Percentages of amount

Key Stage 3

Maths

Percentages

﻿Hello everyone, is Mr. Miller here. Welcome to the fourth person on percentages. And in this lesson, we're going to have a look at finding the percentage of an amount. Okay. So I hope that you're doing well. And let's try this task. So for each bar model, find the missing number and explain how you work it out. So you've got four different missing numbers to find out here in three different examples. And in each one, you can assume that the length of each of these smaller bars are the same. So, pause the video now for a couple of minutes and have a think about how you might work out these answers. Okay. So the first one you are dividing 60 into four equal parts. So you could say that 60 divided by four is equal to 15. So each of these bars are equal to 15 and then the next one, well, I've got five different bars. So I divide 60 by five to get 12. So each of them are now equal to 12. And then the final one, I and just said, there are eight different ones. So 60 divided by eight. I can use long division here if I want to, so eight into 60. Well, I know I have a decimal here, so it goes into 60 seven times because eight times by seven to 56, remainder four and eight goes into 4O five times. So I've got 7.5 here. So my missing value is going to be 7.5. Okay, great. So we're going to use this concept to have a look at the percentages of an amount. So when you're ready let's move on to the connect task. Okay. So here we have a look at the connect tasks. So to work out percentages of an amount we can convert to a fraction first and then use a bar model to work it out. So three examples here find 20% of 45. So what it's saying is, one way to find out percentage is to convert the percentage to a fraction first. Now I know that 20% is 20/100 because we know that percentages are always out of 100. And how would you simplify this fraction? Well, you could divide both sides by 10, cancel that zero and then divide by two. So I have 1/5 here. So really what I'm working out is 1/5 of 45. And I know that I'm finding 1/5 of something is equal to dividing by five. But just to show you with a bar model similar to the try this task. So I've got 45 here, which I'm splitting up into five equal parts and at 45 divided by five is going to be nine. So 20% of 45 is equal to nine. Next one at 25% of 80 and 6% of 45. Feel free to pause the video to see if you can have a go at these first of all. Okay, great. So if you convert it to a fraction first as I did for the first one then well done. So 25% is a quarter. So I can just do 80 divided by four which is 20. Next one I've got 3/5 of 45 and there's a number of ways that you could work this out. The first one is to first of all work out 1/5 of 45 which is, as I worked that before, nine and then to get from 1/5 to 3/5, what do I have to do? Well, I obviously have to multiply by three. So my answer is going to be 27. I could also show this one as a bar model. So again, I will have 45 at the top and I split it into fifths. Each of them is equal to nine. And so I'm looking for three fifths here, which is this region here equal to 27. So I hope that this makes sense and even feel free to copy a couple of these down into your notes so that it can help you out when you go to the independent task which is coming up on the next slide. Lets have a look. Okay so, here's a independent task. So you have got nine calculations that you need to work out. And obviously nine calculations, there are four pairs of calculations that have the same value and of course, one leftovers. So see if you can work out these four pairs and the one leftover. Pause the video for five or six minutes and see if you can work these out. Great. So let me had a nice go with this. Let's have look at the answers. Okay. So here are your parts. You got the 48 as a part, 60 as a part, 20 as a part and 30 as a part with a 45, the one that's leftover. They were quite nice and straightforward but there's just a couple of tricky ones that I want to go through. So first of all, 37.5% of 80 is a really tricky one. But you could have noticed that 37.5% is the same as 3/8. You should know your eighth. So 1/8 is 12.5% and so 3/8 is going to be 37.5%. So once you know that 37.5% is 3/8 it's very straightforward and 33 1/3%, What is that going to be as a fraction? Well, it's going to be 1/3. So 1/3 of 90 is 30. Great. Let's have a look at the explore task to finish off once you're ready. Okay, great, so here's the explore task. And let's have a look at what it says. So just some calculations equivalent to 30% of 60. So you've got 30% of 60 in the middle. And then around that you've got some missing gaps of percentage of amount that will be equal to the same thing. Now, actually you could work out what 30% of 60 is if you did is equal to 18. But actually it turns out you don't need to work this out. And let me explain why with an example, let's have a look at the one at the top 60% of something. Now, if you imagine a 60% of 60, what does that compare, if I said 1/16 of 60 how would that compare to 30% of 60? Well, because you're going from 30% to 60%, you're multiplying by two, so if you kept the amount the same then 6% of 60 would be twice as big as 30% of 60. But you want to keep the calculation equivalent to 30% of 60. So if you're increasing, if you're doubling a percentage, what do you think you have to do to the amount? Well, if you're thinking that you're going to have to half the amounts, then you're absolutely right. So it's going to have to be 60% of 30. Because if you're doubling the percentage to keep the calculation the same, you're going to have to have the amounts. Alright, let's have a look at 15% of something. Even for you to pause the video to have a think of what 15% of something would have to be. Well, if you're thinking 120 really well done because this time you are halving the percentage, so to keep the same value you're going to have to double the amounts. Okay. I hope this should give you some ideas. I'll let you get on with the rest of it yourself. So pause the video now. There's one more to do something percent of 20 and then two more for you to create yourself. So, pause the video and have a go at this. Okay. So first of all, something percentage of 20. Well, going from 60 to 20 you are dividing by three. You're finding a third of 60. So therefore what you're going to need to do is you're going to need to multiply the percentage by three there to get 90% of 20. And you can check all these calculations and you'll find that they're all the same and the ones that are missing. There's a number of things that you could do. So, one that you could do is 5% of something and to get from 30% to 5% you're dividing by six. So you're going to have to multiply 60 by six to get 360. And you could even do a 300% of something. So 300%, this would have to be 300% of six because you're multiplying the percentage by 10, so you have to divide the amount by 10. So you would get a 300% of 6. Great. That is all I've got for you today. So I hope you've enjoyed it, and in the next lesson we're going to be looking at percentages of amount. We're going to have a look at a different way that you could do it. Thanks so much for watching. Have a good one and see you next time. Bye bye.

Percentages of amount

Percentages of amount

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Maths