# Lesson video

In progress...

Hi there, welcome to today's lesson, where we will be solving problems involving the use of percentages, for comparison.

Our agenda for the lesson is to start off by looking at finding the percentage of an amount.

Then we will compare percentages and then you'll do some independent practise.

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

And so we come to our first question.

Jay wants to buy a football with 20% discount.

The price of the football is 4.

80 pounds, and we want to know what will the price be after the discount? After 20% of the price has been taken off.

He says, I know that I have to find 20% of 4.

80 pounds, and then I need to subtract that amount from the original price to find 20% of 4.

80 pounds, I need to divide by 20, which is 24p.

If I take 24p away from 4.

80 pounds, I get 4.

56 pounds.

And that is the new price of the football 4.

56 pounds.

So have a read through of this strategy again and have a think about whether Jay is correct.

Do you agree with his approach to this problem? So this part of Jay's strategy is correct.

He knows that to find the new price, he needs to subtract 20% from the original price.

But his approach to finding 20% is incorrect.

He needs to find 20% of the total and the way he can do that is to find 10% and then double it.

We know that to find 10%, you divide the total by 10.

So 10% of 4.

80 pounds is 48 pence.

And then multiply that by two to find 20%, that is 96 pence.

Now he needs to find the new price by taking the original price of 4.

80 pounds and subtracting the 20%, so subtracting the 96 pence, which gives him a new price of 3.

84 pounds.

You've got two items here which are discounted and you need to find out how much Becca pays for the two items after the discount.

Pause the video now and work through the problem.

They are originally one pound with 40% off.

So the approach to this would be to find 40% of a pound and then subtract it from one pound.

To find 40% we can find 10% and then multiply it by four.

So if one pound is equal to 100 pence, 10% of 100 is 10, and then multiply that by four, 40% of 100 is 40 pence.

Then we can subtract that from the original price.

One Pound, subtract 40 pence is equal to 60 pence.

So that's the new price for the bunch of bananas.

Moving onto the cake, the original price is 3.

60 pounds.

The discount is 20%.

So again, we're looking to find 10% and then multiplying it by two.

The overall strategy is to find 20% of 3.

60 pounds and then subtract it from 3.

60 pounds We know that 3.

60 pounds is equal to 360 pence.

I just find it easier to convert to pence because then it's easier to not have to deal with a decimal number.

10% of 360 is 36 pence therefore 20% is double that, which is 72 pence.

And the final step for this part today was to subtract that 20% from the total.

So that gives us a new price of 2.

88 pounds, but we're not finished there if you were asked, how much does she pay in total? So the final part of the problem was to add the two new prices together.

So the new price of 60 pence for the bananas and 2.

88 pounds for the cake added together is equal to 3.

48 pounds.

So we can see that she actually got both items for less than the price of the cake in the first place.

Now we are going to look at a different strategy, for the finding a percentage of an amount.

So here we have a toy car which costs 3.

80 pounds the original price, but it has 25% off that price.

So here's our first strategy.

This is the one that we've been using already.

So if it's been reduced by 25%, then we find 25%.

We know that's the same as one quarter.

So we divide the whole 3.

80 pounds by four to give us 25% and that is 95 pence.

Then we're going to subtract the 95 pence from the original price to give the new price of 2.

85 pounds.

So that's the strategy that we've been using.

Lets look at another approach, so strategy B.

So if we know that the price has been reduced by 25%, then the new price is 75% of the old price.

25% plus 75% is equal to 100%.

So this time, rather than finding 25% and subtracting it, we can just find 75% and that will give us the new price.

So to find 75% of 3.

We know that it's three times greater than 25%.

So you can find 25% by dividing 3.

80 pounds by four, and then multiplying it by three, which gives us 2.

85 pounds.

So in each of the strategies we end up with the same price, but we've approached it in two different ways.

Strategy A, finding the percentage taken off and subtracting it.

And Strategy B finding the new percentage price.

So now you're going to have a go at using both of the strategies to match the offer to the correct price.

So you're starting with 20% of 36.

50 pounds.

I'd like you to use strategy A strategy B to figure out which of these prices that matches up to, and then do the same for the teapot and the pen.

Pause the video now and do your working out.

50 pounds and then subtracting it from the whole.

So I calculated that 20% was 7.

30 pounds, subtracted it from 36.

50 pounds, which gave me a new price of 29.

20 pounds.

The other strategy is to know that if 20% has been taken off, then the new price is 80% of the original price.

So I found 80% of 36.

50 pounds by finding 10% and then multiplying it by eight.

And that gave me the new price of 29.

20 pounds.

So same answer, two different strategies.

So I can match this one to 29.

20 pounds.

Onto the teapot strategy A I found 25% of 19.

20 pounds, 25% is equal to one quarter so I divided 19.

20 pounds by four, which gave me 4.

80 pounds, subtracted that from the whole to give me a new price of 14.

40 pounds.

The other strategy was knowing that if 25% has been taken off, then the new price is 75% of the whole.

And to find 75%, I found one quarter and multiplied it by three, which also gave me 14.

40 pounds.

And the final one, strategy A, finding 35% of 7.

60 pounds, which is 2.

66 pounds and subtracting that from the whole.

Remember to find 35% I could have found 1% and multiplied it by 35, which gave me the 2.

66 pounds, and then I subtracted it from the original price.

And then the second strategy, if 35% has been taken off, then the new price is 65% of the whole, which again is 4.

94 pounds.

This one was just the odd one out here.

Now it's time for you to do some independent learning.

So pause the video and complete your task and then click restart once you're finished and we'll go through the answers together.

So question one, you were given two balls of chocolate in two different shops and asked which one offered more chocolate.

So each bar weighs 300 grammes.

In the first shop you were given 25% extra.

And in the second shop you would get being given 1/3 extra.

Now you may have looked at these two percentage and fraction and thought, "actually I already know which one is greater." But the question is "how do you know?" So you have to prove it.

So I took the first one and I first of all found 25% of 300 grammes, which is 75 grammes and then I added it onto the 300 grammes because it was extra, 25% extra.

So in the first shop, we ended up with 375 grammes.

In the second shop, I found 1/3 of 300, which is 100 and then added that to the original weight, which means that the new chocolate bar was 400 grammes.

So this one offers more chocolate.

And what you may have, your initial thoughts might have been that 1/3 is around 33%, So I know that that's going to be greater than 25% or the other way round, you may have said 25% is 1/4, and I know that a quarter is less than 1/3.

So it's always good to have those mathematical thoughts in the first place to help you with your estimation.

But then it's about proving that you are correct.

On to question two, so this time the chocolate bars have a different original mass.

So in the first one is 400 grammes and the second one is 360 grammes.

So we're looking at 25% extra on top of 400 grammes.

So 25% of 400 grammes is equal to 100 grammes.

And then adding those back together means that the new chocolate bar weighs 500 grammes.

The second one we find 1/3 of 360 which is 120 and add it to the original weight, which gives us a new weight of 480 grammes, meaning that the first chocolate bar offers more chocolate.

And onto the final question.

So we're comparing test scores, Laura got 75% on a grammar test, which was out of 96 marks.

Mo sat a different test which was out of 80 marks and he got 4/5 correct.

So he got more correct answers.

So I've represented this using bar models.

So here I've got Laura's results, the total was out of 96, then she got 75% correct.

For Mo the total was out of 80 and he got 4/5 correct.

You may have approached this in a few different ways.

You might have thought, I want to deal with both percentages or both fractions so you may have converted 75% to 3/4, or you may have converted 4/5 to 80%, or you may have just kept them as they are.

So now we need to work out how many marks they got.

So Laura got 75% of 96, which is 72 marks and Mo got 4/5 of 80, which 64 marks.

And we can see that Laura got more correct answers.