ratio
proportion
percentage
proportion
percentage
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LearningTranscript
00:00Hello everyone. Welcome to Insightful Maths. In today's session, we are going to discuss
00:06an important topic of class 7. The name of the chapter is Comparing Quantities. This
00:12is the first introduction video of this chapter, wherein we are going to discuss these 3 topics.
00:19What is Ratio? What is Proportion? Percentage? What is the meaning of Percentage? How do
00:25we get the percentage of the 2 numbers or the output? Right? How to convert Fraction
00:32to Percentage, Percentage to Fraction? All these things will be covered in today's session.
00:38In the upcoming videos, we'll take these topics of this chapter ahead, which will include
00:44Profit, Loss, Percentage, Increase, Decrease, Percentage. Right? Simple Interest, Principle
00:51and all those important topics. So, please don't forget to like and subscribe the channel
00:57and please see the video till end. So, let's begin. So, as the name of the chapter is Comparing
01:03Quantities, it has 2 terms. Okay? First thing is Comparing and another thing is Quantities.
01:11Now, what is the meaning of Comparing? Jab hum 2 cheezon ko compare karte hain. Right?
01:17So, what do we actually do? We see which is greater or which is lesser or if the 2
01:24things are equal. In general, we do the comparison like this. Theek hai? That is the Comparing.
01:30Now, what is a Quantity? As the name of the chapter is saying Comparing Quantities. So,
01:36Quantity kya hota hai? Quantity is anything which can be assigned a number. Hain na? Hum
01:43number kis kis cheez ko de sakte hain? It can be your marks. Abhi aap log ka half yearly
01:48hoke chuka hai. You know very well that we are talking so much about numbers these days.
01:53So, it can be your marks. It can be the height of the students. Right? Height can also be
02:00assigned a number. It can be a weight that can also be assigned a number. It can be either
02:08the distance. It can be the volume. It can be anything that you can. It can be the population.
02:15Right? Population, prices of the things, the increase and decrease. So, all these things
02:21which can be assigned a number, they can be compared. Theek hai? So, that's how all these
02:27things will be dealt with in this chapter. Now, coming on to the first topic, what is
02:32a ratio? For example, first take an example to understand what is a ratio. If I say I
02:39have a class of let's say 20 students. Theek hai? This is the total number of students.
02:45Out of these students, if I say let's say 14 are boys. 14 are boys, then how many girls
02:53are there? If the total number of students are 20 and 14 are boys. So, girls kitna ho?
03:00The difference of 20 and 14, that is 6. Theek hai? Ab mujhe compare karna hai, that agar
03:07mujhe batana hai ki meri class mein kitne the boys to girls ka kya ratio hai. If I have
03:14to pair them up, let's say for an activity. To mujhe dekhna hai ki kitne ek group mein
03:19I have to put boys and I have to put girls. So, for that some comparison method has to
03:24be there. Ab aap samjho, if I say the ratio, the symbol of ratio is this colon. These two
03:32vertical dots colon, this is the symbol of ratio. I am comparing two numbers. Agar mujhe
03:39do number compare karna hai, that can be done using a ratio. So, boys ratio girls. First
03:47of all we have written boys, the number of boys 14, the number of girls 6. B ratio G
03:55or we read it as B is to G. Theek hai? Boys is to girl, it is 14 upon 6. Now, it has to
04:03be converted to the simplest form. 2 into 7 is 14 and 2 into 3 is 6. So, my answer is
04:11the ratio of boys to girls is 7 ratio 3. It is 7 ratio 3. That means for every 7 boys,
04:22we are having 3 girls. Agar mujhe ek group banana hai. Theek hai? So, for 7 boys I have
04:28to take and 3 girls in one group, another group 7 boys and 3 girls to be taken. Theek
04:34hai? That is the ratio. If the question would have been girls ratio boys, toh pehle mene
04:40girls likha 6 upon 14. Again 2 3s are 6, 2 7s are 14. My answer is just the reciprocal
04:49of previous one, that is 3 ratio 7. Ab dekho dekhne ne it is looking like a fraction. 7
04:56by 3, 3 by 7. It is not a fraction, although it looks like a fraction. Let us stick to
05:03the basic topic, the basic rule. What is a fraction? Fraction is the part of a whole.
05:10Theek hai? Agar hum girls ratio boys ko hum 3 by 7 pur rahe hai. So, does it mean out
05:17of 7 boys, 3 is girls? It doesn't make any sense. Hai na? 3 girls out of 7 boys. Iska
05:23kya matlab hai? It doesn't make any sense. Okay? So, this is not a whole. Is 7 the whole
05:29in this case? Yaha peh total number of students are 20. Right? For a fraction, denominator
05:35is always the total people. Right? And this is part of this whole. This 3 is separate.
05:42Yeh jo girls ka 3 number hai, yeh boys me se thodi na aaya hai. This is a separate thing.
05:47So, please do not confuse ratio with a fraction, although it looks like a fraction. Theek hai?
05:54Ab ratio agar mujhe 2 numbers compare karna hai, mujhe unka ratio nikalna hai. Theek hai?
06:00Aapko ek basic cheez yaad rakhni hai, both the numbers should be of the same kind. Agar
06:07main height ka ratios nikal rahi hoon, height can be compared with height only. If I am
06:14finding the ratio of weight, weight has to be compared with weight only. Theek hai?
06:20Let me take an example. If I say, what is the ratio of 1 meter to 1 centimeter? Theek
06:29hai? That's my question. What is the ratio of 1 meter to 1 centimeter? Humne dekha yaha
06:34bhi 1 hai, yaha bhi 1. We have written answer 1, ratio 1. That is incorrect. Right? Aap,
06:42you have to check the units. The unit is meter here and the unit is centimeter here. I said,
06:49both the numbers should be of the same kind. In this scenario, although the both of them
06:55are representing the length or the distance, but their units are different. Aap kisi ko
07:00kisi mein bhi convert kar lo, but the unit has to be same. It is advisable, convert bigger
07:07unit to the smaller one. It is an easier one. Agar aap choti ko bade mein convert karoge,
07:13it will be a decimal number. Your calculation will become difficult. Okay? So, what's the
07:18answer for this question? You have to write 1 meter is equal to 100 centimeter. Theek hai?
07:261 meter is 100 centimeter. So, rather than writing 1 meter, I can write 100 centimeter
07:33ratio 1 centimeter. Now, both have the same unit. So, it can be written as 100 ratio 1
07:41because we cannot simplify it further. Theek hai? Jab hum do numbers ko compare karte hain,
07:47that is a ratio. Right? Let us do one or two more examples for ratio and then we'll talk
07:54about the next topic, which is proportion. So, let us give first a quick recap. A ratio
08:00is a comparison of two values expressed as a question. That means, in the form of a fraction.
08:08I told you it is not a fraction. It just looks like a division. Example, we have already
08:15discussed. I'll give you another question. If let's say, get me the ratio of 1 milliliter
08:24to 5 liter. That's the question. Get me the ratio of 1 milliliter to 5 liter. Sabse pehle
08:33hum kya check karengi? Dono ka unit has to be same. This is milliliter and this is liter.
08:39Unit same nahi hai. Iske liye aapko comparison aur conversion aana before zaruri hai. You
08:45should know how to convert two units. We know that 1 liter is equal to 1000 milliliter.
08:54So, 5 liter should have, 1 ki value pata hai, 5 ka nikalna hai. It is just a multiplication
09:01that is 5000 milliliter. So, first number has become 1 milliliter. Second number is
09:095000 milliliter. We cannot simplify 1 and 5000 further. So, your answer is 1 ratio 5000
09:19milliliter. Another question. In a box, let's say I have a box which has three kind of balls.
09:30We have green balls which are 12 in number. We have red balls which are 8 in number. Then
09:40we have blue balls which is let's say 5 in number. My question is, what is the ratio
09:48of blue is to red? What is the ratio of green to total balls? Another is, what is the ratio
09:58of red to green? Right? That's the question. Now, ab aap dekho yeh number of balls hai.
10:06Hai na? Ball to ball hi hai. Ab humein kya karna hai? Question is asking us for the total
10:11number as well. So, we need to for total kitna ball hai? We need to count these three. Total
10:16these three. 12 plus 8, it is 20. 20 plus 5 is 25. So, total we have 25 balls. Let's
10:25take it further. This is now blue ratio red. Ab blue kitna hai? That is 5. Ratio, how many
10:34are red? 8. Can we simplify this further? 5 aur 8 ke beech mein koi bhi common factor
10:41hota hi nahi hai. We cannot simplify this further. That's the final answer here. Theek
10:46hai. Humein aur kuch nahi karna. But please make sure this ratio sign has to be there.
10:51Now, green ratio total. How many green? 12. Pehle 12 kyun liya? Because pehle green written
10:58hai. Uski paath, total. Total is 25. Is there any common factor between 12 and 25? It cannot
11:07be simplified further. Again, that's the final answer. 12 ratio 25. Last we have red ratio
11:15green. Red is 8 and green is 12. Ab aap dekho, these two numbers can be converted to a simplest
11:24form. Yeh dono 4 ke multiples hai. 4 2s are 8, 4 3s are 12. So, your answer is 2 ratio
11:323. Theek hai. Humein yeh sab mein kya kiya? We have done the comparison of the two numbers
11:39and both the numbers should be of the same category or should be having the same unit.
11:46Right? Now, continuation of this topic. Ratio, the basic thing we have understood. It is
11:52the comparison of two numbers and we use a colon symbol for the same. Now, what is a
11:59proportion? Proportion is an equation. Equation means wherein equal to sign is there. So,
12:06proportion is an equation which is the comparison between the two ratios. Jab hum do number
12:13ko compare karte hain, usse ratio se compare karte hain. Jab hum do ratios ko compare karte
12:19hain, usse hum bolte hain proportion and there is a symbol of proportion. Dekho, ratio ka
12:26symbol kya ka? Yeh colon. Humne do numbers ko compare kiya, to ratio aaya. Ab hum do
12:33ratios ko compare karenge, to yeh ratio wala symbol do baar aayega. This is the symbol
12:38of proportion. These colon repeated twice. Right? These four dots. This is the symbol
12:43of proportion. Ab iska matlab kya hai? Let's take an example once again. If I have two
12:50numbers, let's say 20, 40, then I have 40 and 8. Mere paas yeh chaar number hain. First,
12:59second, third and fourth. Beta ratio do numbers se banta hai. So, in do se first ratio banega,
13:05in do se second ratio banega. I need to know if these four numbers are in proportion. Ab
13:12iska kya matlab hai? If the ratio of first two numbers is equal to the ratio of next
13:19two numbers, we say that these four numbers are in proportion. Ji? Now, what is the ratio
13:27of 20 to 40? It is 20 upon 40. 20 ones are 20, 20 twos are 40. To first ratio kitna aaya?
13:361 is to 2. Second ratio is 40 divided by 80. 40 by 80 is again 1 by 2. Aap dekho dono
13:44side, left hand side, right hand side. The value of both the ratios is equal. Aisi ratio
13:51ki value equal hai, unhe hum equivalent ratios bhi kehte hai. To agar do ratios equal hai,
13:58to hum bolte hai those four numbers are in proportion. Ab aap dekho yaha bhi 1 is to
14:042 hai, yaha bhi 1 is to 2 hai. Simplest form dolo ka same hai na? So, how do we write?
14:10We say these four numbers are in proportion and there is a way of writing this. 20 is
14:17to 40. Pehle hum rikhenge 20. Ratio 40. First ratio is in proportion to second ratio. Hum
14:27ne pehle do number ka ratio nikala, symbol of ratio. Last two numbers ka bhi ratio nikala,
14:34symbol of ratio. Ye dono ratio equal hai, iska matlab they are in proportion. So, proportion
14:41symbol in between. Correct? Now, aap hum hi dekho ye check karna hai. For example, this
14:48is the question. Hum hi check karna hai, 2 by 3 ek ratio hai and 12 by 18 ek ratio. Hum
14:56hi check karna hai if this is in proportion or not. Hum ne abhi aapko bataya, four numbers
15:03proportion mein kab hote hain? When their simplest form is same. Abar dono ka ratio
15:08same hai, we say that it is in proportion. Ab this is ratio 1. Ye pehle se ye simplest
15:14form mein 2 ratio 3. We cannot simplify this further. Now, this is 12 by 18. 6 x 2 is
15:21a 12. 6 x 3 is a 18. Iski value bhi same aa rahi hai na? Ratio 2. Theek hai? Iska bhi
15:28simplest form is 2 ratio 3. Now, since ratio 1 is equal to ratio 2, we can say that these
15:37four numbers are in proportion. Hum answer kaise likhenge? 2 ratio 3, it is in proportion
15:45to 12 ratio 18. Ek hi baat hai. 2 is to 3 ya 12 is to 18 ek hi baat hai. Ab ye wali jo
15:54terms hoti hai na, first and the last one, inhe hum bolte hai extreme terms. Okay? These
16:02are known as extreme terms. Second and third, ye jo beech mein hoti hai, inhe hum bolte
16:09hai mean or the middle terms. Theek hai? At times, it is being asked in the question,
16:14which all are the extreme terms. So, first and fourth, last two terms, first and the
16:20fourth one, inhe hum extreme bolte hai. Jo middle mein hoti hai, unhe hum mean terms
16:25hoti hai. Ab ratio ka, ab proportion ka, ab dekho what is the usage. For example, you
16:32are making a recipe. Theek hai? Agar hum kam logon ke liye bana rahe hai, toh hum kaise
16:37bolte hai ki aap apne according, kam zyada kar sakte ho. Ab humein kya pata kitna kam
16:42zyada karna hai? Therein, this ratio is useful. Agar mujhe maan lo, three, let's say for
16:51in a recipe, A ke two parts dalne hote hain and ingredient B ke three parts dalne hote
16:57hain. Toh recipe banane ke liye, it is 2 is to 3, A is to B. Ab mujhe ye zyada logon ke
17:03liye banane hai na? Mujhe quantity ab jaana hai, ab zyada logon ke liye kaise change karu?
17:08Aapko sirf itna savajhna hai, two se, jaise ab doosra number banaoge na, like we make
17:14equivalent fractions, the same concept will go. Agar main upar six se multiply kar rahe
17:20hoon, neeche bhi six se multiply hoga. It will be 12 by 18. Ista matlab, agar aap B
17:26ke 18 parts le rahe hoon, aapko A ke 12 parts lene padege. In the similar manner, agar mujhe
17:32aur zyada banane hai, 2 into 10, 3 into 10. Ista matlab, 20 by 30. Again, this is 2 by
17:403 only. Agar aap B ka 30 parts le rahe hoon, aapko A ka 20 parts lena padega. Theek hai?
17:47So, this is used for decision making and again the comparison of two ratios. I hope this
17:54much is understood. Now, let's move on to the topic which is percent. Percent aapko
18:01bhi, you also want to find the percentage of your marks, aapka score kitna hai na? Let
18:06us understand what is the meaning of this word percentage. Per cent, ki jo cent hota
18:12hai na? Cent ka matlab hota hai hundred. Percent means per hundred, out of hundred.
18:18Hai na? Agar mere paas, aap ye dekho, zero percent. The symbol of percent is like this.
18:25Ye percentage ka symbol hota hai. Agar hundred me se, kisi ke paas zero hai. That is zero
18:32percent. Percent means per hundred. Out of hundred, kitna hai? Is fraction me, jiska
18:39denominator hundred hota hai. Numerator ki jo bhi value hai, that is your percentage.
18:46Yaha pe dekho, 25 out of hundred is 25 percent, 50 out of hundred is 50 percent and 100 out
18:53of hundred is 100 percent. Theek hai? So, percent means per hundred. Aap kuch fraction
19:00hota hai, jinka denominator hundred nahi hota. Phir kaise karein? So, rule one, either
19:07you can convert the denominator to hundred. Theek hai? Let's take an example. For example,
19:13I have a fraction 1 by 2. Mujhe jaana hai, 1 out of 2 is what percent? Percent humein
19:19pata hai, per hundred. Denominator required is hundred. We can easily convert 2 to hundred
19:26using the concept of equivalent fraction. Right? Numerator and denominator has to be
19:32multiplied by the same number. Aap 2 ko hundred kaise banate hain? Multiply it by 50. Similarly,
19:391 has to be multiplied by 50. 1 into 50, that is 50 and 2 into 50 is 100. Dekho, easily
19:48this is converted to a percent. Agar mujhe 50 mila out of hundred, that is 50 percent.
19:55Easy enough? Let's do another example. If I am talking about 4 out of 5. Theek hai?
20:02It 5 marks ka test tha. Mujhe usme se 4 mila hai. I need to know what is my percentage
20:09score. Denominator required is hundred once again. Aap 5 ko hundred kaise banaye? If
20:15I multiply numerator and denominator by 20. 4 into 20, that is 80 and 5 into 20 is 100.
20:26Kitna score kiya aapne? 80 on 100 means it is 80 percent simple. Correct? Ab yeh toh
20:34baat hui, jin denominator ko aap hundred mein convert kar sakte hoon. But there are numbers
20:41which cannot be converted to hundred. Jinka multiple hundred nahi hota. Us case mein
20:47hum kya kare? Ab ab dekho, jab hum percent ki baat karte hain na, humein denominator
20:53100 chahiye. Itni baat theek? Now, if I have, main dekho isi fraction ko aapko karke
20:59bata. Humein pata hai iska answer 80 percent aata hai aur 500 mein convert bhi ho jata
21:06hai. Aap ek basic se cheez samjho, agar aapki paas koi bhi fraction hai. Let's take 4
21:13by 5 only. Kisi bhi fraction ko multiply by 100 and put a percentage sign. Theek hai?
21:22Any fraction multiplied by 100 and putting a percentage sign, it will be converted to
21:28percentage. Let's first recheck the answer. I'll explain you how is it being done. 100
21:34divided by 5, it is 20. And 4 into 20, answer is 80. And we are having a percentage sign.
21:42Dekho, the same answer. Yaha bhi 80 percent aaya tha. Jab humne denominator ko 100 bataya,
21:48this is also giving me the same answer. Ye aisa hota kyu hai? Jab humne liya 4 by 5,
21:54humne kiya 100 up and 100 down. Beta, percentage ye jo symbol hota hai na, iska matlab hota
22:02hai denominator 100. Jab humne denominator 100 hata dete hai na, aap dekho ye percentage
22:08sign ban jata hai. Theek hai? Aap mujhe agar iska percentage banana tha, toh humne up
22:14and niche 100 se multiply kiya, ye wala jo niche wala 100 hai na, I am not going to use
22:20it. This will be used for writing the percentage symbol. Toh humne isko hataya, now we have
22:27got the percentage symbol. Aap jo bhi aapke paas bacha hai, you just need to solve it
22:33and that will be your percentage. So 100 divided by 5 is 20 and 4 into 20, your answer is 80
22:41percent. Right? Let's take one more example. If I have 1 out of 5, I know, I mean I need
22:49to know 1 out of 5 is what percent? CDC bar, fraction, multiply it by 100 and put a percentage
22:57sign. Now 100 divided by 5, it's what? It is 20 and 1 into 20 is 20 percent. That's
23:06your answer? Alright, now what you are supposed to do, your answer is required now to check
23:15your understanding, how much have you understood? I am giving you a fraction 3 by 4, you need
23:21to convert it to percentage. Theek hai? Percentage mein convert karo and please put the comment
23:28what is the answer in the percentage. Right? So this is all for today.