So Hey, how are you doing? And good. Good, good. I'm glad to hear it. Is your friend coming today? What didn't I thought? I thought there was you had a friend Williams or something like that who might be joining the class? Maybe no, I don't know. Maybe he's is not my phone. Maybe he's not your friend. Okay. Well, maybe I think you can ask. Yeah, maybe I'll ask the agency. My. Mom said, you will have two people next class, but I don't know, you don't know, the second class is right. Right? Okay, Yeah. Well, let's see. Let's see if he turns up. And if he doesn't in ten minutes or so, then I'll ask, okay, well, let's why don't we get cracking? In the meantime, we've been having a look at percentage and we want to start doing some worded percentage questions now. So let's just dive right in, sit and start off by working outs. 20% of 500 and then maybe we'll do 15% 40. There's some quick percentage arithmetic so you can wrap your head around these 20% of 500 to begin with. Hmm. One more step, otherwise perfect. That's more. Did us small. 嗯，one. Good. Well done. Absolutely right. So final answer, 100, 100.0 or we just write 100. Very, very good. And 15% of 40. Yeah so remember that 100% of 40 is 40. So to get an answer of 60 webe thinking more, I mean, it would be more than 100%. So just remember that zero 15, the reason why it was only one decimal place that you had to account for in the last one is because 20% is the same thing as 0.20, which we just call 0.2. So this was 0.2 times 500. And that's the reason why having having worked out what two times 500 is a thousand, you only had to adjust one decimal place. But here, what's 15% as a decimal? It's going to be zero point. 15 absolutely right. So we're doing 0.15 times. 14. Now again, just as you did, you did it perfectly. We forget about the decimal, but just notice that unlike in the last question, we're accounting for 12 decimal places here at the end. So our answer isn't 60, but rather. Six, absolutely. And that makes more sense as an answer because we're expecting a number much less than 40. 100% is 40. So 15%, it's going to be quite a lot less than 40. So you can also use that as a kind of as a kind of guide, if that makes sense. 2% of 600. Similarly, we're going to be expecting an answer which is significantly less than 600 for this. It's a tiny little fraction of 600, 2% 600. So make sure that that is reflected in your answer. If you're getting an answer more than 600, something's gone wrong. Good. Good. Well done. Twelve. Absolutely well, fantastic. And finally, 92% of a thousand. Good. Absolutely. 926. Excellent world roand Jack, warming it up into this nicely. Let's extend beyond this and have a look at some percentage increase in decrease questions now. So let's say that Jack bought an iphone or 400 pounds. But dropped the phone one on the way home. I've actually done this before. It's a terrible feeling to buy a phone and then you drop it literally. I remember one time I bought it and I got on my bike and the phone fell out of my pocket onto the pavement and smashed immediately. It was one of the most annoying feelings I've ever experienced. So Jack bought an iphone for 400 pounds, but dropped the phone on the way home, decreasing its value by 20%. What is the phone worth now? Now, we discussed the idea that we could do this two different ways. Do you have an idea of how to do this, Jack, or do you want me to show you how to do this one first? If you think you know how to do it, go ahead. Maybe you can do it. Okay? Great. Give it a go then. And maybe you can try to them. Okay. Yep, sure. Okay. So one way of doing it, I'm gonna we're just gonna to show, I'm gonna to show you two different ways because the first way is I think the more intuitive way, it's certainly how I used to do these questions, but there's a second way, which is a better way of doing it for when questions get a little bit harder. So it is important, I don't mind which you choose to do now, but it is important that you begin to understand the second way as well. We'll just run through the first way. So decreasing, what would does that word mean? Decreasing to decrease? So increasing and decreasing, what does decreasing mean? Deccretion is right down Yeah to become less so it's saying, and that makes sense, right? Because if you drop your phone and it smashes, it's gonna to be worth less than it was worth when it was you know a phone with no damage. So we're going to first of all work out what 20% of 400 is. And again, you can do that just as we've been doing. That's 0.2 times 400. And I can do that quite quickly. I know two times 400 is 800, but I'm accounting for one decimal place. So rather than 800, it's going to be 80. And then I just think about the question. It's saying it decreases by 20%. So that means that that value is taken away from the original value. So if it was originally worth 400, I'm mining 20%, which I've just worked out as 80. And that gives me a final answer of 320 pounds. So I think that's quite an intuitive, understandable way of doing it. There's nothing wrong with doing it like that. It's a good, good method. The other method, which is a better method, again, just for when the questions get a little bit tougher, it's important to understand percentage increase and decrease like this. The second method is to say that a 20% decrease. Is really the same thing as 100%, which is the full amount, -20%, which is 80%. So I start off by going, okay, if I'm working out a 20% decrease, really all I'm working out is 80%. So I dive in that and I go 80% of 400. It's the same thing as 0.8 times 400. I know that eight times 400 would be 3200, but I'm accounting for one decimal place, and I get an answer of 320, exactly the same. So we get to the same place, the same correct answer by two slightly different methods. So you can choose whichever makes more sense to you at the moment. I would do it that way. That said, it is important if the second one makes more sense. That's music to my is Jack fantastic. So definitely do it that way if that's the case because it's it's a it's a slightly deeper understanding that the second one demonstrates of what percentage increase actually is or decrease. So we'll do another one of those. Let's do some. I don't know, spills some some jam on the new. 500 or less than that. Ridiculous. The new 90 pound jeans. That he just bought decreasing. Their value. By 15%. What are his genes worse now? 0.9. So remember, it's not so the percentage is the important part. So the genes are worth 90 pounds, but we're saying a 15% decrease is equal to the full amount 100%-15%. Now what is 100%-15%? 95 probably be 100%-5%. This is 100%-15%. Well, 85, 85. Absolutely. So we're working out 85% of 90. That makes sense. I'm just trying to think if that's 81 minus four, 77, Yeah, very, very good. Fantastic. 76.5 is absolutely right. And remember, because it's money, we always want to give our answer generally if it's money to two decimal places. So 76 pounds 50, not the case with regular numbers. With regular numbers, we would just say 76.5. You're absolutely right. But with money, because money generally with dollars or cents or Chinese dollars, it's it's to two decimal places for the most part. But absolutely fantastic. Very, very good. What about if we save Jack buys an antique sofa for 400 pounds. But is told by an antique expert. Afterwards that the sofa is actually worth. 80% more then he bought it for. How much is the sofa actually worth? So again, the same idea. But just notice now that rather than doing a percentage decrease, we're doing a percentage increase. So you're trying to figure out, first of all, what an 80% increase is equivalent to as a single percentage. 80%. The bus plus 100. Well, it's again an so we write an 80% increase is equal to 100%, but this time we're adding the 80%. So is 100% plus 80%. Good. Absolutely. 180%. So now we're working out what 180% of 400 is. This one. Absolutely. 720. Fantastic. Very, very, very good. Just a couple more of these and then I think you'll you're gonna to doing them perfectly, let's say jacks monthly salary. That's just how much you're paid per month. Used to be. Let's say 2000 pounds, but has since been increased by 30%. How or what is jacks monthly salary? Starting off with a percentage. Alex. Yep, it's not bad, just a slight correction. This, remember, is pushed over. One more space. Because it's the hundredths column, it needs to be further over. So it's going to be six plus zero there, which is six, and zero plus two there, which is two. Yeah, good. Oh, ops, sorry. Can 2000? Yeah. Absolutely. Am I accounting for two decimal places because it's not 130, actually, it's 1.3. So two decimal places there. And what's that number? 2006 brilant calabsolutely one, 2600. Excellent. Okay. One more one more percentage increase in decrease question. Then we're going to move to possibly some reverse percentage, which we touched on last time. But I want to do a little bit more. So again, let's do Sam. Perts. 400 pounds. He hides 400 pounds underneath. It's bad, but let's. Say 15% is stolen by a neighbor. One day. How much money? Does he have left? Under the bad. We're going to think about whether this is a percentage increase or a percentage decrease question. Money is stolen. Are we adding that percentage on to the 100%? Or are we taking it away from 100%? A达。So so we're working out a 15% decrease here. Remember, it's the percentage which is the important thing. And a 15% decrease is the full amount, 100%-15%, which is how many percent. Yes. Good, good. 340. Absolutely right. Very, very, very good. Fantastic. So I think you're beginning to get a good understanding of percentage increase in percentage decrease. We're going to have a look at another style of question now, which is probably the hardest type of percentage question that there is at eleven plus you know in eleven plus exam. So it's a little bit beyond your level, but I think it's great if you can familiarize yourself with these styles of questions as quickly as possible. Remind me, Jack, how old are you now? Eleven. Oh, you are eleven. Okay. Well, in that case, it's perfect. So a reverse percentage question would look something like this. It looks something like Jack. Grows. A lemon tree or draack buys a lemon tree also. And what is it for a year? After a year. The lemon tree grows by 20% and is now. 180 cm tall, how tall? Was the lemon tree when he bought lted? Now a reverse percentage question is recognizable generally, not always, but this is a very common cue by the fact that we're going back in time here. So they've said, now it's worth this, but then they say, or now it's this tool, but how tall was it in the past? And that should when you've got that kind of a question where you're jumping back in time, that should be a little bit of an alarm bell that you've got a reverse percentage question here. So we're gonna to try to order the information as as kind of clearly as possible. So we start off with the fact that the lemon tree grows by 20%. Now if it grows by 20%, is that a percentage increase or a decrease? 嗯。The tree grows, it gets bigger. Is that an increase or a decrease? But growing is an increase. If you if something grows, it gets bigger. So we're saying a 20% increase is equal to 100% plus 20% as we were doing before, which is 120%. And what I'm going to do is I'm just going to introduce a little bit of algebra, algebra I'm sure you've come across before, if you're eleven, it's just when we substitute a letter for an idea or a missing value that we don't know yet, we are gonna to eventually work it out. But at the moment, we're not sure. So I'm gonna to say that p was is the size of the lemon tree when Jack or at the time Jack bought it. And it's really, really helpful sometimes just to assign letters. It could be A P, it could be an x, it could be an a, whatever you want, it doesn't matter. But just something, a letter that helps us to work this out. So what we're saying is that 120% of its original heights, which we're saying is p. Is equal to the new height of 480 cm. So you get p it grows by 20%. And now it's 480. So we can simplify that algebra by saying that 120% is the same thing as 1.2. So I can say 1.2p is equal to 480. And now I don't know if you've done this sort of thing before. If I say three x is equal to 15, what is x equal to? Absolutely. And to be clear, how you got that answer, if we're talking really technically, is you divided both sides by three. He said, okay, well, three de three x divided by three is one x or just x, and 15 divided by three is five. Well, we can do the same thing here. We can say, okay, 1.2p is equal to 480. So I'm going to divide both sides by 1.2, and that's going to give me 1.2. P divided by 1.2 gives me just p and 480 divided by 1.2. You can use a calculator for that if you want to. Another nice way of doing it without a calculator is if you're doing 480 divided by 1.2, we can times both things by ten. As long as we do it to both sides, we're going to get the same answer. So we can say 480 divided by 1.2 is actually the same thing as 4800 divided by twelve. And if I just do that quickly, twelve divide by four. 8012 doesn't go into four, but it does go into 40 84 times. And then I've got zero. So it's original heights is 400 cm. Or you can use a calculator if you want to. I don't mind for these questions, if you want to use calculator. You can see there are a few steps to this. If we just go back to the question again, we'll see if we can make sense of all of it. So Jack buys a lemon tree and waters it for a year. After a year, the lemon tree grows by 20%, and it is now 480 centimetall. How tall was the lemon tree when he bought it? And we started off by saying, okay, it grows by 20%. So that's a 20% increase, which is the same thing as 120%. I assigned a little bit of algebra to the thing that we don't know, which is the height of the lemon tree when you bought it. I said, I'm going to call that pea. Then I said, 120% of p is the new height. 480. I simplified that into algebra I, that 120% of p is the same thing as 1.2 times p or 1.2p. And I had that equal 480, and then I divided by 1.2. And that gave me a final answer of p is equal to 400 cm. So hopefully that's sort of making sense. If it's not, don't worry because we're going to do a few examples of this. And I think just by practicing it, you're gonna to get better. So let's say that, Sam. Find. Ds some potatoes. Eyes a sack of potatoes. He cooks. A roast chicken. With a bed of potate. Using. 20%. Of the potatoes. He had in the sack if he has 24 potatoes. Left now. How many potatoes were there originally in the sack? So again, we want to think about, is this a percentage decrease or a percentage increase? I bought some potatoes and then I cooked some potatoes. So are there going to be more potatoes now or are there going to be fewer than, say, toes now? Are the number of potatoes increasing here? Or are the number of potatoes decreasing? They're decreasing. Absolutely right. I'm using them. So we start off with that. We say, okay, a 20% decrease is equal to. 嗯。Increase equal. Mayus Yeah it's 100%-20%, which is. 80%. Yes, it is fantastic. Well done. And we're going to just make up a bit of algebra for the number of potatoes that there were in the sack. What algebra do you want to use for that? It doesn't really matter. Do your x or y or a or b or d whatever you want. Let's go with pea. So pea is number of potatoes originally. In the sack. So we're saying 80% of p of the number potatoes originally in the sc is equal to how many he has left now, which is 24. So we're saying 0.8p is equal to 24. What is p equal to? 0.8p equals 24. Eight. Well remember zero, we're dividing by 0.8. So we're doing 24 divided by 0.8. And remember what we just said last time that when we're dividing by a decimal, we can get rid of the decimal by times in both by a fact multiple of ten. In this case, we can just times both by ten. So we can say it's the same thing as 240 divided by eight of times, both by ten. See, you know what 240 divided by eight is? We do. Four. Good. So there were 30 potatoes originally, which makes sense as an answer, doesn't it? I had 30. I used 20% of 30 and now I've got 24. So 30 our answer. So I think definitely some more work to be done on that. But really good progress made on percentage increase and decrease. I think that's coming along nicely, which is fantastic to see. We'll return to some more worded questions after. Well done, Jack. That's us done for today. Yeah have a wonderful rest of your week, and I'll see you next time. Take care. Why?