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Onegaishimasu.
Onegaishimasu.
Okay. Onegaishimasu.
Okay, we're going to start our homework answer comparisons
so, please take out handout number nine.
Now I'll have you write it. Please write, right?
Okay, it's this row.
One, two, three, four, five, six.
Okay, then please write it. Okay.
Okay, go ahead.
Go ahead. Please write it. Okay.
I'm going to check it so those of you
who haven't done it,
please hurry and do it, okay?
This... then.
I will hold this microphone... and walk around.
Okay.
Okay, then I'm going to check it
so please show it to me, okay? Okay.
Okay. Oh, great.
Everyone did their homework today
because we're going to be on TV.
Did you copy it?
Just one person...
just one person is a little different.
Arai!
This child... has forgotten his homework.
Please show it to me.
Bancho, you could do it by yourself, right?
Chino?
Are you feeling better now?
Okay. That's fine.
Okay, go ahead.
Arai, please hurry and write it.
It's only you, Arai.
Okay. Okay, then I had you write six so...
We'll compare answers together and verify them.
Okay, number one.
You exchange it and two X is less than 14.
We divide both sides by two,
so the inequality is X is less than seven.
Number two. Transpose and
negative five X is less than negative 10.
Then you're dividing both sides by negative five
so X is greater than or equal to negative two.
Okay, then the third one.
Date, please interpret this.
Multiply all with 10.
Oh, you mean you multiplied 10, right?
Okay. Ten- line up all of the head numbers
and multiply them by 10,
and 12 X minus four X is,
it's already like this, right? Okay.
Six and then 42.
If you organize them like this,
eight X is less than 48 and
X is less than negative six.
And number four is...
take off the brackets and
three X plus 12 is greater than five X plus two.
Then you transpose, and
negative two X is less than minus 10 and�when
you divide both sides
what is wrong at this point?
Where is it wrong here?
If I told you to correct it...
where would you correct it?
Eguchi, here... where should you correct it?
How would you fix this?
Number three and number nine.
That problem is wrong.
Teacher.
Now it's okay, isn't it?
Yes.
Okay. Then how about this?
Oh, negative two X.
Yeah. At the negative two
the inequality sign doesn't change yet.
It's okay as it is. And
when you divide it on both sides
by negative two then the direction is changed
to the opposite and X is less than five. Right?
Huh? It doesn't change when it became negative two?
Even if you combine like terms
there is nothing that can change the inequality sign
so just moving this one thing won't change it.
This is written, so, this is here.
So because this is here, its only at this point
you change the direction, you know.
You don't change it at the negative two part?
Right. You don't change it at this point.
You change the direction while you
divide both sides with this denominator, you know.
I didn't change it like that. Because this-
this changes it to negative two.
Because you do it with this.
Write it like this and...
I was too lazy to write that at the bottom.
People who write it like this are okay.
This corresponds. This is fine. Yes.
It's just that there's this line and this line but...
okay. Then number five. The brackets are removed.
Negative six X is less than negative seven.
Were there any strange points when you were doing it?
Why does it end up as this kind of fraction?
X greater than or equal to seven sixths?
Correct.
Okay, this is fine.
There was one that became a fraction, right?
Then the sixth one.
It seems like it was multiplied by 10
and was all calculated, but...
You need to multiply 10 to this two as well
and make it 20, so...
Please be careful here because you may forget to write this.
Then 13 X is greater than negative 13 and...
X is greater than negative one.
Then... four or more correct is good.
It's a passing mark.
Then...people who could do four or more.
You are paper, okay?
Then people who did less than four are rock, okay?
One, two, and three!
People who had four or more are paper, you know.
People below four are rock.
Arai has zero, right?
Yes. It seems like everyone other than Arai is okay.
Arai.
Let's do our homework from now on, okay?
Huh?
Okay. That's what it's about.
Okay, then today will be the
final part of the sentence problems so, then...
I will have everyone use their heads and
think a little, okay?
Until now we've just done calculation practice,
but today we will have to use your heads a little so...
I'm asking you to use thinking methods.
How to think and how to look for it and
think about it may be a little difficult you know.
More difficult than just simply calculating, that is. Right?
Well then we'll go ahead.
Okay. Well then... please look at... the problem.
Fukuda, can you see it?
Yes?
Can you see?
I can see.
You can see. Okay. Then, Genji.
Please read the problem... in English.
[ BB: Problem 3. You would like to buy 10 cakes all together for less than 2,100 yen. ]
[ BB:One type of cake is 230 yen each and the other cakes are 200 yen each. ]
Okay. Genji, please read the problem.
You would like to buy 10 cakes all together
for less than 2,100 yen.
One type of cake is 230 yen each
and the other cakes are 200 yen each.
Yes.
Do you understand the meaning of the problem?
Arai, do you understand what this problem means?
You have 230-yen cakes and 200-yen cakes, right?
The 230-yen cakes are a bit more expensive.
And... you have 10 family members.
You want to buy cakes for each person.
But, I have only 2,100 yen.
Which cake... seems more delicious?
The 230-yen one.
The more expensive one is somehow more desirable, right?
And so... you want to buy as many
expensive cakes... as you can,
but what's the maximum that you can buy?
That's the problem.
Understand?
[ BB: If you want to buy as many 230-yen cakes as possible, what is the maximum number that you can buy? ]
There are cakes that are 230 yen and 200 yen.
You only have 210 yen.
But you need to buy 10.
But the 230-yen one looks more delicious
so you want to buy as many as possible.
Nine.
But you only have 2,100 yen, so...
so in fact how many 230-yen cakes can you buy?
Nine.
So today I am going to have you think about
how to find the answer.
So now I will pass out paper,
so please try and think about it.
See, you can do it if you do it like this.
See, you can understand- solve it if you do it like this.
I will present the problem in this way, okay?
Use the back, too. Four, five, six.
Two, three, four, five, six.
I didn't pass out the papers so... four, five, six, here.
One, two, three, four, five, here.
One, two, three, four, five, six.
Three, four, five, six. Okay.
I don't care about what kind of method you use
so please think about if you do this, you can buy 230-yen cakes.
Think about how many you could buy and how to figure it out.
Do we solve this problem?
This problem is for ninth graders,
so you can't solve it, so please use the back.
Please use back of the paper and think about it a little.
What do you need to do in order to buy 230-yen cakes
and up to how many can you buy and bring home?
Please think about this for a while.
It's good if you come up with an answer,
but please think about what you need to know
about how many to buy.
Well, we have about three minutes so it's okay
if you do it while you write notes there.
So, think about what you need to do to
find out how many you can buy
and find the answer. Okay, get started.
Please work by yourself at first, okay?
If you were in front of the store and you only had 210 yen
and you had to buy 10. What should you do?
Think about the time that you were in front of the store.
What would you do?
What?
Please think about... that okay?
Then how are you going to think about it?
Please show me how you are thinking about it.
That you can find it if you do such and such.
[ BB: Way of thinking ]
[ BB: Way of thinking ]
Okay. Go ahead.
Can you bargain and lower the price?
Ordinarily they wouldn't bargain, would they?
Although they might bargain if it
were at a vegetable or fish store.
I have never seen them bargain... at a cake store.
They might have bargained if it were Kenchan's Cakes, right?
Oh, don't you know it?
Ah, I did it.
Okay. Please think about it by yourself
for a while. About two minutes left.
I told you not to use this but to use the back, didn't I?
We're buying 10?
We're buying 10 anyhow.
You need to buy 10 so... please buy 10, okay?
Buy 10...
Because... what you really want is
to buy 10 230-yen cakes, right?
But if you buy 10 230-yen cakes how much will it cost?
Two thousand three hundred yen.
It'll end up being two thousand three hundred yen, right?
However, you only have 2,000- 2,100 yen in cash so...
You need to mix, mix it up or you can't buy it, you know?
Because you only have 210 yen in cash.
Then how do you need to think about it...
in order to find out how many 230-yen cakes to buy?
Please think about that.
Please think about it.
I don't care what kind of method you use.
Inequality equation.
Oh, if you want to set up an inequality equation
go ahead, that's fine, too.
If someone else says that they want to
think about it with a different method
because they don't need an inequality equation...
That, that is fine for that person, too.
I want to know how you think about it so...
I will ask you about thinking...
about how you thought about it.
See... being asked to figure out
how to think about it is more difficult
than being asked to solve an equation, isn't it?
Okay, go ahead.
Is it not permissible to buy nine?
I don't get this.
Don't get it?
But, if you really were buying two kinds of cake
you have to think about money,
the money that you have and the bill.
After you ask for the bill you can't say I'm sorry
I want to return this. Can you?
Then you exchange.
That has happened to me a lot, too.
I say oh, sorry! Please return this.
At any rate... please buy 10 cakes.
How are you going to think about it?
It's also okay if it's over 10, right?
Not over 10. Buy 10-
Buy 10?
Ten?
You're buying 10, you know.
Ten.
Ten.
It's not 11 or 12 or eight, but buy exactly 10, okay?
Well, then how can you... find out... how many you can buy?
There are people who...would have them take the cake,
take a 200-yen cake and break it in half
and make it 100-yen.
Okay, then you go to the cake store and
try and request that.
Most people won't do such a thing, you know.
It's different from asking to have
half a Japanese radish, you know.
If you ask them to halve the Japanese radish they'd do it for you.
It's okay... if it's a Japanese radish.
What if you said just the fresh strawberry
on the strawberry cake?
The fresh strawberries on the cakes are sour.
The strawberries on the cake need to be out
in the stores before they are fully ripe,
they are picked while they are sour,
so it can't get sweet. But this is unrelated...
So how do you think about this?
Not by using equations or things like that
but tell me what you have to do to get the answer.
Buying two thousand... two... 2,100 yen exactly...
We don't need to... it's okay if we have change left over, right?
It's okay if there's left over.
It's good if you have change in any case.
Change, or else it's also okay
if you use all of the 2,100 yen, you know.
Well there is one minute of remaining time.
I don't understand this.
You're all good at this setting up an equation
and suddenly spitting out an answer.
Try doing it with that method.
Okay.
Then... we'll have midway presentations.
Okay, please raise your heads.
Then people who think they have a way
that seems to work...
and understand the method
you are paper, right?
Not yet, now.
People who had no idea how to do it...
you're rock... okay?
Okay, people who think it's best to do it this way, but say...
You don't understand... you don't have confidence, are scissors, okay?
Although from looking at what you were writing
it seems like rocks are plentiful.
But, I'll try and ask you, okay?
Okay, then students who understood
the way of thinking are paper.
And then... people who say that you can do it
to some extent and you understand it are paper, okay?
People who say... I don't understand it at all are rock, okay?
People who say that they are in the middle are scissors, okay? Okay.
Then one, two, and... three.
Oh... there are no paper people.
What's paper?
Paper is people who say that they understand it completely.
One person.
Okay.
Then scissors people and paper people,
there are even quite a few rock people who responded, right?
Okay, then I will try and ask a few people, okay?
Okay, then Hara.
How did you think about it?
What?
Okay, go ahead.
I... didn't understand it at all but...
First of all...
I thought that I should calculate...
How many of the 230-yen ones I could buy and...
In the beginning... when I did it with 10...
It ended up being 2,300 yen so...
It's not good because it's over the amount so...
And then next when I did it with nine...
When I did it with nine...
it was 2,070 yen and... it was okay but,
you need to buy 10, so when I calculated it...
to buy one 200-yen cake...
Two... 2,070 plus...
Two hundred yen is...
With 2,270 yen and...
You go over.
You go over, don't you? Okay.
So then... you keep reducing the numbers and...
Keep reducing and... when you do it with eight on this side and two this side, then?
When I did it-
When you did it?
Time ran out and...
Time ran out and...
I couldn't do it to the end.
You couldn't do it to the end.
Okay.
Raise your hand... if you say that
this way of thinking was really similar to yours.
Hara started counting from 10, but...
there may be people who started counting from this side.
People who say that they used this way of thinking.
Okay. Only, Ikui?
Arai?
Okay. Then Ikui, Arai, Joji, right?
Then Ikui... where did you find
an answer that was exactly even?
Or could you not find the answer?
Were you at the point in which you were do-
counting it like this but time ran out?
Did you find it in a flash?
The 230-yen one...
You buy three of them and...
Three? Then how much does it become?
Six hundred ninety yen.
Six hundred ninety yen.
And what about this side?
Seven.
When you buy seven?
Two thousand ninety yen.
Wait a minute.
If you buy seven, if you buy seven
200-yen ones how much does it become?
One thousand four hundred yen.
One thousand four hundred yen. Okay.
How much is it... if you add it?
Two thousand and seventy yen.
Two thousand-
Oh. Two thousand ninety yen.
Ninety yen.
Okay. That's what it's about.
So that means if you buy three 230-yen cakes
and seven 200-yen cakes,
then it becomes 2,090 yen.
You get 10 yen in change.
That's why you could buy three of these.
And as for this, if you buy seven then...
With 2,100 yen there is only 10 yen left.
And with only 10 yen you can't buy anything, so it's this.
You could find an answer... that it was this.
What about yours, Joji?
I'm not done yet.
Middle... You are still in the middle of doing it.
What about yours, Arai?
What?
I'm still doing it.
Still doing it. As for Arai, he couldn't
print out what was in the hard drive in his head, right?
Okay. That's what it's about.
This... then something else...
students who say, "I did this."
Kamon and Luiko and who else?
Other people.
No one?
What's yours, Kamon?
How do you... work it out?
What did you set up?
Huh? How did you do it? Your method?
Inequality equation.
You set up an inequality equation. Okay, what about Luiko's?
Inequality equation.
You set up an inequality equation?
Then what about other people? Isn't there anyone?
No one?
Then the other people can't buy them.
You know, the cakes, counting them one-by-one
is a really ordinary way of doing it, you know.
Isn't there anyone else?
Maruya's was also an inequality equation, right?
We'll get to you later, so wait a little, okay?
Other people.
How did you do yours, Bancho?
Huh?
Yeah.
You wrote multiply by something,
multiply by something, right?
How did you do that?
The same as that.
It's the same as this, right?
And then who else was it now?
Nagase's one also used a ratio, right?
Is it the same as this?
It's different? What is it?
Huh?
Inequality equation.
Inequality equation?
Okay.
Then... are there others?
Who used a completely different way of thinking?
No?
Then... I've thought about it, too, so...
what do you think about this way of thinking?
Do you all understand it?
You bought... ten... 230-yen cakes.
You're told to buy a lot and so in reality
you want to buy all 230 yen cakes, right?
Then how much money is needed?
[ BB: Method of thinking. Ten 230-yen cakes. ]
Two thousand three...
In reality 2,300 yen is required, right?
But you're short 200 yen.
You are short... 200 yen.
You're short. You thought...
that you would buy a cake that is...
30 yen cheaper than... the 230-yen cake.
[ BB: Short 200 yen ]
Buy a cake that is 30 yen cheaper and...
You buy a cheap cake and...
replace this needed 200 yen for a cake
that is 30 yen cheaper, okay?
[ BB: 30-yen cake ]
You're short 200 yen, you know.
But, let's buy them a cake that's not 230 yen
but a cake... that is 30 yen cheaper.
Then 30 yen is going to be saved.
With each, 30 yen is going to be saved.
How many cakes that are 30 yen cheaper do you need
to buy in order to make up the 210 yen shortage?
This needed part.
How many cakes that are 30 yen cheaper do you need
to buy to make up the 210 yen shortage?
Can you make up the 210 yen?
Seven.
Yeah. If you buy six, six times three is 180 yen,
so you are still 20 yen in the red, right?
However... if you buy seven of these...
if you buy seven...
you will have 210 yen left over, right? The money, right?
[ BB: Seven ]
That 210 yen is applied to this 200 yen, you know.
Then if you buy seven of the cakes that are 30 yen cheaper,
if you do that, then what about this side?
Three.
It's three... did anyone do it like that?
Someone who did it like this?
There probably isn't anyone, right?
Start off by buying 10.
You're short 200 yen so... let's make up for the
missing cost with cake that is 30 yen cheaper.
You can make up for it if you buy seven,
so this is three. In that way.
It was good, right? Then I'll ask you.
Okay... Luiko.
Then how did you think... about this one?
The total 230 yen, oh...
It's for some amount and make that amount X and...
You need to buy 10 of the 200-yen ones.
So 10... make it 10 minus X and...
And the total has some amount of two- 230-yen ones.
And the 230-yen ones are 230 X. And...
the 200-yen one is 200...
bracket 10 minus X... And then... then...
200- 230 X plus 200 bracket 10 minus X...
is less than, minus, less than or equal to 2,100 yen.
And you form the inequality equation.
Okay.
You said that this was the inequality equation, right?
Okay.
Did you understand the meaning?
Perfect.
You get it better with Luiko's explanation than with mine.
Okay. Try and raise your hands.
People who say that they got it with Luiko's explanation.
One person?
Only Maruya? Two people? Three people?
Four people? Just four people is it? Five people? Okay.
Then... please explain it next, Ryo.
Please explain it in a way that is a little more understandable.
Try and explain it in a way in which...
a few more people will say... that they understood.
The method of explanation is okay with this.
Okay.
Go ahead.
Okay. Go ahead.
You can't do it?
You don't know?
Okay. Then... I'll start talking from this point okay?
To tell you the truth I was going to
talk about today, what Luiko set up.
But I wanted you to find a number...
of ways to come up with it so...
I did it so that I would have you think about it, right?
Three, four, five, six. Okay.
One, two, three, four, five, six.
Okay.
One, two, three, four, five, six.
Oh, it's not five, six...
there's five people here.
One, two, three, four, five, six. Here.
Okay. From there, and so...
While talking so that everyone will say,
"I see," while understanding Luiko's explanation,
we are going to try and do it using that problem,
using an inequality equation problem, okay?
You want to buy a total of 10 cakes in which
one is 200-yen and the other is 230 yen.
And you want to make the total less than 2,100 yen.
In order to buy as many 230-yen cakes as possible,
what is the maximum that you can buy?
That is the problem.
And what is the thing that you want to find? ***?
What do you need to answer?
How many 230 yen cakes you buy.
It's a problem asking how many 230 yen cakes
you can buy, so...
So that's why you're going to think of it
as changing the 230-yen cake into X.
I'm asking how many can you buy,
so you should think of changing the 230-yen cake into X.
[ BB: Buy X amount of 230-yen cakes ]
When doing that... you need to buy
10 cakes all together. You need to buy ten.
Right?
Then, Qumi? If it's six of this cake, then...
how many of this cake do you need to buy?
Four.
Four. How did you calculate it?
What?
Four.
So how do you calculate it?
How do you know that this is four?
What?
Because it's not enough.
Yeah, so how do you calculate it?
What's the equation here?
Add.
Huh?
What do you add to six to get this ten?
Then... then how many is it here?
X.
What?
That's why you're in trouble
if you are fooled by the number here.
If this is six then it's probably how many here, Ryusaki?
Qumi is saying that it's four,
but how do you get this here?
It's four, but how do you come up with four?
Ryusaki, how do you come up with four here?
Subtract.
You need to subtract, right?
It's good if 10 minus six is four here.
If it was seven here, then you would
write 10 minus seven, right?
If this were nine here then you would
think of this as 10 minus nine.
So if you subtract one of the numbers
from this number, from the total number,
then you get the remaining number.
And the problem is,
if you make the number on this side X,
then what will this be if you do that?
Here.
Joji. What will this become?
Here.
You haven't been listening, have you.
If this were three,
then this can be found by going 10 minus three.
If this were four, then this is 10 minus four.
If this is five, then this is 10 minus five.
Then if this is X, then what is this?
Ten minus X.
Yeah. It'll become ten minus X.
What this is saying is that you can only buy
10 minus X number of the 200-yen cakes.
It will come up here.
It's 10 altogether and if you make this X,
then here... you need to subtract this number.
If you subtract this number from 10
then you'll always arrive at the number left over.
That's why it'll be the case that
you can buy this many 200-yen cakes.
The amount you bought, right?
This will be the amount here.
If you do that, what would the cost be
if you bought only X number of 230-yen cakes?
If you multiply the 230-yen cakes at this price
by X then you'll get the total cost, right?
It's 230 X, you know.
Because you're only going to buy 10 minus X
of the 200-yen cakes, the cost will be this.
Then since you only have 2,100 yen with you,
you'll be in trouble...
if it isn't less than this.
And so you will get this equation, okay?
What is the equation?
Oh, I can't write it, can I?
I'm wondering what the equation is so...
The equation is 230 X plus
200 bracket 10 minus X is less than or equal to...
[ BB: Equation ]
Two thousand one hundred.
Okay, then let's try and solve this, okay?
Okay, the 230 of this 230 X stays the same.
Okay, Sakai,
how much is it here when you take the parentheses off?
Huh?
I took the brackets off now, so here.
Multiply this and this.
Mm?
How much is it when you multiply it?
How much is it if you take off the brackets?
Well then how do you do two bracket X plus three?
Two X.
Well then remove the brackets.
I did it. I did it.
Four plus five.
You multiply it, right?
Huh?
Bracket... 200 times 10 is see...
Two thousand.
Oh, 2,000, right? Two thousand. Okay.
Two thousand... minus, you multiply this so...
this time on this side so okay.
Two hundred X.
Two, 200 X. Okay. Less than or equal to 2,100.
Okay. Then which is the next one that you transpose?
Two thousand.
Two thousand. Okay.
We're going to bring the plus 2,000 to the other side.
And 230 X minus 200 X is
less than or equal to 2,100 minus 2,000.
The sign changes, so please be careful, okay?
When you transpose it, okay?
Then 30 X... 30 X is less than or equal to...
100. Okay.
Then you're going to divide both by 30 on both sides,
so it becomes X is less than equal to...
100... thirtieths but...
I'll erase the zero here, okay? It'll become 10-
Thirds.
Thirds.
What will 10 become if you write it in decimals?
Three point three three three three three, right?
If I asked you to find the largest integer...
that is smaller than three point three...
it will come out as three.
I can't really write the answer, but okay...
you can buy three... up to three... of the 230-yen...
thirty yen... cakes.
If you present it... like this... it's good.
Things presented like this are
solved using an inequality equation.
[ BB: You can buy up to three of the 230-yen cakes. ]
Which is easier, doing it one-by-one or
using an inequality equation?
An inequality equation.
It's easier to use the inequality equation, isn't it?
And so today what I would like you to do from here is,
we already did this in the method of thinking but...
Inequality equation.
I would like you... to know...
the good qualities of...
finding the answer by...
setting up an... inequality equation,
right... inequality equation so...
we thought about it... with a problem like this.
[ BB: Learning the good qualities of finding the answer by setting up an inequality equation. ]
If you were to solve it without using an inequality equation
you need to check it out quite a lot, one-by-one, a lot.
Hara could solve it because it was 10,
but what if you were to buy
100 of these two cakes together...
Ninety- figure out 100,
and figure out 99, and figure out 98,
and figure out 97, and-
You need to figure out all of the numbers
between one and 100, don't you?
However, if you used a method like this that Luiko used...
you will arrive at the answer quickly.
Therefore, you don't need to figure out each number one-by-one.
So working it out by making...
an inequality equation has a lot more...
good qualities... than counting it one-by-one.
That's what it's about, all right?
So then and so...
if there are good qualities like that then...
we're saying that.
So there are two problems on the right side.
This time, please buy 20 apples and oranges altogether.
If you count it one-by-one
you will be in an incredibly terrible situation.
As we just did in the cake situation,
set up an inequality equation by yourself and
find out up to how many apples you can buy.
Or if you're doing the problem at the bottom,
try to solve the problem about
how many pears you can buy by setting up an inequality equation.
Work it out and find an answer.
Because finding the answers one-by-one is hard-
I wonder if you see the numerous good points
of setting up inequality equations,
and, well, that you'll set up
inequality equations yourself and
try to find the solutions.
That's what it's all about, okay?
Is it okay?
Okay. Then and so...
people who haven't written this here,
write it, and then do problem one.
Try to set up an inequality equation
by yourself in the same way and
try to solve the problem.
Okay. Go ahead.
This is... the total so...
you don't have it... see?
This is attached.
It's faster than counting, right?
It's okay. Now, work out the problem.
This expresses this in the same way as this.
Oh, solve this on the top.
That's good.
It's like this, you know.
Twelve times.
Not 12, it's 70 times 20, you know.
This is 20, isn't it?
It's a bracket so, okay?
It's not a 12, you know.
I got it. Twenty.
You couldn't read the
numbers that you wrote, could you?
It's okay, Tanizaki, here.
Try this and work it out like this.
Sakai's one is also good, isn't it?
Okay, you've got it.
Then now it's easy, right?
It's easy, right?
This isn't X here, but...
you're going to buy 20 in all, right?
So here you will get the number you subtracted...
from the total amount of 20.
And so 20 minus... negative X.
And so the price here...
you multiply the price of one of them, and
this amount, so this becomes 120 X. Okay?
And what about this one?
It becomes 70 parentheses.
You can't write it... if it's like that.
Please write the 70 sort of more on the side.
And what about here?
Twenty minus X.
Okay. Now you've got it.
And then put these together and
make this smaller than four.
What about you, Uchida?
Huh? Two hundred.
Just a moment. It's all right now, right?
Oh, Ueda, that's good. Okay, it's done.
Oh, Ueda, yours is good, too.
You've arrived at the answer, right? Okay.
Where'd it go, Waka?
This is okay, you know?
This is... 120 X plus,
how much is this if you multiply it by this?
Two times seven, 14, right?
One thousand four hundred seventy two thousand.
This is four. Then you have to transpose it.
There is seven, 700.
Twent- this is 70 times 20, so next is four, right?
Okay.
[ BB: 120-yen apples ]
[ BB: 70-yen tangerines ]
[ BB: Total ]
Okay, I guess I'll have you write it.
Are you done?
[ BB: Buying Fifteen. Seventy-yen pears. Fifty-yen persimmons. Basket. Total. ]
Did you do it?
Then work it out there... will you?
This should be fine, right?
[ BB: Buying Twenty. One hundred twenty-yen apples. Seventy-yen tangerines. Total. ]
Could you write it?
Isn't it good? It's good.
Divide, you can divide it.
Then... Bancho.
Please write number two, okay?
Look at the figure and set up an equation
and work it out, okay?
What number?
Number two.
Number two?
Yeah.
Write it without looking at anything, okay?
Because I wrote-wrote that you would buy 15.
Mm, I just saw someone's eyes.
Okay, Watabe.
Uh, wait a second.
Watabe, please write number one, okay?
Okay, go ahead.
You don't understand if you don't look at anything.
It's not written.
This is going to appear in the equation.
Oh, how much is it for the baskets?
Oh yeah, I didn't write the basket prices. Sorry.
The basket price is...
Eighty yen, isn't it?
Eighty yen.
The total... was 1,000 yen, wasn't it?
Hm? Oh. I should write the totals, too, shouldn't I? The total, sorry.
Less than 1,000 yen.
Watabe's is less than 2,000 yen.
Two thousand?
Please write 2,000 yen here. Oh, okay.
Try hard and work it out.
Just one more step, just the answer.
Oh, you need to display the answer.
Eight?
It's wrong?
What?
What is this?
What?
It's wrong. This, the answer
of this inequality equation is wrong, isn't it?
Isn't it okay? Because... this is 10, right?
Is this... the answer?
With 80?
It's this value here.
Two times nine?
What about eight?
Seven hundred fifty.
Aren't you missing the 50 here?
Oh... the response is okay with this.
The answer is not this though, is it?
Huh?
The answer is-
What is the answer?
Is it this?
This is good.
This is the answer to the inequality equation.
But, the answer to the problem has to be this, right?
When asked to work out this inequality problem,
this is- This has to be the answer here, right?
However, this won't be the answer to the applied problem so-
One hundred seventy over 20.
Seventeen over two, right?
So teacher, if you do it like this, is it correct?
That should be that way, right? Okay.
Ueda, how far did you go?
Fifty times 15 is look...
Not yet?
It's 75, you know. Then it becomes 750.
For example, how do we write the answer?
What are you going to write?
The problem asks up to how many can you buy.
What? Pears, right?
Up to how many pears can you buy?
It's 70 times 20, so it's not 140,
but it's only one zero, right?
Who can read this?
Who can't read this?
There the six is... 60... you're missing one zero, aren't you?
Okay... that's what it's about.
Please look at number one first. If you say that you will buy only X 120-yen apples then...
You're going to buy a total of 20.
So, as for the tangerines, you need to buy only the total 20 minus X tangerines.
And the price of the apples is 120 X.
And the price of the tangerines is 70 parentheses 20 minus X.
And the total that you have is 2,000 yen, you know.
So you're asked to make it less than 2,000 yen so...
One hundred twenty X plus 70, parentheses 20, minus X, is less than or equal to 2,000.
And if you try to find the answer you get X is less than or equal to 12.
That's why you can buy up to 12 apples.
We're going to try to see if this is true or not, okay?
You buy 12 120-yen apples.
Then what is the cost?
Is there anyone who knows what is 12 times 12?
Didn't I teach this to you before?
One hundred forty four.
It's 144, right? Okay. One thousand four hundred forty yen. This is the price of the apples.
Then, you need to buy eight of the 70-yen tangerines so seven times eight, 56.
And all together it's exactly 2,000 yen.
About it being exactly 2,000 yen, why did it become exactly 2,000 yen here?
Since it's divisible.
Because here we got 12, a number that was divisible, right?
Right. We got it because the 12 could be divided perfectly into it here, right?
That's why it ended up being exactly 2,000 yen.
However, this side. Okay.
You find it in the same way. The pears are X and you're going to buy 15, so the persimmons are 15 minus X.
The price of the pears and the price of the persimmons... and even the basket will be included as well this time, right?
It's asking you to limit it to 1,000 yen all together. So, if you set up an inequality equation you get this kind of equation.
Seventy X plus 50, parentheses 15, minus X, plus 80, is less than or equal to 1,000. Please work this out.
This is the answer of the inequality equation, okay?
You need to present this, okay?
Instead of just suddenly writing the answer eight- if you first work this out...
You get an answer of 17 halves, okay?
You need to find this first. Now you need to pinpoint it like this.
Then... if you buy eight 70-yen pears, then seven times eight equals 560 yen.
If you do that, then how many 50-yen persimmons do you buy?
You buy seven? Then seven times five equals 350 yen. All together... 910 yen.
Then... you'll have 90 yen in change coming back.
What?
The basket price.
Oh, there's the price of the basket.
The basket price is 80 yen so...
It's altogether 990 yen, and you'll only get 10 yen in change. That's what it's about.
What we talked about today was... the answer from inequality equations... that is...
When solving problems it's often easier to set up an inequality equation and find the answer,
than count things one-by-one and find the number.
That's why although it may be tedious... for the applied problems of inequality equations, okay?
Instead of looking for the answer one-by-one you find it by changing the parts written in Japanese to mathematical terms and solving it.
Because an inequality equation has a good quality like this. This is what we talked about.
Is it okay?
Is it okay?
Yes, okay.
Then I'll pass out the problems and finish off. What number should I pass out, today?
Is it number nine?
It's number nine. Number 10.
Then I'll hand out the problems for number 10 and finish.
From what number to what number are there?
It ends with 10.
Inequality equations end with this.
One, two, okay.
Four more.
Four more? Okay.
One, two, three, four, okay.
One, two, three, four, five, okay.
One, two, three, four, five, six, okay.
Okay.
Okay. Then we'll say our greetings and finish off.
Student officer. Lead with strong voices since we're finished.
Please get ready to bow.
Stand.
Thank you very much.
Thank you very much.