What is 73% of 85?

What is 71.69% of 92.4?

100% of any number is simply the number itself.

What is 730.4% of 730.4?

30% of 90 is the same as 90% of 30.

Percentage recap

﻿Hello and welcome to this lesson on growth and decay percentage change. Really important that you've got that pen and paper at hand so that you can write things down and that you're ready to learn. And you are in that quiet space so you can concentrate really well. Make sure you've got a calculator as well, be lots and lots of things that we need to be able to calculate so it's really important that you got one so you can access the lesson appropriately. So, without further ado, I'm Mr. Thomas, let's take it away with today's lesson. For your try this today, what I'd like you to consider is the labels below and I'd like you to attach them to the clothing items. So in the first instance, the shop owner makes profit on every single item and then the second option is going to be that the shop owner makes the most profit if someone buys one of everything. So pause the video now and have a go at that. I'll give you ten minutes to do that. Off you go. Excellent, let's go through it then. So to make a profit on every item he's going to have to make sure or she's going to have to make sure that every single one of those items sells for something that is below the, sorry above the cost for the shop. So if you take 30% off the jumper just there, that would be a one pound 80 off. So you get, of course the cost of the customer that'd be four pound 20, right? So that would result in four pound 20 then. The next one would be three pound 20 as a result of seeing that price slashed. The next one, there would be at 15 pounds. Just see they're still all above the cost price of the shop. Five percent off would be, five percent would be 40 P off that so seven pounds 60, and then 15 percent off the cost for the customer. There would be eight pound 50. So do you see that we satisfied all of our constraints there. We make a profit on every single one of those items. But in order to maximise our profit, to make the most of our profit, if we buy everything we need to basically say, well we've got all the costs remaining the same. So what we want to do is increase our, what we call revenue, the amount of sales we're making. The amount of money we're making of sales rather, in order to make the most amount of profit. So we need to reduce the top item, which is the shoes by the least amount and reduce the t-shirt which is the least costly item in our infantry here in our shop, by the least amount. So we get these and then we just put it in orders, with the amounts that they are. So hopefully that makes some sort of sense now. So if you're connect, what I want us to do is explore the idea of decimal multipliers further percentage increase and decrease. Now, one as a base number is incredibly helpful because if you multiply anything by one, it just stays the same. So one times five will give us five. One times, you know, 5,032 will be equal to 5,032. So if there's no percentage change. So, we're not increasing or decreasing until we have our base number of one. Now if I want to add three percent onto something What I do, is I start off by doing equals one and then adding on 0.03. So, all I have done there, all I have done there is I have converted this part here into a decimal. I have seen am adding on so just do add. So am using that base number of one because that means that the number stays the same and now increasing it so then when I add one to 0.03 I get 1.03. So if I want it to do an increase say of 58%, that would be of course equal to 1.58. If I want to increase it by 305%, it could be more adventurous here. I can then say well convert that to a decimal and then add it on so that So you have to, one plus 3.05, and that is equal to 4.05. So you can see there, there's quite a lot of little things there that can make it a little bit tricky when you get above a hundred percent. So a hundred percent is an increase doubling it, right? You're adding the same amount on. So with that in mind, it's quite, it's quite weird to think, Oh, okay, you're going to have to also why by 4.05 to increase it by 305%, remember you've already got a hundred percent. So we're going to explore that concept a little bit more in our next video, but for now we're focusing on this. So if I want to do it as a decrease though, let me scrap. My board here, what I want to do is decrease. What I could do is I can start off with that base number of one, but I'm just going to decrease it now. So I'm going to subtract. So if I wanted to do, for example, 4% decrease, I do, subtract 0.04 and one subtract 0.04 gives me 0.96. So that works really nicely. Doesn't it. If I wanted to do say a decrease of, should we go with 59%? That would be one minus 0.59. And that will, of course give us 0.41. So I know my decimal multiplier is going to be 0.41. If I want to a, a decrease of 91.6, 5%, that would be one subtract 0.9165. And if I do that, what would I get? You may have to use your calculator for this one. What would you get if you do that shattered out. Very good. Multiply it by 0.0835. So remember, really really important that you can do that confidently and accurately as well. So let's have a go at doing these ones. If I wanted to increase a hundred pounds by 30%, what I do is I do a hundred multiplied by 1.30, 1.3, same thing. And that gives me 130 pounds. Hopefully you can do it. After you have had enough time to think of too much. If I want to increase, 54 pound 23 by 53.9% I do 54 pound 23 multiplied by 1.539. Just converted that into a decimal number. So that gives me when I get to that. Channel that into our calculator, What does that give us? That gives us 83.46, 83 pound 46 to the nearest P. What about them decreasing 93 pounds 20 well, 93 pounds 20, times by and you got to do one subtract 0.21, which gives you of course zero point, what does it give us? 79 isn't, very good. So, 0.79 that, and that is equal cost to go ratio. What you're going to get? Oh, you've probably beaten me. I've got 73.63 to the nearest Pence. Yeah, decrease 107 pound 20 by 92.9% a very big decrease, 107 then pounds 20 times by while one subtract 0.929 is going to give us what would they give us if we did that in our calculator, 0.071. Right? And multiply by that 107.20. multiply by that gives us £7.61Pence So very good. If you've got those answers actually quicker than me and your quicker on your calculator as well. Very good. So what I'd like you to do if your independent task is to have to go increasing and decreasing those amounts using a decimal multipliers in your calculator. So have a go at that task. Now I'm going to give you 12 minutes to do that. Off you go. Very good. Did you get these answers here? I've run a tonne of them to the nearest penny, but hopefully nothing too tricky there, so remember that there is going to be 1.40. You need to multiply by. Yeah, exactly. Very very similar to what we were doing just a moment ago in our connect task. The only one that may have posted real difficulty would be the bottom one, increasing the a hundred pounds by 10% and decrease. My 10 pounds, 10% again. Well that one is actually dropped by 1% compared to the initial a hundred pounds you have, that's saying we're going to explore later on in our series. Okay. So we've got our explore task now. And I want you to think about what you'd need to do here is you need to put in some numbers and you need to explore it. So you need to think increasing blank by 40% is the same as decreasing blank by 40%. So try and think of some different numbers you can put in there and play around with it. Hopefully you can get to a pattern or notice something. If you can't just have a think about what different numbers you can put in and seeing if you can get them close to equaling each other, I'm going to give you 10 minutes to play around with that. I'll be on this next slide for some support. If you need it. Off you go. So I've got an example here that works for this bit here. Now we could increase 12 by 40%. If I increase 12 by 40%, but then turn to your calculator, do 12 times 1.4 and you get 16.8. So it gets 16.8, then if we take 28 decreased by 40%, what would that give us? Well, 28 times 0.6. That gives us 16.8. So by playing around with it, we see that we've actually got the same answer there. And what we notice is that in relation the 28 in relation to 12, I can say that 12 is three sevens of this. So that is what we noticed as a result of that. That's really tricky to realise so well done. If you've got that really, really good. So that brings us to the end of our lesson. Really, really impressive stuff. If you managed to do that last part, but for the most part emotionally, you've got the decimal multipliers by increasing and decreasing. If you did very, very well done. I just want to say, make sure you do that exit quiz smashes and do it to the best of your ability so that you can prove to everyone how much you have learned in today's lesson five questions. They're not too tricky if you've been paying attention and doing the work as we've been going along. So for now take care and I'll see you in our next episode. Bye bye.

If the amount of flour in a bag increased by 20%, it would always mean we add 20g on to the amount.

If I increase 200kg by 30%, then the new amount I have is...

The decimal multiplier to increase an amount by 53% would be...

It is possible to increase an amount by more than 100%

If you decreased an amount by 60%, the decimal multiplier would be 1.60.

Percentage change

In this lesson, we will learn about percentage change. We will investigate how to increase or decrease an amount by a given percentage.

Maths

Y9 Maths

Key Stage 3

Year 9

Growth and decay

Ratio and proportion

THEME

UNIT

Finding 100%

Repeated percentage change

Compound appreciation and depreciation (Part 1)

Compound appreciation and depreciation (Part 2)

To the power of n

Exponential growth

If I decreased the amount I paid for my car insurance by 90% to £36.50 per year, how much did I pay previously for my car insurance?

If I know something costs £2.10 in a 30% off sale, then I would calculate £2.10 = 70% and scale accordingly to get that 100% = £3 to find the original amount.

y = 9^x would cut the y-axis at the coordinate...

If I deposited £500 in a bank account and left it there for 6 years at a rate of 4% compound interest, how much would I have at the end of the 6 years?

If 53 increased by 23% for 'n' number of years, which of the following would provide a general formula to work out how much it had grown to?

If an antique appreciates by 6% per year for 11 years, the decimal multiplier would be 1.06^11.

The decimal multiplier to increase an amount by 6% for 5 years would be...

£100.00 decreases by 5% in one year, followed by an increase of 5% in the next year, and then decreases again by 2% for 8 years. What would the final amount be?

Starting with 100 bacteria, how many would there be after 1 hour if the number of bacteria increases by 20% every 12 minutes?

If I buy a car in a 20% off sale and it costs £30,000, how much did the car originally cost?

If y = 5^n, what is the value of y when n = -3?

Decreasing £100 by 5% for 8 years would give a final balance of...

If an antique grew 6.5% a year for 7 years from the purchase price of £55, it would be worth £85.46 (to the nearest penny).

In order to increase an amount by 7.5% for 3 years, I would need to multiply the amount by 1.075^3

If a bacterium increases by 1% in 2 minutes, would this form an exponential curve?

If an investment doubled every 3 years, would the growth of the investment form an exponential curve?

Lesson overview:Percentage change

Core Content

Growth and decay: