Lesson video

Hello everyone, it's Mr. Millar here.

Welcome to the final lesson on percentages and in this lesson, we're going to learn how to decrease an amount by a percentage.

So, first of all, I hope that you're all doing well and well done for getting to the end this unit, this is the last lesson and where we are looking at decreasing an amount by a percentage.

So, last lesson we looked at increasing, here we're doing decreasing.

So again, Zaki and Cala are discussing how to decrease 240 by 30%.

So Zaki is saying I can find 30% of 240 and then subtract it from 240.

So, again we should be used to, how to do this method.

So finding 10% first and then 30%, and then subtracting from 240.

So pause the video, see if you can complete what is missing in this speech bubble and see if you can decrease 240 by 30%.

Okay.

So well done if you manage to do that.

So 10% of 240 is 24.

So 30%, we're going to use that, times that by three to give us 72.

And then we're decreasing by 30% so, you know, we can imagine a bar, which is 100% which is 240, but then we are cutting off 30%.

So we're decreasing by 30%, which is 72.

So we're going to have to subtract 240 minus 72, and we can put into a calculator or we can work it out ourselves.

And that should give us if my math is right, 168.

So that is how to decrease an amount by a percentage, find that percentage and then take it away from the original amount.

What's coming up on the next slide of course, is the shortcut similar to what we looked at in the last lesson.

So let's have a look at the Connect slide when you're ready.

Oh hey, so here is the other idea.

So to decrease 240 by 30%, I can do it in one step by doing 240 times by something.

So, this should be nice and straightforward and you should be able to get it before I tell you.

So here I have 240, which is 100% and I'm taking away this green area, which is 30%.

So have a think, what percentage do I have left? Well, of course that is 70% left because 100 minus 30 equals 70.

So if I've got 70% of 240 left, what is 70% as a decimal multiplier? Well of course it's 0.

7 because 70 over 100 or 70% is 70 over 100, which is 0.

7.

So, to get my answer, all I'm going to have to do is do 240 times by 0.

7 because I've got 70% left.

So let's say I was decreasing instead by, I don't know, 5%.

What would I multiply by if I was decreasing by 5%? Well, I would just do 100 minus five, of course, which is 95%.

So I'm finding 95% of the original amount.

So I would multiply by 0.

95.

Okay.

Let's have a look at some independent task.

I think that you're ready to do this.

Okay.

So here, we've got six questions, some which say decrease some which say increase.

You can use a calculator to help you if you want.

I've tried to make these so that you could do without one, but yeah, if you didn't have a calculator, you can do it.

Or you can use your calculator on your phone or your computer, but let's have a go at these six questions.

Pause the video and have a go at answering all of these six questions and then ordering them in size order.

Okay.

Great.

And answers are coming up now.

Okay, so here are the answers.

You can see that 212.

5 is the biggest, 180 is the smallest.

And yeah, let's just go through a couple of these.

So decreasing by 40%.

Well we, if we take away 40% from 100%, we get 60% left.

So that is 0.

6 as our multiplier.

And if we increase by 30%, well, we've got the original 100% and then adding on 30%, which is 130%, which is 1.

3.

So hope that you've got all of these, well done if you did, and make sure that if you're not quite sure you go back to watch the video again, so that you're really sure about all of this.

Let's move on to the Explore task when you're ready.

Okay, so here is the final slide of this unit.

So let's have a look.

Yasmin and Zaki are arguing over what happens when you increase and then decrease a number by the same percentage.

So Zaki says, if I increase a number by 20% and then decrease it by 20%, I will get the same number I started off with.

Sounds reasonable maybe but Yasmin is saying, I disagree.

If you try it with 100, you get a lower number than what you started off with.

So it's a really interesting problem this.

You know how to increase by a percentage, you know how to decrease by a percentage.

let's put them together.

So what I want you to do is you're going to start off with 100.

You are first of all, going to increase it by 20%.

And then once you get the answer, you're then going to decrease that by 20%.

And I want you to find out what answer you get.

Pause the video and have a go.

Okay.

Great.

So increasing by 20%, first of all, that is going to be times by 1.

2, so we get 120.

And then decreasing by 80%.

Well, the multiplier for that is if we decrease by 20%, we have 80% left.

So we're going to times that by 0.

8.

And actually what we turn out to get is 96.

So we actually get less than the original amount of 100.

So who is right? Yasmin is correct.

And this may seem strange because we're increasing by 20% and then decreasing by 20% so why does this happen? Well, if you think about it, the reason why it happens is that we're increasing, we're increasing a number by a percentage, but then what, the number that we're decreasing by a percentage is actually larger than the original number that we increased by.

So with, the amount that we're taking away from 120 is bigger than the amount that we added to 100, because 120 is a larger number than 100.

And actually, if you have a look at the times 1.

2 and the times 0.

8, and you can actually figure out that if you did this all in one step.

So times by 1.

2 times by 0.

8, that is the same thing as multiplying by 0.

96.

So you can actually do the two steps in one go.

So anyway, this leads to quite a surprising result, I think.

So it just shows the how of percentages and the importance of understanding them and not assuming anything.

So if you understood this slide, if you want to, if you were able to increase by 20% and then decreasing by 20%, then really well done, you've really understood this units.

And then if you've understood why this is the case, then extremely well done, it is tricky.

But yeah, it's quite interesting.

Anyway, that is the final slide.

That is the end of the unit so really well done, I hope you've enjoyed it.

And if you'd like, you can share your results on Twitter using the hashtag which will come up here.

So yeah, that is the hashtag that you can use if you'd like to share your work on Twitter, of course, ask your parent or carer for permission before you do that.

Thanks very much for watching all these lessons and I hope you've enjoyed them.

I really enjoyed doing them for you and yeah, have a nice day.

Bye bye.