All right guys, it's time. I hope you are doing well. Even we don't have too much to do, that's totally fine. We can just continue here. I believe since it's recorded, you are checking. I mean, if you couldn't join, you are taking those recordings at home later on, hopefully. And I hope it's available and it's helpful for you anyway. So today we're gonna talk about percents and percent problem, how percent works. Before we do that, I have warmup question for you. Please check that really quick. If you get some sort of answer, or even if you get some sort of methods to how to start, some sort of ways to work with those type of questions, just share with us, please. Then we'll go from there. Let's start timer. Well, it has been 40 seconds. And it has been one minute guys, do you have any answer? If you do, please share with us in the chat, then we can go from there. If the length and the width of the rectangle were increased by 10% each, then the area of that rectangle would increase by what, 10, 20, 21, 100 or 121%? What do you think is going on here? We have just one friend join us, so maybe that person would like to work a little bit. Alright, I'm going to wait a little bit more so maybe I can get something in the chat. Remember, I don't necessarily want you guys to give us the answer, even if you give us how to start, so give us some hints maybe that works for our friends. We got one person who said C. Oh, they all want to say something to you, okay. We have C, anyone else? Anyone says A, B, D or E, come on. I believe some of you will keep updating me. So far, only one of our friends says 21, let's see. Look, regularly guys, if you would like to use algebraic weights, since it's a geometric question, I would still create some sort of rectangle and put side lengths as X and Y, let's see. Again, if you want to use algebraic weights. So, this is the length and width, then the rectangle would increase by 10% each. Well, for the first case, area is going to be XY, am I right? You just multiply length and width. For the second case, it says they were those length and width, X and Y, both increased by 10% each. Well, if you increase by 10% each, guys, 10% of X means we should have X times 10%, which is, well, 1X and 0.1, basically 0.1X. But they said they increased by 10%. At the end, I'm going to put 0.1X plus X gives us 1.1X. If we use the same method for Y, you will get 1.1Y as a new width. So, we get 1.1X and we have 1.1Y. At the end, when I just look for the area of the second case, I would say 1.1 times 1.1 times X times Y, it's going to give us 1.21XY. When you compare 1.21XY and XY, you will get 1.21 only. But as you see, guys, they say the area increased by, yes, I know when you do 1.21XY over XY, you should get 1.21, which is 1.21% here, should be E. But they said increase increment amount. Then you got to do 1.21% minus 100%. 1.21 minus 100% gives us 0.21, which is 21%. But here is the question, guys. Since this is algebraic way when we use X and Y, do we really need to use this way? I mean, to be honest, I don't think so. You don't have to use only this way. Look, let me tell you what I meant. We know that this is a geometric question. Yeah, let's just create some sort of rectangle. Even you can make it square because we all know that square is also special rectangle anyway. So can I say length and width are 10 units? Yeah, why not? It doesn't tell us it's different. The side lengths are different. If I do 10 and 10, guys, then I can say area is equal to 100. We just multiply that. In second case, you are going to increase those sides by 10%. Well, let's just do that. We both know that 10% of 10 is or 0.1 times 10 is just 1. When you increase, you get 11. With the same logic, length and width, they both 11. And area is 1.21. Then you multiply 11, 11, 11. Well, as you see, you got to compare 1.21 and 100. Let's just do that. 400 gives us 1.21. But this is the final amount. To be able to find increment, you got to do 1.21 minus 100%, which is just 1. You get 21. It represents 21% length. All right, class, any questions for that one? What do you think? Again, either first one or second method might be easier to you. I don't know. I'm not saying one way is better than another. Whichever method is easiest to you, that method is best for you. No worries. I believe we are good. So I don't see anyone asking questions. Am I right? I'm going to move on. Let's move on. Okay, thanks so much. All right, guys. You know this is our fourth week. And we are going to work about and talk about percent today. So four steps. Please make sure you understand the problem, plan how to solve them. Carry out your plan. Do some sort of algebraic ways, tables. And whatever best method works for you, you can just draw a shape. Also, like I just did before, look back and check and reflect. Make sure your answer makes sense. Or your way makes sense how to solve it. Okay, percent means for each 100, percent symbol is here. You know, x and that percent. Which also means x over 100. For 30% or 30 over 100, 30 is the part and 100 is the whole. 100% represents basically part over whole or percent. Even percent number divided by 100. Percent fraction and decimal are different for us to represent a number. And they are interchangeable. That means they all here represent the same thing. 123% is equal to 1.23 is also equal to 123 over 100. They all equal as you see. 100% means a whole, you know. You will basically multiply those percent and the number. You know, 30% here in that case is equal to 30 over 100. Then you got to multiply by 50. Or as you know, guys, 30% of 50 is equal to also 50% of 30. It's the same thing because you can just swap them. It's one of the properties of the multiplication and division. I'm going to move on. Percent of increase or decrease, how do you find that? Remember, new value minus original value divided by original value. For the previous question, remember, the original value was 100%. That's the reason I just take out 100% from 121%. Then we just get the 121 at the end. So when you solve a percent problem, you need to know the percent of what number they are asking. Percent more or less, basically. 20% more than 40 means adding 20% of 40 to 40. Remember, first you got to find 20% of 40. Then you will add that amount to 40 to be able to find 20% more than 40. As you see, the number at the end you find should be greater than 40 because you have 20% more than 40. Or with the same case, 20% less than 40 means subtracting 20% of 40 from 40 or basically finding 80% of 40 When you do 100% minus 20%, it also gives us 80%, guys. That means you can use these two. Or any question for this one, guys? You can raise your hand. I mean, I cannot see if you raise your hand, but you can just ask in the chat. Then we can check that. If there is anything, I believe Sohan is going to just let me know. There is nothing, I believe. Thanks so much. That means we are good. Okay, this is what you said. No question means you got everything. This is your responsibility. And the question here just for you. Number one from 2006. Number 13. Let's see what we are going to get here, guys. I'm going to start timeout shortly. Then we discuss. Remember, I don't necessarily want you to give us answer. Even you give us some sort of starting point, that works too. Thank you. Bye-bye. Bye-bye. Bye. Thank you. and it is one minute well well well so do we get some answers or not yet we got one for d we have only one answer and our friend says it should be d anyone else Okay, guys, I believe we have no one else and I'm going to start solving it, all right. Let's see if it is D or not. As you see here, we have Mark, Matthew and Peter, we're saving the money to buy a tent, okay. We have three friends or whatever, maybe family members. They are putting some money to buy a tent, as you see. In that case, guys, I will kind of create a chart. This is Mark, this is Matthew and this is Peter. Mark had 60% of the total money. He gave a lot of money for the tent, as you see. And Matthew gave 40% of the remaining, look, guys, this is the important part. As you see, if they said Matthew gave 40% of the amount, not the remaining, they would Mark and Matthew already 100% and Peter wouldn't give us anything. But since Matthew gave 40% of the remaining, it's going to be a different amount. First of all, the remaining amount after 60% is, we have 100% minus 60%, give us 40%, as you see. This is the remaining amount, which is 40%. But as we see that Matthew gave 40% of the 40%, well, remember, finding percent of a number, guys, basically, you will multiply percent by a number. You got to do the same thing here. Finding percent of percent means you will multiply that percent by another percent. So 40% times 40%, look, I don't really know if you just directly multiply or don't, but I recommend you to just simplify first if it's possible. We have two zeros at the top and two zeros at the bottom, give us nothing at the bottom here, at least four times four is 16, over, we have just 100. That means, guys, you get 16%, as you see. So here is the tricky part. You know that Matthew didn't give 40%, Matthew gave at least, I mean, actually 16%. And they say Peter gave 30% to complete. That means, guys, Peter gave the rest. Well, the question we have, Mark gave 60%, let me just write it here. We are going to find the amount of percent Peter is supposed to contribute. So we know Mark gives 60%, and Matthew is 16%, and the rest is for Peter. At the end, we have 100% minus this one is 76%, as you see, gives us, I'm not sure, 24%, I guess. All right. So 24% of total is the amount of money Peter is supposed to give, which is $30. Or I can say in parameters, this is 24%. Well, well, well, if this is the case, you know how they find 30%. 24% times total amount, which is x, gives us 30%. Then you would solve this. 24% means 0.24. If you divide both sides by 0.24, you would get something. I don't know what's that. I will just use my calculator, you know. So 30 divided by 0.24 gives us 125, guys. The total amount they need to pay for tent is 125. Any question about this, guys? okay that means you got everything you understood everything am i right if someone asks a question something like that in that form you can solve it easily look even it's Sunday you are coming here to you know hang with us solve the questions together that means a lot guys and I hope you're gonna do you're gonna get great results on your math congrats that's it all right I will clear everything then then you go to the next one here is my another gift for you number two from 2019 question number 15 please check this one and share your answer with us let's start the timer first 10 seconds You got one answer for C. Okay, one answer for C. Look at that. Alright. Anyone else? I believe not yet, guys. It has been... 1 minute and 16 seconds. I believe it's enough, you know. Okay, Jane is playing basketball. Okay. So, whoever says C, let's just keep pushing you. Whoever says C, what should be the first step, guys? Or others as well. How am I supposed to start with that question? Please tell me what operation I need to start with. so long do we have anyone give us first step should be something by 55% of 20 okay 5% of 10 okay in a series of 20 shots Jane's course first 5% of time yeah let's just do that if it's 5% of 20 means guys we get just gonna multiply those you know it's 5% of 20 equals again we can justify with some of you know those zeros it's 5 times 10 to I mean 5 times 2 should be 110 by 10 is 11 as you see guys that person Jane had 11 shots out of 20 I mean 11 scores anyway after 5 more shot her score increased to 56 remember at the beginning she had total 20 and you add 5 more well it's gonna be 25 so on how many of the last 5 shots did she score well if we have X amount of out of 25 she gets score the result should be 56% as you see this is guys how you create proportion hold right by I mean part of a whole is equal to person or whatever but still part of a whole so let's just do some cross multiplication you can do that to remember to be able to find that or you know what we both know that hundred divide by four is 25 let's just try it 55 56 by 4 to get X basically because that relation works for between numerators and denominators in the same way well 6 divided by 4 should be 14 it gives us X equals 14 X X is 14 but you gotta ask but sir there is no 14 is an answer I know I know so here is the deal she start with 55% which mean which meant she get 11 of those shots made so what we are looking for 14 score so 14 minus 11 gives us three guys class doesn't make sense if you want to say yes please type Y in the chat box if it doesn't make sense at all please type N in the chat box and we can move on people understand all right thanks so much but I'm not gonna feel like crazy okay number three all right check this one please First 17 seconds. 44 seconds We got one answer for D. Yes, someone says D. What about others? Okay, it's right now it's one minute, please tell me how should I start this you don't necessarily find the answer yet What is the first step I am supposed to start Add 85 and 75? Okay, let's just do that. What's next? I believe they said just numbers, not percent. They're saying add 85 and 75 and then subtract 100 to get the answer. So... My great handwriting. So guys, here is the deal. It says 60 and you can say yeah, that's 60%. But the question is, why do you add those numbers and why do you subtract 100? Let's say something guys, chat something, I mean type something in the chat box. I don't want to study with the screen, you know, or teach to the computer screen here. I want to teach to you. It's about communication guys, interaction. You cannot just learn a lot if you only watch that. And you can try, you can just watch a lot of YouTube videos, if it's gonna help, I don't know. If you just watch. You still need interaction and you still need some practice. So the reason the student did 85 plus 75 minus 100 is because the max you can have is 100%. Okay, that works. Thanks so much guys. So I believe what you meant guys, we will just add total numbers to find, I mean total numbers to get a certain number for that in that country. And they say 70% speak English, but we both know that someone in that 75% speak both of languages. It's same thing, oh my bad, it says 85% speak English, oh my bad, with same logic, 85% talk English, I mean speak English, but some of them speak both of those languages, but we don't know that, like that's number of percent who has, who can speak both of those languages. Since you add that, that extra 60% represents guys, you add some people, you count some people twice. Since they can speak both languages, you count those people, then you have English speakers and then you have French speakers, that's the reason you get extra, then you're gonna take out that extra from 100 to get the answer. So guys, if you want, we can use Venn diagram, something like that, let's see this English speakers and this is French, French speakers, at the end, look, we know that 85% can speak English, this 85% is English, that means that little tiny piece represents people who are only speak French, which is 15%, I believe you all figured out that 100 minus 85 is 50. Same logic guys, if I focus, oh what's wrong, if I focus here guys, they say 75% can speak French, if you cover only, if you cover French part and you take out 100, if you take out 75 from 100, you get 25% represents only English speakers, as you see, well, at the end, of course, we got to have 100%, 25% plus 15% plus x% gives us 100, you know, x is 100%, that means guys, if you do the calculation, you will see 60% is equal to x, which method is easier for you, first method or second method, I'm not asking a question, I just don't know that, but please follow whichever is easier to you, okay, any question for that, number 3, so can I continue or should I wait, let's move on, alright, number 4 from 2003 and question number 20, I really wonder who is going to give us the first step for that question, not necessarily the answer. What is the first step guys? Can we get anyone with some answer? So guys, you are saying no one figured out how to start this question? Is that it? Got nothing in the chat. Wow. Okay. At least you would guess. Or I assume that you are thinking, guys. So here is the deal. They say fresh mushroom contains 90% of volume. OK. That means any amount of fresh mushroom contains 10% of the solid part. Let's just say mushroom meat, maybe. It says, how many kilograms of fresh mushrooms are needed in order to make 1 kilogram dried mushroom contain 11% of water? From that percent in the first sentence, we can say that 1 kilogram dried mushroom contains, as you see, we have 10.1 kilogram mushroom meat. Am I right, guys? And meat. Also, they say, we are looking for 1 kilogram dried mushroom contains 11% of water. Well, we know that 11% of 1 kilogram is 11% times 1, which is, again, 11%, which is 0.11, guys. So that amount is water, but we don't need that water. We need the other piece, which is 1 minus 0.11. Gives us 0.89, as you see. 0.89 mushroom meat. That part includes. Well, do you think we can just have a proportion if we have that ratio, 0.1, to be able to have 0.1 kilogram mushroom meat, we need to have 1 kilogram. Well, 0.1 over 1 is equal to, we don't know how many fresh mushroom we need, the total x, to be able to have 0.89 mushroom meat. If you kind of do, someone says butterflies, someone says cross-multiplication, whatever works for you guys, we get x times 0.1 or 0.1x is equal to 0.89 times 1, just 0.89. You're going to divide both sides by. to get only x equals 8.9 years. Does that make sense, class? You need 8.9 kilogram fresh mushroom to be able to get one kilogram dry mushrooms containing 11 percent of water. Do we have any questions, Soran? Is there anything not clear? Are we good? Can I continue? No. Okay. Guys, I assume that if you have questions, you should ask already, I mean, you're not shy, am I right? I mean, no one is going to know it's you. It's fine. We cannot even tell your name. You are good. I mean, if you have questions, just ask, yeah, you know. All right. And number five, it's from 2014, question number 20, it's for you guys. Let's see. Okay. Please give us the first step to solve. I'm going to start timer as well. All right guys, it's been 1 minute 15 seconds. I hope we have some friends tell us how to start. Remember, I'll ask you the answer. So, do we have some answers? No, I mean, guys, remember, can you just type to the chat box how you start to solve this problem. Somebody answered C. I didn't ask about the answer yet, but I mean, thanks to you, brother. Remember, how do you start? This is my question. What is going to be the first step here? All right guys, I believe no one has answered about how to start. All right. So we have two average, the average of two positive numbers is 30% less than one of them. Okay. By what percent is average greater than the other number? So look, finding average means you got to add those two positive numbers, remember, then divide by two. This is what we know that. So let's say, since we are talking about percent, I would say, let's just say we have 10x and 10y. Okay. These are two numbers. Finding average means guys, we should do 10x plus 10y divided by two. That results is equal to, they say, 30 less than 30% less than one of them. Well, let's say we keep x as a first number. 30% less than 10x means basically we know that 30% of 10 is three. And when you take out three, you get seven. So we get 7x here as you see guys. After we create that equation, we can just solve it by canceling two first, because this is a fraction. We have 10x plus 10y is equal to 14x as you see. When you take out x's, we get 10y is equal to 4x as you see. I hope we are good so far. And they say, you know, 10y is equal to 4x, that 4x is second number. Second number is equal to 4 times x, not necessarily 10x, you know, anyway. So they say what, by what percentage is the average greater than the other number? So the average is 7x. And second number is 4x. Well, what do you do? Remember, you got to find the difference. Finding percent difference means first amount minus final amount over final amount gives us 3x over 4x. Or you can say basically, what was that 3 over 4 if you just do the division guys? Yeah, 3 over 4. When you do 3 over 4, to be able to find the percent guys, you just multiply this number by 100. So 3 over 4 times 100 gives us 75. That means we have 75% guys. It was not 30%. I don't know who said 30% but it was actually 75%. Okay. The question I have for you here is, does that make sense or not really? I choose 10x and 10y specifically to be able to help you to get easier, get easily. Any question about number 5? No? Solon, do we have any question? Oh, someone was asking on when we subtract 14x and 10x, we get 4x. The x doesn't cancel. Which part? So they were asking if the x cancels when we do 14x minus 10x. So remember guys, we do not do division here. I mean, only division kind of get rid of those x's. Still, we are talking about x terms. Think about if they were canceling, if I do 14x minus 10x, give us only 4. In that case, I will ask you, you are saying that 10x plus 4 is equal to 14x. Does it make sense to you guys? Remember, since I can have only 10 plus 4 gives us 14 if you ignore x's. But if you have 10x and 4, you cannot add them. Remember, because these are not like terms. I mean, think about if you have 10 apples and 4 apples, you can add them. But if you have 10 apples and 4 oranges, you cannot add them because these are different terms. I am not talking about the quantities. I am talking about the term as well. Apple and orange, they are totally different things. So you cannot just add them. You can combine them. As a group, you can say 10x plus 4, but you cannot say total 14. I mean, when I add 10 apples and 4 oranges, I cannot say 14 apples or 14 oranges. Still, I have 14 fruits, but still I have 10 apples and 4 oranges. Does it make sense? Or not at all? Or you have no idea what I am talking about? Say something. Or chat with Soham. He is going to chat with us. I cannot necessarily chat with you. More questions, Soham? Are we good? I am going to move on. Are we good? Because I couldn't hear you. So we can move on. All right. I am making your life easier, not necessarily confuse you. Okay, if it lets me, I'm going to click number 6. All right. Check number 6 from 2021, question number 21. Nice. Just a couple of years ago, they asked this question. I haven't start timer but I will, it's not necessary right now. Remember guys, I'm looking only for the first step, please guide me with the first step. How should I start? What am I supposed to do? Okay guys, any of you, can you give us the first step please? What do you do when you try to solve this question? What was your first step guys? Oh, we've got some answers for C. Okay, we get C, I guess. All right. Let's see, guys. So in a particular fraction, the numerator and denominator are both positive. Look, guys, this is in a particular fraction. And since it's about percent, can I say my fraction is 10 over 10? Look, as you see, they didn't say numerator and denominator are supposed to be different or whatever. So I can just keep that. And these are both positive, yes. The numerator of this fraction increased by 40%. We both know that 40% of 10 is 4. Since it increased, 4 plus 10 is 14. So second case, I am making this fraction 14 over something. Remember, I didn't put the denominator yet. Because by what percentage should its denominator decrease so that new fraction is double the original fraction? Well, the original fraction has a numerical value of 1. When I double, I just make it 2, you know. Let's just say 14 over x is 2. Well, we both know that 14 is equal to 2x. It gives us 7 equals x. In that case, second case, I made... Let's just use different color. The first number becomes 14. I add 4. And second number becomes 7. As you see, I just subtract 3 to make it 7. So by what percentage should its denominator be decreased so the new fraction is double the original fraction? When you make 10 by 7, that means, guys, we decrease 10 by 30% to make it 7. Because we all know that 30% of 10 is 3, guys. Which is our number here. In that case, whoever says C, they were correct. I am proud of you guys. Thank you so much. All right. You should be proud of yourself too. You can go and eat ice cream or do whatever. I don't know. Get something, man. Yeah, okay. I don't have a chance to give you some little gifts. I can be proud of you. All right. Number 7 from 2020 and number 24. As you see, only two years ago. One of the last questions. It might be a little interesting. Please check that carefully. If you don't understand the question, don't feel terrible. You are not the first one who couldn't get the question. I have been hearing the same comment from other kiddos as well. It's fine. Just try to give us the first step you worked on. All right. It says we have about four minutes left guys It says even three minutes left. Oh gosh Can I start guys? What do you think? Or do you feel you need more time? Okay, I'm waiting maybe one minute or something yeah All right guys, I gave you a little more time. If there is no answer, I will start guys. It's almost time. I wanna end on time. No answer given. That's so sad, man. All right. So here is the deal guys. As you see, the painter is supposed to mix two liters of blue with three liters of yellow. But interestingly, by mistake or something happened, I don't know, he was sick, he wasn't feeling well, he did something, I don't know. Okay, by mistake, he used three liters of blue. Well, think about it. First of all, guys, we have one liter of extra blue, am I right? Based on the smallest amount of this green paint he was throwing. Because even we have the rate of three to two, we have to find this rate of two to three. So since we had three liters of blue, but we had to have two liters of blue, two minus three, I mean, three minus two gives us one liters of extra blue we have. So we gotta throw away this one. But here is the deal. As you see in that mix, we have every three liters of blue, we have two liters of yellow. With the same ratio, since we need to get rid of one liter of blue, if you divide both sides by three, you should get one liter of blue represents two thirds of yellow, am I right? You know, since you are going to get rid of that mixture, which is green, green, you know, they mix blue and yellow to make green. Well, from at least, I mean, the smallest amount, one liter of blue you need to get rid of. Also, to be able to keep the same ratio, you have to get rid of two thirds liter of another color. Two thirds liter of another color. I mean, these are not blue and yellow anymore. These are just green, but still we are trying to keep the same ratio. So one plus two thirds is three over three plus two thirds gives us five over three liters of green paint you need to throw away. Is that make sense? Or no? It's only one minute. I mean, I took your one minute extra, sorry. Does that make sense? Any questions do you have? Wow, that's interesting. So thanks for sharing. Do you like the question, Soham? May you have that one? Or not really, not at all. Hey, I got that one correct when I initially... Oh, okay. I mean, would you like to explain to us how you did that? Imagine... I pretty much did it the same way. Like there's three blue and two yellow, but we need two liters of blue. So if you subtract out one blue, you also need to subtract two thirds of yellow. So it's five thirds. Okay, class, any question do we have? Soham, anyone texting you? I cannot see that. You got no questions? All right, guys. I enjoyed our session. It was really cool. I hope you enjoyed as well. If you don't, please give me the comment. I cannot read that comment after I left anyway. So I am going to see you next week, I guess. Until that time, take care, guys. Bye.

math lesson

percent problems

percent increase

algebraic methods

geometric interpretations

student participation

problem-solving strategies

percent conversion

exam-style questions

teaching methods