Hello everyone, welcome back to our new video.
The topic we are going to cover in today's video is about
percentage.
You must have heard about it somewhere and you must have
used it.
And you must have seen it in report card.
So, we are going to do the same today.
We are going to understand what is percentage?
How do we calculate the percentage of anything?
We will learn that in today's lecture.
Before starting today's lecture, the relation of percentage
is also related to fraction.
So, let me tell you about fraction.
Let us recall what fraction was.
So, if we see fraction, fraction was of which form?
Fraction was of p by q form.
In which denominator will always be non-zero.
And p and q will be of natural number.
If I tell you about fraction diagram wise,
If we take a square, we divide this square into two equal
parts.
See, I have divided it into two equal parts.
Now, it is divided into two equal rectangles.
And I have shaded one rectangle.
So, tell me, what will be the fraction of shaded area?
So, if we have to tell about shaded area, how will we tell
it?
We had two equal rectangles in total.
So, we will write the total in divide.
So, total was two. So, I have written two.
From that, how much shaded portion we have? Shaded is only
one part.
One part of two is shaded.
So, one by two.
So, how much shaded portion we have?
It is half.
So, below we will write total.
Above we will write one.
Similarly, if I ask about non-shaded portion, what will be
the result?
It will also be one by two.
Because non-shaded is also one part.
So, divided by total.
So, below we are seeing in fraction, what is happening
below?
Total is being written.
And above, whatever we have been asked, tell us about this
thing.
We are writing as much as we are given.
So, this is the fraction.
You must have seen fraction in circle.
So, if we are taking out in this case, it was in equal
parts.
These two parts were our equal parts.
If I tell you a new thing, suppose we have one more
rectangle.
That is square.
But now, this square is divided into four equal portions.
Now, it was divided into two equal portions.
Now, it is divided into four equal portions.
So, in four equal portions, we have shaded portion.
This is our shaded portion.
So, tell us in fraction, how much is shaded portion?
So, first of all, if we write in fraction, what will we
write in divide?
In divide, we will write in denominator, whatever is the
total.
So, how many equal squares, equal sub-squares, or tiles are
there?
Four.
So, it will be divided into four.
And for shaded, for what are we taking out?
We are taking out area for shaded.
So, how much portion is there for shaded?
Three tiles are covered.
Which are they?
First is this, second is this, and third is this.
So, three tiles are covered.
So, three by four will be our shaded portion.
Did you understand three by four?
Now, if we do the same, if we divide the same square into
how many parts? 100 equal parts.
100 equal parts.
And out of that, we are saying that 30 are shaded.
So, tell us the fraction of this.
30 squares, sub-squares are shaded.
30 parts are shaded.
How many are left? 70 parts.
70 parts are non-shaded.
So, tell us the fraction of shaded.
Tell us the fraction.
So, what will you tell?
First of all, you will write the total.
Total divided into 100.
And if we are asking about shaded, then we will write the
quantity of shaded on the top.
So, this becomes 30 by 100.
Which means we have 30 tiles shaded.
Out of how many tiles?
Out of total 100 tiles, we have 30 tiles shaded.
So, this is the fraction.
You can also write it in short form.
3 by 10.
In lowest form.
3 by 10.
So, this becomes the shaded portion.
This much.
Now, if it becomes handed, as soon as it becomes handed,
then we will get to know that out of 100, total is handed.
Out of that, 30 are shaded.
So, the same criteria is going on.
In percentage.
In percentage, if we are telling about any 100 parts, if we
are telling about any 100th portion, that will be called
percentage.
Percentage means 1 by 100.
Out of 100, how many terms are coming?
That will be called percentage.
So, percentage sign is this.
This is the sign of percentage.
If we want to convert percentage into fraction, if we want
to convert it into fraction, then what happens?
If we want to convert percentage, then what should we do?
Just divide it by 100.
Divide it by 100.
If we want to convert percentage into fraction, then divide
it by 100.
If percentage is not looking good, because it is 1 by 100,
then there should be some quantity here also.
So, what does 1% mean? 1 by 100.
Which means, divide 1 by 100.
So, here it is coming.
What is the indirect meaning of this?
Out of 100, only 1 portion is necessary.
1 portion is required.
So, that is what we have.
Total percentage is 100%.
Out of 100, we are taking only 1 portion.
So, that is what we have.
If we want to convert it into percentage, then that is 1%
Now, look here.
If I want to convert 2% into fraction, then what will be
2%? 2 into 1 by 100.
1 by 100.
So, what is this? 1 by 50.
So, 2% means 1 by 50.
Similarly, we can take 3% also.
4% and so on.
10, 50, 100.
So, whenever we take 100, we can take 1, 2, 3, anything.
Now, if I take 100% 100%.
So, what we have to do in 100%? 100 100 by 100.
So, we will subtract percentage.
So, that is 1.
So, this is what I told you from here also.
That the whole percentage is whole.
If we are taking whole percentage, that is, if we have
these two tiles, both these portions are shaded.
So, our whole portion is shaded.
So, what will be the fraction of this? 2 by 2.
Because shaded is also 2 and total is also 2.
So, we have 1.
1 means, if we want to say it in layman terms, then it is
100% shaded.
Means, it is completely shaded.
So, 1, if we are looking at whole quantity, and taking
whole quantity 1, and giving equal to that 1, whole
percentage, that is equal to 100%.
So, what is 100%?
It is a whole quantity.
Means, if we are taking for sure, that it must be 100%.
Like, what is 100% surety?
Sun always rises.
Sun is there.
There is one sun. This is 100% sure.
So, what is that?
Our surety.
In what you will study this?
The concept of surety and uncertainty.
You will study this in probability.
There is some relation of that.
That 1, whole quantity, will be your 100% percentage.
You have done this much.
You have understood 100%.
100% is our 1.
That is for sure, full quantity.
Now, what we will learn?
Now, we will learn in next thing.
You have learned percentage.
Yes, of 1% what percentage?
Can it be more than 100?
Obviously, if our of fraction, if till now we have P by Q,
I will tell you in fraction, but you must have heard that I
am 200% sure, I am 1000% sure or 1000% trust or have faith
on someone.
So what does that mean? When we use more than 100% we use
it in speaking, so that we know
that we are 100% sure about something or have faith in
something.
So it is used in comparison
if we ask more than 100% or if there is something more than
100% in comparison, then we will say that it is an
increment.
If there is a particular increment of something, then
obviously it will be more than 100%, then we can use it in
comparison.
So it can be used in comparison.
So it is not that when we take out percentage in class,
then what is our total percentage?
Maximum percentage is 100%.
So it is not that when we take out percentage in class, then
what is our total percentage? Maximum percentage is 100%.
Then we take out percentage of other students related to
it, that how much percentage is being made out of 100, 90%
or 80%, so in that we take maximum 100%.
And anyway if we see in general, then we take whole 100%
only. It is also used in comparison or in telling that
which quantity is how much, how much
increase is there, how much change is there in it. So next
we move to conversion.
So next we move to conversion.
What all is there in conversion? We have two types of
conversion.
One is conversion from percentage to fraction and second is
vice versa that is conversion from percentage to fraction
and second is conversion from percentage to fraction
and second is vice versa that is conversion from fraction
to percentage.
So in percentage to fraction, you have just learnt in last
that what should I change fraction, change fraction sign to
divide by 100, means multiply that quantity by 100.
So if we have, like what
we did just now, we did half case, half, sorry, half became
number.
So if we have to take out any percentage, let us suppose we
have to take out 25%.
In which we have to convert 25%? You tell us in fraction
term, what is the meaning of it in fraction.
So in fraction term, what is the meaning of it? What you
have to do is divide it by 100.
So it will be 25 into, we will remove percentage sign and
instead of that we will write 1 by 100. If you cancel it
out, it will be 1 by 4.
So what is the meaning of 25%? 1 by 4.
And 1
by 4, I just explained to you, means we will have total 4
things, out of that only 1 thing
is being used.
So that will be 1 by 4.
Or we can say 1 fourth, means 1 part of 4.
of 4, we are using 1 part only.
So if we see it percentage wise, we are using 25%.
if we multiply 25% by 4, we will get 100.
Obviously. So if we see it this way, if 4
will go here, then 4 into 25, we should always get 100%.
Similarly, if you have 50%, 50%
will be known to everyone as half.
100% is 1.
What is 100%? 1.
50% will be 50 into 1
by 100.
That is half.
Means out of total 2 things, only 1 thing is being used.
We call
half as 50%.
Similarly, you can take out 75%.
What will 75% be? 75 into 1 by 100.
this will be 3 by 4.
So now the 3 by 4 diagram that I showed you, this is 3 by 4.
this means that 75% of the tiles are shaded.
75% of the tiles are colored.
Now how many
tiles are shaded? 75% of the tiles are shaded.
So 75% of the tiles are colored.
Now how many
tiles are shaded? How many tiles are colored? 25%. How is
25%? Because the total is 100%.
So how much all the remaining is left? 25%.
So this what you know.
It will be very easy
to convert percentage into fraction.
Divide by 100.
Nothing else.
Next, if I tell you
One small thing is that if you take out, let's understand
through a question, let's understand through a question
that, let me write its general form once, let me write the
general form once that if you, what will be the general
form?
General form, if you have any x percent, in which you have
to change it?
Then what will that be? x divided by 100, because x into 1
by 100, that is equal to x by 100.
So this is your general form to convert any percentage.
You can have any number x, if you have to take out its
percent, then divide it by 100, it will come in your
fraction term.
So next, what I was telling you with the help of question,
with the help of question, what is yours, that we have to
take out 25 percent of 20.
We have to take this out and one more thing, now
interchange it, 20 percent of 25.
These two things you have to take out.
Take it out, see what is it? 25 percent of 20, means we
have to take out 25 percent of 20.
And what is 25 percent?
One-fourth, so we have to tell one-fourth of 20.
What is the meaning of off in maths?
Off means into in maths.
So you do, 25 divided by 100, if you subtract the
percentage sign, into, off's into 20.
So solve this, so what will come?
One-fourth, and four-fifth.
This is your 5's equal.
Now solve this, 20 percent of 25, means 20, 20 percent of
what we have to take out, total we have 25, we have to tell
20 percent of it.
And what will be 20 percent?
See, it will be 1 by 5.
How? 20 percent will be subtracted by 100, off will be
subtracted by into, this is 25.
So cancel 0 from 0.
1, 5, 1, 5.
So by solving this also, what will come? 5's equal.
So both the things are equal.
And see in this question, what was the difference?
That both the numbers are interchanging.
Earlier we were taking out 25 percent of 20, or take out 20
percent of 25.
What is the meaning of both?
What will be the answer of both?
It will be equal.
The meaning is a little different.
That we are taking out 25 percent of 20, the meaning is
different.
But the answer that is coming, that would come the same.
So if we write in general, x percent of y will always be
equal to y percent of x.
This is called general.
So this second conversion, the second conversion that I am
telling you, that is, what did we do?
We did percentage to fraction.
Now its opposite, fraction to percentage.
For percentage, what did we do?
We did divide by 100.
Now we are doing the opposite of division.
What is the opposite of division? Multiply.
So earlier we were dividing by 100.
Now we will do with 100 percentage.
We will multiply.
Because what is the value of 1? 100 percent.
100 percent is equal to 1.
So if we take any fraction, suppose we have taken half,
then we can do half into 1. And instead of 1, put 100
percent.
So half into 100 percentage.
Not equal to, if we want to convert it into percentage.
This is not equal to.
When we are converting it into percentage.
So how much will half become?
It will become 50 percent.
If we solve, what will it be? 50 percent.
So what do we have to do with fraction in percentage?
If I take out a fraction of the numerator, it is less than
the denominator.
But if I do 5 by 4, then the numerator is greater than the
denominator.
So if I divide it, now I have to take out the numerator in
percentage, so if I do into handed percent, then 1s are 25
and 25 5s are 125 percent.
So if I take out the fraction in decimal, then it is
greater than 1.22 something, right?
So if I take out the numerator in percentage, then it is
greater than 1.
So we have 4 in total, but what we are required or what we
have been asked is 5.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
So if I take out the numerator in percentage, then it is
greater than 1.
Let the smaller number be a and the bigger number be b.
So, the difference between the two is obviously bigger
number minus smaller number.
So, b minus a, according to the question, b minus a, the
difference is 100.
Difference means the subtraction.
That you have is 100.
If 15%, then what is said further, 15% of smaller number.
Smaller number is a. 15% of a is equal to 10% of bigger
number, that is 10% of b.
Solve it. 15% of a, 15 by 100 into a is equal to 10 by 100
into b.
Cancel these two 100 from the bottom.
Then 10, 5 2's and 5 3's.
So, what is this? 3a is equal to 2b.
This is the relation.
And we have this relation of a.
So, from here, you take the value of a and keep it here.
Keep the value of b.
If we subtract b from here, what will be the value of b?
Your b will be a plus 100.
Because a is on the other side, minus.
Minus here and plus there.
So, if you put the value of b here, it will be equal to 2a
plus 100.
Whose value will be equal? 3a is equal.
Now, 3a is equal to 2a plus 100.
In the variable of a, our question has changed.
We can find out the value of that.
So, solve this. 2a plus 200.
2a will go here.
So, 3a minus 2a will be equal to a.
So, the value of a is 200.
Means, what was a?
We had a smaller number.
So, the value of smaller number is 200.
So, where will the value of bigger number come from?
Put the value of a in this equation.
b is equal to a plus 200.
So, the value of b is 300.
200 plus 100 is 300.
So, what will be the value of smaller number? 200.
And what will be the value of bigger number? 300.
Was the question easy?
Both the questions were easy.
And whatever we have learnt today, we will do more deep
down questions in the next video.
Till then, you revise and practice.
Thank you for watching the video.
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