Lesson video

Welcome to our third lesson in the percentage and statistics topic, today we learn to solve problems involving the calculation of percentages of amounts.

All you'll need is a pencil and piece of paper, so pause the video and get your things together if you haven't done so already.

So here's our agenda for today's lesson, we're going to look at solving problems involving the calculation of percentages of amounts.

And we'll look at percentage decrease, we'll look at efficient strategies for calculating percentage, we'll look at percentages versus fractions, and then you'll do some independent learning and a final quiz.

So I want you to have a think about this question, when might you see percentage decrease? You might want to pause the video now to make some notes.

So we see percentage decrease in things like where there's a reduction in price, so you see sales and shops where they have a different percentage taken off the full price of the item, or you might see it in a reduction of an amount say for example, Elizabeth drank 20% of her 500 ml drink and your job would be there to find out what 20% was so how much she drank.

So let's have a look at some questions involving percentage decrease and how we would approach these.

So here's our first question.

Iman goes shopping in her local supermarket and she buys two items which are both on offer.

How much does she pay? So she buys a bunch of bananas and their original price was 96p, but there's 50% off that price.

And then she also buys a cake, which is £3.

60, but that is reduced by 15%.

15% of that has been taken off the full price.

So we're going to do these two questions together let's start with the bananas.

So we know that 50% has been taken off the price of the bananas, we know that 50% is equivalent to one half 50% as a fraction is 50 over 100 which simplifies to one half.

So they're half their original price.

So how much does she pay for the bananas? Now to find half of an amount, I can divide it into two equal parts.

And here you can see on the bar model, that the original price is 96p, and then the new price will be the original price take away half of that take away 50%.

So I know that fifth, that 96 divided by two is equal to 48, so the bananas will now cost 48 pence.

Let's move on to the cake.

So, here the cake is £3.

60 and it has been reduced by 15%.

So we're going to consider two different strategies for approaching this problem, and we'll start with strategy one.

In strategy one, we'll find 15% of the whole and then subtract this from the original price.

So we've got the original price at the top of the bar model, and we're going to find 15% of it and take it away from the original price, to give us the new price.

Now, to find 15% of the whole, we're going to use partitioning, we know that 15% can be partitioned into 10% and 5%.

And then we can find these percentages in order to find 15% altogether.

So, first of all, we'll find 10% of the whole and we find 10% by dividing by 10.

So 10% of £3.

60 is 36p, £3.

60 divided by 10 is 36p.

Now to find 5% before we already know 10%, then 5% is half of 10%.

So we'll find 5% by having the 10% price.

And that's 18 pence.

So half of 36p is 18p.

Now we found 10% and 5% there but we were looking for 15%, so we need to add these two values together, and that will give us 15%.

So 15% of £3.

60 is 54p.

And that came from adding 10% and 5%.

But we're not done, because it's 15% off the original price.

So we now need to subtract that from the original price, £3.

60 subtract 54p is equal to £3.

06.

So that means that the cake will end up costing £3.

06.

Now we're going to stick with the cake, we're going to look at a different strategy.

So if the price is reduced by 15%, then the new price is 85% of the original price.

So if you think about the original price as 100%, if you take 15% away from that, you're left with 85%.

So in this strategy we calculate cost by calculating 85% of the whole.

Now we're going to approach this, this is our second strategy we're going to approach it in exactly the same way we're going to be using partitioning, 85% can be partitioned into 50%, 30% and 5%.

So if you look back at my bar model this time, rather than finding 15% and subtracting, we're just going to find 85% of the whole because we know that the new price is 85% of the whole.

So now we've got our partitioned 85%, we'll start with 50%.

We know that to find 50%, which is half we divide the original price by two.

So 50% of £3.

60 is £1.

80.

Then we're going to find 5%, so we're going to think about what is the relationship between 50% and 5%.

Well I know that 5% is 10 times less than 50% or 50 sorry, five is 50 divided by 10, so to find 5%, I'm going to divide this number by ten 5% of £3.

60 is 18p.

So, you can imagine these arrows showing the relationship, I would divide by 10, 50 divided by 10 is five, so 180 divided by 10 is 18p.

Then I can find 35% sorry, 30% by finding 10%, which is 36p.

Remember, it's the whole divided by 10, and then multiplying it by three to give me £1.

08.

So now I have 50%, 5% and 30% and that equals 85%, now I need to add them together, which gives me the price of £3.

06 which is the same price that we got on the previous slide, just a different strategy.

So we'll go back to the original question, how much does Iman pay for both of these things? We found that 50% of 96 was 48p and 15% off £3.

60 or 85% of £3.

60 is £3.

06.

So all together if we add those two numbers together she spent £3.

54.

Let's have a look at another one together, and we're going to do the two strategies again.

So here we have a football and the original price is £9.

80 but 65% has been taken off.

So, if we look at this in a bar model, the original price is £9.

80 65% has been taken off, so the new price is 35% of the original price.

35 plus 65 is equal to 100%.

And remember the original price is 100%.

So if we look at strategy one, we're going to find 65% of the whole, and then we're going to subtract it from the whole.

I've partitioned 65 into 50, 10 and five, and I can find those percentages quite easily.

I know 50% is half of the whole, so 50% of £9.

80 is £4.

90, then I know that to find 10% I divide the whole by 10 which is 98P and then I'm finding 5%, so I find half of 10%, which is 49p, and you may also notice the link between 50% and 5% remember 5% is 10 times less than 50% and 49p is 10 times less than £4.

90.

So there's different ways of getting to the percentages, you didn't have to just do half of 10%, then I need to add them all together to find 65%, which is equal to £6.

37 and then don't forget the last step I have to subtract the 65% to find the new price, so £9.

80 the original price subtract £6.

36 which is 65% of the original price is equal to £3.

43.

So the new price of the football is £3.

43.

So for our second strategy, we've got the same original price £9.

80 and it's been reduced by 65%.

So for this strategy, rather than subtracting 65% of the whole, we're finding 35% of the whole, which is the new price.

So for strategy two, I have partitioned 35% into 30% and 5% to find 30% I find 10% and then multiply by three, so 10% of £9.

80 is 98p multiplied by three is £2.

94.

Then to find 5%, I just have 10%, 10% was 98p so 5% is 49p, and then to find actually 35% all together I have to add 30% and 5%, which gives me £3.

43.

So it's the same prices on the previous slide, but this time we found the new price straight away rather than subtracting the discount.

Now it's your turn to have a go independently, so I would like you to pause the video and solve the problem using your preferred strategy.

So you're either subtracting finding 65% and subtracting it or finding the new percentage which in this case would be 35%.

So pause the video now and have a go.

Let's start with the cake, so the cake was £7.

00, 65% has been taken off it, so the new price is 35% and you were to choose whichever is your preferred strategy, so I'll go through both, in strategy one, I find 65% and subtract it from the whole, I know that 65 can be partitioned into 50%, 10% and 5%, 50% is half of £7.

00 which is £3.

50, 10% you divide by 10 so that 70p, 5% is half of 10% so that's 35p.

Then you add those three numbers together to get 65% which is £4.

55 and then you remember the final stage where you have to subtract that from the whole £7.

00 subtract £4.

55 is equal to £2.

45.

In your second strategy, you were finding 35% of the original price to get the new price so 35% can be partitioned into 30% and 5% to find 30%, you need to find 10% which is 70p and then multiply it by three, which is £2.

10, 5% is half of 10%, so 70p divided by two is 35p, and then add those two amounts together to find 35% which is £2.

45.

We look at the car problem next so again, we could have used either strategy, finding 25% and subtracting or finding 75%, we know that 25% is equivalent to one quarter as well, so you may have used that as a strategy finding one quarter, dividing by four, or you may have found 10% and then multiply it by two to find 20% and divided it to find 5%, but 25% of £3.

80 is 95p, and then subtract that from the original price gives us £2.

85.

In the second strategy we're looking for 75%, we know that 75% is equivalent to three quarters, so, what you may have done is taken the price of one quarter 95p and multiplied it by three, which gives us a cost, a new price of £2.

85 so same solution different strategy.

Now we're going to look at a more efficient strategy for calculating a percentage of an amount, so partitioning is great, but when sometimes it's quite a long process because we have to partition into lots of different numbers, let's have a look at this strategy now, in the more efficient strategy, we find 1% of the whole, and then we use this to find the percentage of the amount.

So if I'm looking to find 36% of 200, if I were to partition it, I would partition it into 30%, 5%, and 1% then to find 30% I'd have to find 10% and multiply it by three, then to find 5%, I'd have to find 10% divided by two so you see that this is quite a long process, in this strategy, I find 1% so if 200 is the whole, that's 100%, 1% is 200 divided by 100 which equals two, so to find 1%, we divide the whole by 100 and then to convert that into 36%, I just multiply it by 36, okay, so two times that 36 is equal to 72.

So find 1% by dividing by 100 and then multiply it by the percentage that you were trying to find.

So your turn to have a go independently now to find 54% of 1,400, if you're still not feeling confident no worries, just keep watching the video and I'll go through the solution.

So if I'm finding 1%, I'm going to divide the whole by 100, 1% of 1,400 is equal to 14, now if I'm finding 54%, I have to multiply that number by 54.

See 1% multiply by 54 gives me 54%, so I do it to the other side as well.

14 multiplied by 54 gives me 756.

So 54% of 1,400 is equal to 756.

And also, if you just think about this using your number sense, you know that 54% is just a bit more than 50%, 50% of 1,400 is 700.

So it makes sense for 54% to be just over 700.

Now, one more type of question before you do some independent learning, this is percentages verses fractions.

So a regular bar of chocolate weighs 300 grammes, and it's on offer in two different shops.

So I want to know which offer has more chocolate and how do ? So the whole is the same in each case, it's 300 grammes, and then the first offer you get 25% extra, and in the second offer you get one-third extra.

So we can think about these we can't compare really when one's a percentage and one's a fraction, so we need them to be in the same units, so if I think about my knowledge of percentages, I know that 25% is equivalent to one quarter.

And I know that one quarter is less than one-third, so therefore this bar giving one-third extra, will be giving me more.

And then if I think about it in the other way round converting a third to a percentage, I know that a third is equivalent to 33.

3% recurring, and that is greater than 25%.

Therefore, I know that this offer, the second offer will give me more chocolate.

So if you have a question which is asking you to compare fractions and percentages, you know to convert them both into the same units, whichever one you find easier in order to compare them properly.

So, let's have a go at some independent learning, pause the video and complete your task and then click restart once you're finished.

For question one, you had two different items, which had discounts taken from them, and you were asked to calculate the new prices for the objects.

So for the first one, the bananas, it's 25, 20% off 75p.

So you will either have found 20% and subtracted it or found 80% to give the new price.

So 20% of 75p is 15p and you could calculate that by finding five sorry 10% by dividing by 10, and then multiplying by two, and then to find 20% off, you are subtracting the 20% from 75% so sorry, from 75 which gives the 60p.

For the dartboard, which was originally £17.

00 you're taking off 55%, so 55% can be partitioned into 50% and 5%, and then those two numbers added together and subtracted from the original £17.

00 to give you £7.

65.

You may also, have used our more efficient strategy by finding 1% of £17.

00 which is 17 pence, and then multiplying it by 55 and then subtracting it from the whole.

If a question two Hassan scored 75% on a grammar test and the whole was 96, so it was out of 96 marks and then Lawind sat a different test with 80 marks, so the whole was 80, and he got four-fifths correct.

So I want to know who got more correct answers.

So the first job is to find 75% of 96 to give us Hassan score, we know that 75% is equivalent to three quarters, so I found one quarter by dividing 96 by four, and then multiply it by three to find three quarters, which means that Hassan scored 72 out of 96 on his test, you may also have found 1% of 96 and then multiplied it by 75, or you may have partitioned 75 into something like 50, 20 and 5%.

Then Lawind, he scored four out to five, so he got four-fifths of them correct, and that's equivalent to 80%, so I found 80% of 80 by dividing it by 10 and then multiply it by eight to give 64, or you may have just used the fraction there and divided the whole by five to find one-fifth and then multiplied it by four.

So we can see that Hassan got more correct answers on his test.

In question three, we've got two supermarkets which have offers on identical bunches of bananas, and Youcef decides that the offer at supermarket A is cheaper, because they are offering a greater percentage decrease.

So we want to know, is he correct? So in supermarket A it's 60% off the price in B, it's only 25% off, but, in supermarket A, the original price is almost double that in supermarket B £1.

80 versus 92p.

So we need to work out which one will be cheaper after the discount.

So finding, taking 60% off £1.

80, we find 10%, which is 18p multiply it by six to find 60%, which is £1.

08 and then subtract that from £1.

80 gives us 72p.

So the new price for supermarket A is 72p for supermarket B we find 25% of 92p with 25% as a quarter, so 92 divided by four is equal to 23p and subtract that from the whole gives the new price of 69p.

So actually, supermarket B is cheaper because even though they were taking less off, their original price was so much less than supermarket A.

So for question four, you are given the prices of some items in a shop and their discounted amounts.

So the first job was to find their new price biscuits 50% off 54p is 27p, the oven chips were 25% off £1.

60, we know 25% is equal to one quarter, so find a quarter of £1.

60 and subtract it from the whole, which gives us £1.

20.

The crisps for a six pack of crisps were £1.

20 now 35% off, so you were to find 35% and subtract it from the whole, which gives us 78p and lemonade was 55p with 20% off, which gives us 44p.

And 20% is equivalent to one-fifth, so that's worth remembering, so one-fifth of 55p is 11p and then subtract that from the whole gives us 44p.

So now you have your shopping list and you were to find out what your, the cost would be for purchasing all of these items at discounted prices.

So two bottles of lemonade, two lots of 44p gives us 88p.

One six pack of crisps is 78p four packets of biscuits is four times 27p which is £1.

08, and one bag of chips is £1.

20 and then add all of those costs together, gives us a total price of £3.

94.

Now it's time for you to complete your final quiz, so pause the video and click restart once you're finished.

In our next lesson, we'll be calculating the mean as an average, I'm looking forward to seeing you then.