Lesson video

Hello everyone, it's Mr. Millar here.

In this lesson we're going to be increasing numbers by percentage.

So first of all, I hope that you're all doing well.

And if you remember last lesson we looked at the idea of using a decimal multiplier to work out a percentage of an amount.

And we're going to find out that this lesson this same idea is going to be really useful when it comes to increasing an amount by a percentage.

But to start off with, let's have a look at the try this task.

So as you can see Zaki and Cala are discussing how to increase 240 by 40%.

So what I want you to do is I want you to read both statements, see if you can complete Cala's statement, and then see if you can work out how to increase 240 by 40%.

Pause video now for one or two minutes to try and find this out.

Great, so hope that you worked this out and it wasn't too tricky.

And the first thing that you needed to do of course was to find 10% of 240 which you should be very comfortable with.

So 10% of 240 is going to be 24, because we just take off the zero.

And then if we know 10%, we can very easily find 40%.

That's going to be 24 times by four, which is 96.

And so if I'm increasing 240 by 40%, well, I can draw a bar model.

This represents 240, that's a hundred percent.

And then I'm just adding on 40%.

So I can add on 40% here, which I found out to be 96.

And then the whole thing, I just need to add 240 to 96, and it's going to give me 336.

So this is one way to increase an amount by percentage, which we have actually seen before.

But now we're going to have a look at another way using the idea of a decimal multiplier.

So when you're ready let's have a look at the connect task.

Okay, so the connect task, Xavier has another idea.

She says to increase 240 by 40%, I can do it in one step by doing it 240 multiplied by something, where this thing that you need to multiply 240 by, it's going to be a decimal multiplier.

Now, it's you're going to be your job to figure out what that's going to be, and to help you, I thankfully did a bar model below and actually it's the same bar model that we just drew in the try this task, where you start off with 240, you find 40%, which turned out to be 96.

But this bar model is going to be useful to help you find out what this decimal multiplier is going to be.

So pause the video, 30 seconds.

See if you can work it out.

Okay, great, so hope that the bar model was useful for you.

And the key is to notice that if we're increasing an amount by 40%, what do we have after we do that? Well, we've got a hundred percent plus 40%, which is now 140%.

Now, what is 140% as a decimal? Well, we know that when we have a percentage we're going to be dividing by a hundred.

So 140% is equal to 140 divided by a hundred, which is equal to 1.

4.

So 140% as a decimal is 1.

4, and therefore 1.

4 is going to be a decimal multiplier that we're going to use.

So we're going to do 240 multiplied by 1.

4.

And if you put that into your calculator or worked it out, you would find that it came to 336, and we get the same answer as before.

Now, this is obviously really, really useful because knowing this allows us to increase an amount by any percentage in just one step, particularly if you've got a calculator it's really, really easy to do.

So we're going to practise at doing some more in the independent task.

It may be worth copying down this example, but when you're ready let's move on to the independent task.

Okay, great, so here's the independent tasks.

You've got seven questions to do.

And in each case it may be worth drawing a bar model to help you out.

So for example, the first question, increase 500 by 60%.

Well, I'm just going to draw the percentages then, I know that I start off with a hundred percent.

I'm always going to start off with a hundred percent and I'm increasing it by 60%, so there is add 60%.

So what do I have now in total? I've got 160%, which is equal to 160 over a hundred, which is equal to 1.

6.

So the calculation I'm going to do is going to be 500 multiplied by 1.

6 and put that into your calculator, use the calculator on your phone or your computer if you don't have one and you find out the answer.

So seven more for you to do.

Pause the video now, four or five minutes to have a go at the rest of these questions.

Great, and when you're ready the answers are going to be on the next slide.

Okay, so here are all of the answers, and well done for getting these.

Let's just go through a couple of these together.

So question four, increase 30 by 6%.

So again, if I draw the bar model here is a hundred percent, which is our starting amount, 30 and we're increasing it by 6%.

So what do I have in total? 106%, which is equal to 106 over a hundred, which is equal to 1.

06.

So that is why if I'm increasing an amount by 6%, I multiply it by 1.

06.

Finally I want to go over question seven, it's a little bit tricky, if I'm increasing by 135%, but I can just think of that as starting off with a hundred percent again.

And if I'm increasing by 135%, well, there is 135%.

So overall in total, I've got 235% which as a decimal multiplier is equal to 2.

35.

Okay, when you're ready, let's move on to the explorer task.

Okay, let's have a look at the explore task, it's a nice and quick one.

So Yasmin is thinking of a number.

She increases it by 25% to get 80.

What number is she thinking of? So what I want you to do here is I want you to try different numbers, increase it by 25% until you get 80.

It might take a few different tries.

So pause the video now and see if you can work out what this starting number is.

Okay, great, so well done for having a go.

And the key here is to realise that if you're increasing by 25%, you are going to be multiplying by 1.

25, and you could have tried different numbers.

You could have tried, for example, if you tried 50 and did 50 times by 1.

25, you would have got 62.

5.

So you would need to start off with a higher number.

And it turns out that the actual answer was 64.

So well done if you got that.

It might take me a few tries so well done if you got that, but some of you might've actually spotted a little trick here.

And that trick is to realise that if you actually divide 80 by 1.

25, you get the answer 64 straight away, which may not come as a surprise to you because you know that division is the reverse operation or the inverse operation of multiplication.

So if you're multiplying a number by 1.

25, to get a number then dividing that ending number by 1.

25 would get you the original number.

So that is actually it for today.

Thanks very much for watching, hope that you have enjoyed this lesson.

And next time, it's going to be final lesson in the series where we are going to be looking at decreasing a number by a percentage.

So thanks very much for watching.

Have a great day, take care and see you next time, bye bye.