Uploaded by MuchoMath on 03.08.2008

Transcript:

>> Professor Perez: Hey!

This is Professor Perez from Saddleback College.

We're going to continue our work with fractions.

Now, in this video, our fractions are going to have different denominators and we're going

to throw in some whole numbers just to spice it up a bit.

Anyway, let's see what Charlie's up to.

He better be ready to go!

Charlie, what are you doing over there?

>> Charlie: Huh?

>> Professor Perez: Are you ready to go?

>> Charlie: Yeah!

>> Professor Perez: You better be.

All right, so here we go, Charlie.

Let's put some number lines up there.

Now, here's our problem, 3 halves subtract 2 thirds plus 5 sixths.

Now, this is the problem we finished in the last video.

Right? But we were doing it on a number line.

Now we're going to show, how do you change denominators of fractions using arithmetic.

You'll see right now.

So here we go, Charlie, 3 halves subtract 2 thirds plus 5 sixths.

Now, we're going to start with 3 halves.

Now, if we look at the number line, 3 halves can be written with the denominator of 6, right?

We know 3 halves is the same as 9 sixths.

But how do we use arithmetic to do this?

Well, here we go.

We know 3 halves is going to be written with a denominator of 6.

Now, what we're really going to do is we're going to take 3 halves and multiply by 1.

That's right.

Because, what's 3 halves times 1, Charlie?

>> Charlie: 3 halves.

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

Remember, if you multiply a number by 1, you don't change it.

But we're going to use a specific form of 1.

We're going to write 1 as a fraction.

Now here's where it gets tricky.

In order to do this, I have to jump ahead and tell you how to multiply fractions.

Now, pay attention to this Charlie.

The way you multiply fractions is you go straight

across the top and straight across the bottom.

You'll see what I mean in a second.

Okay, now, we're going to multiply 3 halves times 1,

but we want to make the denominator 6, right Charlie?

Okay, so here's what you do.

Charlie, what do I multiply 2 by to get 6?

>> Charlie: 3.

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

now, if you have a fraction and you multiply the denominator by 3,

you must also multiply the numerator by 3.

It has to be the same number because think about that...look at those brackets.

What's 3 over 3, Charlie?

>> Charlie: 1.

>> Professor Perez: It's 1, remember 3 divided by 3 is 1.

So realistically, you're taking 3 halves and multiplying by 1.

You're not changing the fraction!

But 1 is written as 3 over 3.

And remember, how do you multiply fractions Charlie?

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

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

That's right.

What's 3 times 3?

>> Charlie: 9.

>> Professor Perez: 9, and on the bottom, what's 2 times 3, Charlie?

>> Charlie: 6.

>> Professor Perez: There's your 9 sixths.

So 3 halves has now been changed to the fraction 9 sixths

and we saw that on the number line, right?

All right, now we're going to subtract 2 thirds.

Now once again, we have to change the 2 thirds and make the denominator 6, right?

So here we go.

Now, 2 thirds on the number line, we see that it is 4 sixths.

How do we do this?

Again, we're going to take 2 thirds,

write it with a denominator of 6 by multiplying it by a 1.

But the question is, what form of the 1 do we want to write?

I mean, how do we write 1 as a fraction so that we can multiply 2 thirds

by it to get the denominator of 6?

The way it goes here is you look at the denominator, 3, 3 times what is 6, Charlie?

>> Charlie: 2.

>> Professor Perez: It's a 2.

But if I multiply the denominator by 2, I must multiply the numerator by 2.

So there you see it.

2 thirds is essentially being multiplied by 1, but 1 is written in the form 2 over 2.

And how do you multiply fractions, Charlie?

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

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

That's right.

Okay, now Charlie, what's 2 times 2?

>> Charlie: 4.

>> Professor Perez: 4, and what's 3 times 2?

>> Charlie: 6.

>> Professor Perez: And there we go!

2 thirds is written as a fraction 4 sixths, right?

Now, we have the 5 sixths, we don't need to do anything to that, right?

Because 5 sixths has a denominator of 6 and there you go.

All right.

Now notice, all of our denominators are 6 and therefore, we can just basically do arithmetic.

So here we go.

9 sixths take away 4 sixths is...?

>> Charlie: 5...

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

And you add 5 sixths, that's what, Charlie?

>> Charlie: 10 sixths.

>> Professor Perez: 10 sixths.

Very nice.

So let's do it again.

Showing our work, we have a fraction bar with a 6 and it's just basic arithmetic.

9 subtract 4 plus 5 is all you're really doing.

So here it is again.

You take 9, right?

Subtract 4...plus 5, but it's all sixths.

And so our answer is 10 over 6.

Now, just like in the last video, we saw that 10 sixths can be written as what, Charlie?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds.

Now this is called reducing.

Now, up there, we...we took 3 halves and multiplied top and bottom by 3,

and we also took the 2 thirds and multiplied the top and the bottom by 2.

Now, when you reduce fractions, this 10 sixths,

we're going to divide the top and bottom by the same number.

And so you have to think, what number divides evenly into a 10 and a 6, Charlie?

>> Charlie: 2.

>> Professor Perez: It's a 2, that's right.

And what's 10 divided by 2?

>> Charlie: 5.

>> Professor Perez: That's right, and 6 divided by 2?

>> Charlie: 3.

>> Professor Perez: Is 3 and so our answer is 5 thirds, and that's reducing a fraction.

We'll talk more about reducing fractions in a future video.

But that's our answer there.

Okay, that was fun, let's do another one!

Now here, we have 4 thirds subtract 1 half plus 2.

Now don't get scared!

Just use the force!

Anyway, here we go, Charlie.

Now, 4 thirds, again, what is our lowest common denominator?

Well, it's 6, again, we'll talk about finding the lowest common denominators

in the next video, more in detail.

Anyway, Charlie, here we go.

We have 4 thirds here Charlie.

Now, 4 thirds can be changed to what?

>> Charlie: 8 sixths?

>> Professor Perez: 8 sixths, that's right.

Now, how do we write 4 thirds?

Again, we're going to multiply 4 thirds by 1.

But, we look at that denominator, 3, and what do I multiply 3 by to get 6, Charlie?

>> Charlie: 2.

>> Professor Perez: 2.

And if I multiply the bottom number by 2, I must multiply the top number by 2, the numerator.

And how do you multiply fractions, Charlie?

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

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

That's right!

And what's 4 times 2?

>> Charlie: 8.

>> Professor Perez: That's 8, and 3 times 2 is 6.

There you go.

Let's go to the next one.

Here we're going to subtract 1 half.

Now, again, 1 half is what fraction Charlie?

>> Charlie: 3 sixths.

>> Professor Perez: 3 sixths.

Again, same process, how do we write 1 half with a denominator of 6.

We've got to multiply 1 half by a 1 and the way we do this,

is we say, okay, 2 times what is 6 Charlie?

>> Charlie: 3.

>> Professor Perez: 3, but if I multiply the bottom number by 3, the top number has

to be multiplied by 3 also, the numerator, right?

And essentially you're taking 1 half and multiplying by 1, but it's 3 over 3.

And how do you multiply fractions, Charlie?

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

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

That's right!

Now what's 1 times 3?

>> Charlie: 3.

>> Professor Perez: 3, and 2 times 3 is 6.

There you go.

Now, we go to our whole number, the 2.

Now the 2 is not a fraction, right?

Although you could write it as a fraction by simply putting it over 1.

2 over 1. So try that if you want.

What we're going to do is say, hey, how do you write 2 with a denominator of 6?

Well, here it is, it's 12 over 6 because what's 12 divided by 6 Charlie?

>> Charlie: 2.

>> Professor Perez: It's 2.

If you understand that, then you just say, oh, I know how to write 2 with a denominator of 6,

12 over 6, because 12 divided by 6 is 2.

Again, if you wanted to write 2 as a fraction, you put it as 2 over 1

and you would multiply top and bottom by 6 and you'll see you'll get 12 sixths.

Do that on your own though, that's your homework!

Now, 2 can be written in different ways, you could write it as 4

over 2 because 4 divided by 2 is 2.

You could write it as 6 over 3 because 6 divided by 3 is 2.

But in this case we are dealing with 6 as our common denominator, and so we want 12 over 6.

All right, so let's finish this problem.

We have 8 sixths subtract 3 sixths, plus 12 sixths.

Which is how many sixths, Charlie?

>> Charlie: 17 sixths.

>> Professor Perez: 17!

Again, if we want to show our work, we put our fraction bar, 6 as our denominator,

write in those numerators, and again it's basic arithmetic.

We take 8 subtract 3 plus 12, which gives us 17, but it's 17 what, Charlie?

>> Charlie: Sixths.

>> Professor Perez: Sixths, that's right, and that would be your answer.

Remember, when you're doing arithmetic, 8 subtract 3 plus 12,

you must do the arithmetic left to right.

Remember? Addition and subtraction are done

at the same time working left to right, whatever comes first.

Anyway, our answer is 17 over 6.

In our next video, we'll talk about finding the lowest common denominator!

Oh what fun!

See you soon!

This is Professor Perez from Saddleback College.

We're going to continue our work with fractions.

Now, in this video, our fractions are going to have different denominators and we're going

to throw in some whole numbers just to spice it up a bit.

Anyway, let's see what Charlie's up to.

He better be ready to go!

Charlie, what are you doing over there?

>> Charlie: Huh?

>> Professor Perez: Are you ready to go?

>> Charlie: Yeah!

>> Professor Perez: You better be.

All right, so here we go, Charlie.

Let's put some number lines up there.

Now, here's our problem, 3 halves subtract 2 thirds plus 5 sixths.

Now, this is the problem we finished in the last video.

Right? But we were doing it on a number line.

Now we're going to show, how do you change denominators of fractions using arithmetic.

You'll see right now.

So here we go, Charlie, 3 halves subtract 2 thirds plus 5 sixths.

Now, we're going to start with 3 halves.

Now, if we look at the number line, 3 halves can be written with the denominator of 6, right?

We know 3 halves is the same as 9 sixths.

But how do we use arithmetic to do this?

Well, here we go.

We know 3 halves is going to be written with a denominator of 6.

Now, what we're really going to do is we're going to take 3 halves and multiply by 1.

That's right.

Because, what's 3 halves times 1, Charlie?

>> Charlie: 3 halves.

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

Remember, if you multiply a number by 1, you don't change it.

But we're going to use a specific form of 1.

We're going to write 1 as a fraction.

Now here's where it gets tricky.

In order to do this, I have to jump ahead and tell you how to multiply fractions.

Now, pay attention to this Charlie.

The way you multiply fractions is you go straight

across the top and straight across the bottom.

You'll see what I mean in a second.

Okay, now, we're going to multiply 3 halves times 1,

but we want to make the denominator 6, right Charlie?

Okay, so here's what you do.

Charlie, what do I multiply 2 by to get 6?

>> Charlie: 3.

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

now, if you have a fraction and you multiply the denominator by 3,

you must also multiply the numerator by 3.

It has to be the same number because think about that...look at those brackets.

What's 3 over 3, Charlie?

>> Charlie: 1.

>> Professor Perez: It's 1, remember 3 divided by 3 is 1.

So realistically, you're taking 3 halves and multiplying by 1.

You're not changing the fraction!

But 1 is written as 3 over 3.

And remember, how do you multiply fractions Charlie?

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

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

That's right.

What's 3 times 3?

>> Charlie: 9.

>> Professor Perez: 9, and on the bottom, what's 2 times 3, Charlie?

>> Charlie: 6.

>> Professor Perez: There's your 9 sixths.

So 3 halves has now been changed to the fraction 9 sixths

and we saw that on the number line, right?

All right, now we're going to subtract 2 thirds.

Now once again, we have to change the 2 thirds and make the denominator 6, right?

So here we go.

Now, 2 thirds on the number line, we see that it is 4 sixths.

How do we do this?

Again, we're going to take 2 thirds,

write it with a denominator of 6 by multiplying it by a 1.

But the question is, what form of the 1 do we want to write?

I mean, how do we write 1 as a fraction so that we can multiply 2 thirds

by it to get the denominator of 6?

The way it goes here is you look at the denominator, 3, 3 times what is 6, Charlie?

>> Charlie: 2.

>> Professor Perez: It's a 2.

But if I multiply the denominator by 2, I must multiply the numerator by 2.

So there you see it.

2 thirds is essentially being multiplied by 1, but 1 is written in the form 2 over 2.

And how do you multiply fractions, Charlie?

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

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

That's right.

Okay, now Charlie, what's 2 times 2?

>> Charlie: 4.

>> Professor Perez: 4, and what's 3 times 2?

>> Charlie: 6.

>> Professor Perez: And there we go!

2 thirds is written as a fraction 4 sixths, right?

Now, we have the 5 sixths, we don't need to do anything to that, right?

Because 5 sixths has a denominator of 6 and there you go.

All right.

Now notice, all of our denominators are 6 and therefore, we can just basically do arithmetic.

So here we go.

9 sixths take away 4 sixths is...?

>> Charlie: 5...

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

And you add 5 sixths, that's what, Charlie?

>> Charlie: 10 sixths.

>> Professor Perez: 10 sixths.

Very nice.

So let's do it again.

Showing our work, we have a fraction bar with a 6 and it's just basic arithmetic.

9 subtract 4 plus 5 is all you're really doing.

So here it is again.

You take 9, right?

Subtract 4...plus 5, but it's all sixths.

And so our answer is 10 over 6.

Now, just like in the last video, we saw that 10 sixths can be written as what, Charlie?

>> Charlie: 5 thirds.

>> Professor Perez: 5 thirds.

Now this is called reducing.

Now, up there, we...we took 3 halves and multiplied top and bottom by 3,

and we also took the 2 thirds and multiplied the top and the bottom by 2.

Now, when you reduce fractions, this 10 sixths,

we're going to divide the top and bottom by the same number.

And so you have to think, what number divides evenly into a 10 and a 6, Charlie?

>> Charlie: 2.

>> Professor Perez: It's a 2, that's right.

And what's 10 divided by 2?

>> Charlie: 5.

>> Professor Perez: That's right, and 6 divided by 2?

>> Charlie: 3.

>> Professor Perez: Is 3 and so our answer is 5 thirds, and that's reducing a fraction.

We'll talk more about reducing fractions in a future video.

But that's our answer there.

Okay, that was fun, let's do another one!

Now here, we have 4 thirds subtract 1 half plus 2.

Now don't get scared!

Just use the force!

Anyway, here we go, Charlie.

Now, 4 thirds, again, what is our lowest common denominator?

Well, it's 6, again, we'll talk about finding the lowest common denominators

in the next video, more in detail.

Anyway, Charlie, here we go.

We have 4 thirds here Charlie.

Now, 4 thirds can be changed to what?

>> Charlie: 8 sixths?

>> Professor Perez: 8 sixths, that's right.

Now, how do we write 4 thirds?

Again, we're going to multiply 4 thirds by 1.

But, we look at that denominator, 3, and what do I multiply 3 by to get 6, Charlie?

>> Charlie: 2.

>> Professor Perez: 2.

And if I multiply the bottom number by 2, I must multiply the top number by 2, the numerator.

And how do you multiply fractions, Charlie?

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

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

That's right!

And what's 4 times 2?

>> Charlie: 8.

>> Professor Perez: That's 8, and 3 times 2 is 6.

There you go.

Let's go to the next one.

Here we're going to subtract 1 half.

Now, again, 1 half is what fraction Charlie?

>> Charlie: 3 sixths.

>> Professor Perez: 3 sixths.

Again, same process, how do we write 1 half with a denominator of 6.

We've got to multiply 1 half by a 1 and the way we do this,

is we say, okay, 2 times what is 6 Charlie?

>> Charlie: 3.

>> Professor Perez: 3, but if I multiply the bottom number by 3, the top number has

to be multiplied by 3 also, the numerator, right?

And essentially you're taking 1 half and multiplying by 1, but it's 3 over 3.

And how do you multiply fractions, Charlie?

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

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

That's right!

Now what's 1 times 3?

>> Charlie: 3.

>> Professor Perez: 3, and 2 times 3 is 6.

There you go.

Now, we go to our whole number, the 2.

Now the 2 is not a fraction, right?

Although you could write it as a fraction by simply putting it over 1.

2 over 1. So try that if you want.

What we're going to do is say, hey, how do you write 2 with a denominator of 6?

Well, here it is, it's 12 over 6 because what's 12 divided by 6 Charlie?

>> Charlie: 2.

>> Professor Perez: It's 2.

If you understand that, then you just say, oh, I know how to write 2 with a denominator of 6,

12 over 6, because 12 divided by 6 is 2.

Again, if you wanted to write 2 as a fraction, you put it as 2 over 1

and you would multiply top and bottom by 6 and you'll see you'll get 12 sixths.

Do that on your own though, that's your homework!

Now, 2 can be written in different ways, you could write it as 4

over 2 because 4 divided by 2 is 2.

You could write it as 6 over 3 because 6 divided by 3 is 2.

But in this case we are dealing with 6 as our common denominator, and so we want 12 over 6.

All right, so let's finish this problem.

We have 8 sixths subtract 3 sixths, plus 12 sixths.

Which is how many sixths, Charlie?

>> Charlie: 17 sixths.

>> Professor Perez: 17!

Again, if we want to show our work, we put our fraction bar, 6 as our denominator,

write in those numerators, and again it's basic arithmetic.

We take 8 subtract 3 plus 12, which gives us 17, but it's 17 what, Charlie?

>> Charlie: Sixths.

>> Professor Perez: Sixths, that's right, and that would be your answer.

Remember, when you're doing arithmetic, 8 subtract 3 plus 12,

you must do the arithmetic left to right.

Remember? Addition and subtraction are done

at the same time working left to right, whatever comes first.

Anyway, our answer is 17 over 6.

In our next video, we'll talk about finding the lowest common denominator!

Oh what fun!

See you soon!