Okay! Now, let's do our Kung-Fu fraction technique, Charlie.

6 goes into 12...

>> Charlie: 2 times.

>> Professor Perez: And 2 times 11?

>> Charlie: 22.

>> Professor Perez: Very nice there.

Bring down your subtraction.

3 goes into 12...

>> Charlie: 4 times.

>> Professor Perez: And 4 times 2?

>> Charlie: 8.

>> Professor Perez: Very nice there Charlie.

Okay, 4 goes into 12?

>> Charlie: 3.

>> Professor Perez: And 3 times 3?

>> Charlie: 9.

>> Professor Perez: Very nice.

Bring down your addition.

And now, 2 goes into 12...

>> Charlie: 6 times.

>> Professor Perez: And 6 times 3?

>> Charlie: 18.

>> Professor Perez: 18.

Very nice there!

Now, what's 22 subtract 8, Charlie?

>> Charlie: 14.

>> Professor Perez: And 9 plus 18?

>> Charlie: 27.

>> Professor Perez: 27.

Very nice.

That's some Kung-Fu right there!

There you go!

That was so much fun, let's do another one!

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

Don't get scared!

Okay, Charlie.

Notice we have a whole number there, but don't worry about that.

Just look at the fractions, there's one on top, two on the bottom,

and what is the lowest common denominator for all three of those fractions?

>> Charlie: 20.

>> Professor Perez: Very nice there, Charlie.

So now, we're going to multiply both top and the bottom by that 20.

And we're going to do what, Charlie?

>> Charlie: Distribute.

>> Professor Perez: That's right, distribute.

There we go, and we'll do another one, and we come to the bottom and bring it home

with that one, and there's another one for you.

Anyway, now, let's do our clearing fraction, or Kung-Fu fraction technique, Charlie.

4 goes into 20...

>> Charlie: 5 times.

>> Professor Perez: And 5 times 5?

>> Charlie: 25.

>> Professor Perez: Very nice.

Bring down your subtraction.

Now, don't forget, every term has to be multiplied by 20.

So, you have to do 20 times 2 which is what, Charlie?

>> Charlie: 40.

>> Professor Perez: Very nice.

Now, 5 goes into 20...and 4 times 6?

>> Charlie: 24.

>> Professor Perez: Very nice.

And 2 goes into 20?

>> Charlie: 10 times.

>> Professor Perez: And 10 times 3?

>> Charlie: 30.

>> Professor Perez: Is 30.

Very nice.

Now, let's check your arithmetic.

25 subtract 40, Charlie.

>> Charlie: Negative 15.

>> Professor Perez: That's right.

And 24 plus 30?

>> Charlie: 54.

>> Professor Perez: 54.

Very nice there, Charlie.

Now, Charlie, are these numbers divisible by 3?

Oh, okay, let me review something for you.

Remember, and this is for you too, if you sum up the digits to any number

and that sum is divisible by 3, it means the number is divisible by 3.

Watch. 1 plus 5 is 6, and 6 is divisible by 3 which means 15 is divisible by 3.

54, 5 plus 4 is 9, and since that sum, 9, is divisible by 3, 54 is divisible by 3.

That works for any number.

Okay, Charlie, we'll put the negative in front, what's 15 divided by 3?

>> Charlie: 5.

>> Professor Perez: And 54 divided by 3?

Work that one out.

Don't get scared, don't get distracted, Charlie.

>> Charlie: Shhh!

>> Professor Perez: All right, Charlie, time's up.

What did you get?

>> Charlie: 18.

>> Professor Perez: 18.

So our answer is negative 5 over 18.

Don't forget to box your answer, and that's it for today.

So, phew! We'll see you all again soon!