This video teaches strategic methods for calculating percentages by transforming numbers to use known percentage-fraction relationships. The key techniques include: (1) Converting percentages to fractions (e.g., 37.5% = 3/8, 87.5% = 7/8), (2) Using the property that 'a% of b equals b% of a' to simplify calculations, (3) Scaling numbers by dividing or multiplying both the percentage and base number by the same factor (e.g., dividing by 10 and multiplying by 10) to transform unfamiliar percentages into familiar ones, and (4) Applying the butterfly method for multiplication. These techniques allow students to solve percentage problems efficiently without relying solely on memorization.
Deep Dive
Prerequisite Knowledge
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Deep Dive
PERCENTAGE CALCULATIONAdded:
Yeah. So this calculation if you observe 4.8 percentage of 625 we know percentage value 62.5 percentage.
So I can make this number 62.5%. What I have to do to make it 62.5%? Can you tell once again?
Yes. You have to do divid by 10. So if you do divided by 10 you can multiply other side um what what you have to multiply you have to multiply by 10.
Yes.
So if you multip you if you do division by 10 here you have to multiply by 10 this side then it becomes 48 percentage of 625 I mean 62.5.
So we have one property a percentage of b is equal to b percentage of a then this number I can write it 62.5 percentage of 48 then it will be 5 by 8 5 by 8 of 48 so this we can do faster easily or can you tell what how to do this?
>> Yes sir. Um so 12 by 8 is uh 1x8 percentage we will um >> yes 12 >> yeah 1x 8 into 288 >> correct 1x8 into 288 because directly we know 12.5 percentage here no need to conversion see if you don't have mean whatever I give list in percentage table if you don't have any number in that list then I try to modify the numbers is it here.
>> Yes sir.
>> Okay. This is okay. Now this see actually if you know this value we can do one two methods I will teach you. One method 18.75 actually I'm not giving list but little bit changes 1x 16. Can you tell 1x6 value in percentage table?
>> 6.25.
>> Very good. 6.25 percentage. Then if you multiply into three it will be 18.75.
>> Yes sir.
>> Then it will be 3x 60. Clear.
>> Yes sir.
>> But the problem is we can't recognize which table it is 18.75. We don't know.
I mean this is okay. I just I teach you that's why you understand. But how to do faster way means uh we can't recognize actually 18.75 we can't recall it then how to do it I will teach you another approach so if you remember I taught one method suppose 32 into 15 how to multiply how you multiply tell me 32 into 15 how you multiply basically So the we keep it like 32 and then 15 below and then we do cross multiplication.
>> Okay. Butterfly method. Yes, you can do that. Can you do because we know 15 1 means method 2 30 + 2 also.
>> Yes sir.
>> 15 into 30 + 15 into 2 that is 450 + 30 480.
Correct?
>> Yes. Yes. one more method. Okay, just before that I will I will ask one more question. Uh suppose this is okay.
Suppose 45 into suppose 18 if I want to multiply can you tell answer without pen and paper.
Okay time up. I will give one more number. Can you tell 90 into 9? Answer 90 into 9 99 99 is >> sir 810 >> 810 see here you can tell faster way right >> yes sir >> here also answer same 8 10 that what I'm doing just into 2 / 2 I'm just I change it into 2ID by 2 is it clear so previously previously we are multiplying divid 10 into 10 correct?
>> Yes.
>> In this example, same method. No, no need to multiply only 10. We can do 2, three, whatever we need. So just I do into 2I by 2. If I do into two, it become 90. If I do 18 by 2, it will be 9. So 90. I hope you understood this. Is it clear?
>> Yes sir, I understood.
>> Okay. Now, same approach here. I can obtain 18.75 of 3 640 I don't know 18.75 percentage but luckily I have five see whenever in percentage if you get it five you can try to change to zero to make it zero can I multiply into 2 by 2 >> yes sir >> now if you do it it will be 37.5 correct 18 double 36 6 75 double it will be 1.5 it is 80 37.5 but luckily we know 37.5% what is 37.5% fraction value >> 3x 8 >> yes it will be 3x 8 3x 8 of 320 see this is easily we can calculate so instead of this I change to this is it clear >> yes sir >> just now Okay, this you already know how to calculate. Can you tell how we will calculate this?
Since 3x which one sir? Yeah, this fourth one >> 37 3 by 8 into um no no 1 by 3x 8 into 248 >> correct how you will calculate this >> uh 5 by 8 into 4 32 >> correct yeah this I will teach you okay sixth one see now sixth one can you what I can change this number 1250 if you observe what I can do it What I can change?
What you know from this number? 1 1250.
Can you guess? Can I make this number 12.5?
>> Yes sir. 12.5.
>> Yeah. To make it 12.5 what I have to do here I have 2.4 percentage of 1250. to make it uh 12.5 what I have to do which number I have to do division >> sir um 100 >> yes it is 100 because we have to keep it two points if you do division by 100 can I multiply here by 100 >> yes >> it is now percentage I will move it this side because a b is equal to b% of a now it is 12.5% of two mean 24 mean 24 into I mean 2.4 into 240 that is 1 by8 of 240. Is it clear?
>> Yes sir. Understood.
>> Yes. Now now here also just I will change it. Okay. I hope you understood what you can make this number this number if you observe what you can make it here 1.25 what you can change >> uh 12.5.
>> Yes. So you have 1.25 25 to make it 12.5 what you have to do here >> 12 into 10 >> very good we have to multiply by into 10 if you multiply into 10 it will move this side if you do multiplication into 10 here you have to do divid by 10 you understood right >> yes it will become 640 >> yes then it will become 1 by 8 of 640 I hope you understood this.
>> Yes, you understood.
>> Yeah.
So, this already we know how to calculate 87.5 plus of 144. So, what is the fraction value of 18 87.5?
>> So, 7 by 8.
>> Yes. 7 by 8. So 87.5 is 7 by 8 of 144 that you can know you got 162x3 or 16.66 both are same how to calculate 16.66 or 162x3 percentage >> sir I can't hear you >> okay is it is it why is not clear now I can hear >> okay what is 16.66% 66 percentage fraction value or 16 2x3 both are same >> 1x 6 >> very good so this is 1x 6 of 540 I can do this is also we know 33.33 how you will calculate >> 1x3 >> good 1x3 yeah this is yeah it is important how based on your what you know what you will change 7.2 into percentage of 250 what you can make it can you guess here if you observe because this number we have in our table means small modification >> yes 1 by 4 you have to divide it by 10 >> yes very good so we can make it 25% correct >> 25% yes >> to we can make it 25% means divid by 10 if you do divid by 10 can I multiply into 10 >> yes sir >> then it will be 1x4 of 72 correct?
>> Yes sir.
>> Then 4 1's are 4 18.
So your answer will be that I hope you understood this. Next. Yeah. What? Yeah.
What you can make it because we discussed many times this 5.6 percentage of 1250. What you make? What you can make it 1250?
>> So 1250 we can make it 12.5.
>> Very good. So we'll divide by 100 and multiply there by 100.
>> Very good. Divided by 100 and multiplied by 100.
Then it is 1x 8 of 560. Correct?
>> Yes sir.
>> 1x 8 of 560.
Good.
Next.
Yeah. Can you tell what? Okay. This this you know this you know 1x7 but 22.5 we don't have in our table correct in our percentage table we don't have 22.5 percentage but yeah we can make it one more 225 percentage I can make it if I want can I make it 225 percentage >> sir what >> can I make this number 225 percentage >> uh yes sir >> to to method one if I make it 225 percentage can I multiply into 10 >> here by this >> 225 percentage means 225 divided by 125 95 4 Z that is method one of 16 this is method one is it clear method one you're not getting >> yes sir but no I did not understand >> okay just See this number we we don't have in our table like 22.5 related number I don't have understood this this question this number in our table in our table I don't have like in percentage table related to this I don't have any number clear >> yes understood >> now I can do instead of 22.5 225 percentage of 16 correct Yes sir, we can.
>> Yes, that is one way. Another way, can I rate it into two divid by two also?
>> Yes sir.
>> That become 45% of 80. Still I have five. Can I make it again into 2ID by 2 again? That will be 90% of 40. I hope you understood now.
9 4 36 9 4 are 36 easily I can calculate okay this already we know 6.25% is 1x 16 correct >> yes sir >> but how you will do this yeah you tell you only tell this 3.2 into percentage of 625. How you'll do? Because we have related this number. Can you tell how we'll do?
>> Uh yes sir, we we'll try to make it 62.5.
>> Very good. To make we can make it uh 6.
>> So we divide by 10.
>> Exactly. If you do by 10 multiply by 10.
>> Exactly. So we can do by 10 and multiply by 10 then it will be 5 by 8. Correct?
5 by 8 of >> 32 >> 32 This is the way we have to solve it.
Is it clear?
>> Yes sir.
>> Even can you tell what you you can do here? Let's see.
>> Uh yes sir. We'll try to make it 25%. So we'll divide by 100.
>> Very good. Divid by 100 into 100.
Correct.
>> And then multiply by 100. Yes.
>> Exactly. Exactly. See here we don't have number. This number we don't have. So this number we don't have in our table because 28 related events 175 related we don't have. But can I do into 2ID by two?
>> Yes sir.
>> Where I have to do into two. Wherever you have five there you do into two.
>> Into two.
>> Yeah. Here I do divid by two because I need to change five to zero. That's why wherever you have five you do multiplication by two divid by two. Then can I write this number is 350 this is 14 correct?
>> Yes sir.
>> Again I have five. Can I make it again into 2ID by 2 means it will be 700. It will be 7%.
>> Yes sir.
>> Now easily can calculate 7 7th of 49.
Clear?
>> Yes sir.
>> Yes.
What you will do here? Can you tell?
0.8%. and 8% of 6250 I will do.
>> So now we'll try to make it 62.5. So we'll divide by 100 and multiply by 100.
>> Correct? Very good. But this number we don't have in our table. Then I do into 2ID by 2. Correct? Because I have five in my questions. Most of the numbers are like this 9.375 percentage of 320.
So you do if you do into 2 year it will be 18.75 percentage of 160.
Still if you don't know 18.75 can I do into two again divid by 2 that will be 37.5 percentage of 80. So this we know I think 37.5 percentage is 8.
>> Yes sir we know. I hope you understood now how you how to calculate.
>> Yes sir.
>> Okay fine.
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