The following material has been developed by state and provincial organizations
along with the Education Television Agency.
Together, at the service of education.
Music
What?
Yes.
That's the one I want.
Yes.
No, that's the one I want.
Oh, how much does it cost?
89.95.
It costs almost 30 pesos more than what I have.
Hmm.
What else?
That other one is also pretty good.
It only costs 57 pesos.
No, no, I want this one.
But you don't have enough money.
I only have to get it.
The only way to make money fast is by selling something.
What do you think, lemonade?
No, there's not much to mention about that.
Besides, it's for kids.
It can always be in a store.
Hey, we had one last year.
Hi, girl.
Hi, mom.
Hi, Mrs. Marsh.
I'm glad you're home.
I was just about to go shopping.
But, and the dead?
Your brother is making pizza.
Pizza?
What?
What's wrong with you?
No, nothing.
How about we go to John's Pizza for the bathroom
to have some extra money?
I don't think so.
Are you going to pay for the ingredients?
Yes.
And are you going to clean the kitchen?
Yes.
Okay.
Is that okay?
Yes.
Okay, thank you.
Just a minute.
Let me sort this out.
Do you want to do business selling my pizza?
Yes, we'll take care of the dough and divide it.
You make the pizza and we divide the dough.
By equal parts?
Yes.
Forget it.
I couldn't even think of doing it
by less than two thirds of the dough.
Two thirds?
How many are two thirds?
Well, two thirds are two thirds.
And you know, two out of three parts.
I don't understand.
Okay.
Let's suppose we have a profit of $12.
And each of these pepperoni slices is worth one.
One dollar.
Now, 12 pepperoni slices equals 12.
Do you understand?
Yes.
So how much does two thirds cost?
I'm thinking about it.
Our profit is a total of 12 cents, so we know that two thirds is less than 12.
Correct.
We want two thirds of 12.
So we divide the pepperoni slices with these seven thirds.
Now think.
We know that we multiply by thirds.
And you take 12 each third?
That's right.
So let's divide the pepperoni slices into three groups.
And take two out of three groups.
Now think.
Each third has four pepperoni slices.
So two thirds would be eight slices.
That's weird.
In general, multiplying by thirds is a lot of work.
Yes, but when you multiply by fractions less than one, the result is less than the initial number.
Is that so?
That's how it's verified.
Look, we only had 12 cents, right?
And we know that half of 12 is six.
And the total of 12 is 12.
And since two thirds are between one half and the other, our result should be between six and 12.
And that's right.
Come on, check it out.
Just multiply the numbers.
Sorry, we have a profit of 12 pesos and we have two thirds of 12.
So let's multiply.
Wait a minute.
I thought we couldn't multiply fractions and whole numbers together.
Can we?
Yes, we can write 12 as a fraction when we write 12 whole or 12 over one.
Then we can multiply 12 over one by two thirds.
Can we?
Of course.
First, we multiply the numbers.
12 times two equals 24.
Then the denominators.
One times three equals three.
And 24 thirds is eight.
John is right, that's how it's verified.
So what you get when you multiply by two thirds is that you get a profit of 12 pesos.
And you get eight.
And Lucy and I have to divide four.
Four between us.
That's my offer.
Come on, girls.
If you don't have to sell my pizzas.
That's not fair.
Take it or leave it.
Okay, we accept.
Oh, that's good.
I'd say it's not a good start.
Sure, but at least John and Lucy learned that when they multiply a fraction less than one,
they get a smaller number than the beginning.
That's easy to remember if you understand why.
Of course, if you just divide a part of something, it'll be smaller.
But you also get a smaller part of a total when you multiply a fraction by a mixed number.
That's true.
Just like Jennifer and Lucy are about to find out.
Thank you, Mrs. Grayson.
Mrs. Grayson wants two pizzas with mushrooms for six.
That's great. That's a total of six now.
It's better if you prepare some dough.
Do you have a dough recipe?
No, we'll have to duplicate it.
Jenny, read the numbers we need and see if we have everything we need.
Okay, we have to multiply everything by two.
Five cups of flour is ten.
One teaspoon of salt is two.
Four teaspoons of olive oil is eight.
Two packages of yeast is four.
And two cups and three eighths of warm water.
Oh no, the fractions again.
How do we multiply two and three eighths by two?
In the same way you did the auto-multiplication,
first you go through all the fractions.
Oh, okay.
We have to multiply two and three eighths by two.
So we go through two and three eighths by fraction.
Two eighths would be sixteen eighths.
Plus three eighths would be nineteen eighths.
Yes, nineteen.
Now we multiply the eighteen eighths by two over one.
What would be thirty-eight eighths?
Or four cups and six eighths of water.
Correct.
Six eighths of cups is the same as three quarters.
Three cups and three quarters.
Good.
Now let's work.
Wait.
First of all, we have to check the rationality of this answer.
Two and three eighths is almost two and a half.
Two and a half by two is five.
And our answer four and three quarters is almost five.
So we check?
Of course.
Can we please go back to work?
Of course.
Thank you.
Did you see that?
The hypermultiplication multiplied a single number by a whole number.
Yes.
And it didn't take long, once you realized that the process is the same.
The only thing that happens is that the fractions multiply.
Besides, I remembered to estimate to find out that your answer was reasonable.
If you go up or down the whole number closer, you can see that we are close to the result.
You know, the kitchen is not the only place where it helps to understand the multiplication of fractions.
The craftsmen, architects, and carpenters, all multiply fractions all the time as part of their work.
That is forty-nine and three eighths.
According to the plan, to build this wall we need eighty-six pieces of forty-nine and three eighths.
How much material do you think I need to ask?
The smarts, Percivali.
Design games for television and movies.
Why is it necessary to understand fractions to make a painting?
Well, generally, when designing a piece of furniture or a game,
the piece that is going to be built never matches the exact measurements.
Why should the majority of fractions in the measurements be exact?
The reason for the exactitude is that if it is not exact,
for example, the windows and doors would not fit in place adequately.
For example, in these windows, what would be done is to take the complete length
and divide it by the number of panels of the same window.
And by doing this, if not giving an entire number,
we will have to multiply fractions to obtain the exact measurements,
with all the pieces equal.
What does this fraction mean in this plane?
This plane is drawn to be a scale that is reduced from the real size of the object to be built.
Half an inch represents a foot,
so what we do is take a tape to measure or a ruler and obtain the exact size of the plane.
In this case, this window is two inches wide, which represents four and a half feet.
Do you understand?
Thank you very much, Mark.
Now let's see how the pizza business continues.
Yes, Mr. Blanc, I understand.
You want a large pizza with a third part of mushrooms,
a third part of pineapple, and a third of anchoitas.
And you want us to cut the pizza so that four people can divide it into equal parts,
and each person can look for each point.
Yes, Mr. Blanc, thank you, Mr. D'Apieu.
Is Mr. Blanc a pizza like that?
Well, at least he wants each pizza in the third part of the total.
You could have asked us to mix everything.
Well, I like it.
We have a problem here.
What?
How are we going to cut the pizza so that each person can share the three points equally?
It's easy, solve it.
Oh no, fractions again?
Yes, you know.
Wait a minute, I think I have it.
The pizza has three different points, and four people want to share it equally.
Which means that you have to multiply thirds by quarters, fractions by fractions.
It's not that difficult.
Look, we know that each point covers a third of the pizza.
A third of mushrooms, a third of pineapple, and a third of anchoitas.
And four people want to share the pizza equally.
So now we divide the three sections into quarters.
And that pizza looks like this.
12 portions.
Each person takes three.
Each person has a quarter of each section.
One quarter is a third.
Each portion is a twelfth part of the total.
Well, looks like it's correct.
Let's check.
Multiply a third by a quarter, we get a double part.
Does it make sense?
Multiply the denominators to the size of the fractional part.
It's still smaller.
It's true, there are four people.
Each person has a proportional part of each third of the entire pizza.
Okay, one double part is like a part or a portion, a quarter of a third.
And since there are three thirds, each person gets three portions of each class of points.
Did we do it?
Yes, yes.
That was bad, girls.
And for having carried out the great mathematical challenge, each one receives a beautiful,
anchoitas, dead.
Well, I think John got into a nice dance.
Yeah, I think so.
Well, I think Jennifer will pay enough money to buy a Skype phone.
If she pays enough, she'll feel the sales.
I think you've heard that before.
Ah, it doesn't matter what happens.
Jennifer and Luigi have learned that multiplying fractions can be very useful.
When a fraction is multiplied by a fraction that is smaller than one by another fraction that is smaller than one,
an answer that is smaller than each number is always obtained.
Yes, since it's taking one part of something, it must be smaller.
And that's it.
Just remember to think things through.
And you'll see that multiplying fractions can be fun.
And also easy.
Presuelvelo.
This program was supported in part by the National Science Foundation.