Lesson video

Hi, everyone, my name is Ms. Cou, and I'm really happy to be learning with you today.

In today's lesson, we'll be looking at percentages.

And percentages is so important as they appear so much in everyday life.

I really hope you enjoy the lesson.

So let's make a start.

Hi, everyone, and welcome to this lesson on percentage profit and loss under the unit percentages.

And by the end of the lesson, you'll be able to calculate percentage profit and percentage loss.

So let's have a look at these keywords.

What is percentage profit? Well, percentage profit is the increase when referencing something that is sold for more than the cost price given as a percentage of the original amount.

And percentage loss is the decrease when referencing something that is sold for less than the cost price given as a percentage of the original amount.

We'll be looking at these keywords through the lesson.

Today's lesson will be broken into two parts.

First of all, we'll be reviewing percentage change, and then we'll be looking at percentage profit and loss.

So let's make a start reviewing percentage change.

Now, at the beginning of the year, Alex and Andeep did an assessment.

And then they did a second assessment a month later.

Now, the Oak teacher wrote these comments in the book.

So if you have a look what Alex scored in the first assessment, he got 80, and in the second assessment, Alex got 120.

And the teacher wrote, "Good progress." Andeep got 50 in the first assessment, and in the second assessment got 80, and the teacher wrote, "Superb progress." Alex says, "Why does Andeep's say 'Superb progress' and mine says, 'Good progress' when I got more marks than him?" What do you think? Have a little think.

Well, let's visualise this using bar models.

We're gonna look at Alex's original mark first.

Well, his original mark was 80, and it increased by 40 to give 120.

Andeep's original mark was 50, and this increased by 30 to give 80.

So using a bar model, we know the original mark for Alex was 80.

And using a bar model for Andeep, we know the original mark was 50.

Using a bar model, I've split it into five equal parts.

So that means each part is 16, and for Andeep, I've done the same again, I've split it into five equal parts so I know each part is 10.

Now, given the fact that Alex's mark increased by 40, that means this is the fraction it's increased by or the proportion it's increased compared to his original mark of 80.

Looking at Andeep's, this is the fraction or the proportion of marks that increased for Andeep using the original mark of 50.

So you can see that although Alex's mark has increased by more than Andeep's, using the proportional of the original marks, you can see Andeep's increased more.

You can see that using the bar model.

Sometimes it's appropriate to consider percentage change rather than exact numerical change.

In other words, looking at the number of marks Alex has increased by was 40, and looking at the number of marks Andeep increased by is 30, that doesn't really tell you the progress.

So working out the percentage change is more appropriate.

So you can see, Alex has actually improved by 50%, but Andeep improved by 60%.

So Andeep made 60% progress from his first assessment, and Alex made 50%.

Both very good improvements, but you can see why the Oak teacher wrote, "Superb progress" for Andeep.

We can also represent these problems on double number lines to make it easier to see that percentage change.

So we know 100% will be the original, as we want to know what percentage of the original the increase is.

So we're going to say the 100% is 80 marks, given the fact that Alex got 80 marks in his first assessment.

Given the fact he went up 40 marks, we need to find out, well, what is that percentage increase? What if we multiply 80 by D of 120? Well, that multiply was 120 over 80, so we're going to do the same to the percentage.

Multiply 100 by 120 over 80.

So you can see we've got a 50% increase.

So calculating the percentage change, we know it's a 50% increase.

Now let's have a look at Andeep.

100% will be the original as we want to know what percentage of the original the increase is.

So in the first assessment, Andeep got 50, and the second assessment he got 80.

So what is that new percent? Well, the multiplier would be 80 over 50, so that means the multiplier for our percentage would also be 80 over 50, giving us the new percentage to be 160%.

That means we can see our percentage change, it's 60%.

Now we can see that as a percentage of their original marks, Andeep's improvement was greater.

I also want to transfer the same information into a ratio table.

100% was the original mark scored for Alex, and then we're going to find out, well, what would be 120 marks as a percentage? Let's examine that multiplier a little bit more.

The reason why we divide by 80 is because we're finding what one mark is as a percentage.

And then from here, we can multiply by 120 to work out what 120 marks is as a percentage.

That's how that multiplier works.

So you can see, from our ratio table, it confirms that Alex has increased by 50%.

The multiplicative relationship allows you to find the amount as a percentage and multiply accordingly.

Now, I want you to use the same approach, but with Andeep.

I want you to use this in a check question.

Fill in that ratio table and show you're working out to show Andeep made a progress of 60%.

Give it a go.

Press pause if you need more time.

Great work.

Let's see how you got on.

Well, we know the original mark was 50, so we're calling that 100%.

When we divide by 50, we know what one mark is as a percentage.

We know in the second assessment he got 80 marks.

So that means we multiply by 80, giving us 160% is 80.

So this shows Andeep's score increased by 60%.

Double number lines and ratio tables are good approaches to find the percentage change.

And in addition, we can also use our knowledge on multipliers.

Here we have Aisha and Jacob have both bought of a T-shirt in a sale.

They know the original cost and how much they paid.

Who got the best percentage discount? Well, Aisha said, "Mine was 20 pounds" and she paid 15 pounds for it.

And Jacob says his was 30 pounds, and he paid 24 pounds for it.

So let's see what we can work out.

An amount of 20 pounds is 15 pounds, so we need to find out what proportion of the 20 pounds is that 15 pounds.

Well, to work it out, let's look at that word "of," and we're going to replace it with multiplication.

So p multiply by 20 is equal to 15 pounds.

Then I'm gonna rearrange to find p.

So, therefore, p is equal to 15 over 20.

So, therefore, p is equal to 0.

75.

Remember, this shows the proportion of 20 pounds, which is 15 pounds.

In other words, to convert p into a percentage, we're going to multiply it by 100.

So that means we know p as a percentage is 75%.

So that means Aisha got a 25% discount on her T-shirt because she only paid 75% of the 20 pounds.

Now let's have a look at Jacob.

Let's work out Jacob's.

Well, we need to find out what proportion of 30 pounds is 24? We can replace that word "of" with multiplication to give us p multiplied by 30 equals 24 pounds.

Then rearranging to find p, p is equal to 24 over 30, which is 0.

8.

Now writing this proportion as percentage, we're gonna times it by 100, thus giving me 80%.

So we know 80% of 30 pounds is 24 pounds.

What discount did Jacob get? Well, Jacob got a 20% discount on his T-shirt.

So that means, Aisha got the best percentage discount.

She got 25% off her T-shirt and Jacob only got 20% off of the T-shirt.

Great work, everybody.

So now let's have a look at a check.

I'll do the first part and I'd like you to do the second part.

An Oak teacher's car insurance has increased from 62 pounds to 76.

88 pounds.

What was the percentage increase? Well, let's see what we can do.

We do know a proportion of 62 has given us 76.

88 pounds.

So let's replace that word "of" with multiply.

So our calculation is p multiply by 62 is equal to 76.

88.

Dividing so we can find out the value of p, we now have 1.

24, and I'm gonna change this into a percentage.

So that means I have 124%.

So in other words, 124% of 62 is 76.

88 pounds.

So what's the increase? Well, that means the increase is 24%.

Now, I'd like you to do a question.

Alex has 600 millilitres of water in his water bottle.

He drinks some water and now has 440 millilitres of water left.

What percentage of the water did he drink? See if you can give it a go.

Press pause for more time.

Great work, everybody.

So let's see how you got on.

A portion of 600 gives us 444.

Then I'm gonna rewrite "of" with multiplication, giving me p multiply by 600 is 440.

Rearranging, I've got p is equal to 0.

74.

So that means as a percentage, p represents 74%.

In other words, 74% of 600 is 444.

That means Alex has only 74% leftover, which means he's drank 26% of his water.

Well done if you got this one right.

Great work, everybody.

Now it's time for your task.

Without a calculator, work out each percentage change.

The first has been done for you.

See if you can give it a go.

Press pause if you need more time.

Great work.

Let's move on to question 2.

Use a calculator to work how each percentage change to the nearest 1%.

See if you can give it a go.

Press pause for more time.

Well done.

Let's move on to question 3.

The Oak teacher has a cat and its mass was 4.

8 kilogrammes.

The cat now has a mass of 6 kilogrammes.

Work out the cat's percentage gain in mass.

And for question 4, crayons used to come in boxes at 24, but now they come in boxes of 18 for the same price.

What is the percentage loss of crayons? See if you can give them a go.

Press pause for more time.

Great work.

Let's move on to question 5.

Aisha wants to increase the size of her vanilla cake and here is the original recipe, 125 grammes of self-raising flour, 100 grammes of butter, 115 grammes of sugar, and two eggs.

But she only has the following ingredients in her cupboard.

150 grammes of flour, 150 grammes of butter, and 144 grammes of sugar, and four eggs.

But what is the maximum percentage change she can increase her cake by? See if you can give it a go.

Press pause for more time.

Great work, everybody.

So let's move on to these answers.

I'd like you to mark these answers and press pause if you need more time.

Well done.

For question 2, I'd like you to mark these answers and press pause if you need more time to have a little look and mark.

Great work.

For question 3, let's work out that percentage gain.

You should have done 65 by 4.

8, which is 1.

25.

So that means there's a percentage gain of 25%.

For the crayons, well, you should have done this calculation, 18 divided by 24 which is 0.

75.

So that means there's a percentage loss of 25%.

For question 5, well, let's have a look at raising flour.

She's only got enough flour to increase the cake by 20%.

For butter, she's only got enough butter to increase the cake by 50%.

She only has enough sugar to increase the cake by 25%, two significant figures.

And for eggs, she's got enough eggs to increase the cake by 100%.

So that means, overall, the maximum percentage she can increase the cake by is 20%.

Well done if you got this one right.

Great work, everybody.

Now it's time for the second part of our lesson, percentage profit and loss.

Now, percentage profit is the increase when referencing something that is sold for more than the cost price given as a percentage of the original amount.

And percentage loss is the decrease when referencing something that is sold for less than the cost price given as a percentage of the original amount.

So far we've looked at three approaches to find percentage change, double number lines, ratio tables, and multipliers.

My favourite is multipliers.

Any one of those approaches can be used to work out percentage profit or percentage loss.

However, we can also use a formula based on these methods.

Percentage change is equal to the new amount, subtract the original amount over the original amount.

Let's look at a question and a couple approaches to find the answer.

For example, a phone was bought for 380 pounds and is sold for 494 pounds, and we're asked to work out the percentage profit.

I'm going to be using multipliers first.

Well, we need to find out what proportion of 380 gives 494.

Rearranging it, p is equal to 494 divided by 380, so that means p is equal to 1.

3.

Working this out, we know p as a percentage is 130%.

In other words, 130% of 380 is 494.

So that means, there is a percentage profit of 30%.

Another way to work it out is using the formula.

So remember the formula states, percentage change is equal to the new amount.

Subtract the original amount over the original amount.

That means, 494 subtract 380 over 380, is equal to 114 over 380, which works out to be 0.

3, which works out to be a 30% percentage profit.

So both methods show the increase of 30%.

Which method do you prefer? For me, I enjoy using the multiplier, but I also see the benefit in using the formula too.

Both have their advantages and disadvantages.

Using multipliers allows you to calculate the percentage profit quickly, but don't forget to subtract 100% in order to give the profit.

And using the formula might take a lot longer, but there is no need to subtract as the final answer is the percentage profit.

Now let's have a look at another question.

I want you to use multipliers for this.

A sound system was bought for 260 pounds and sold for 143 pounds.

Work out the percentage loss.

See if you can give it a go.

Press pause for more time.

Well done.

Let's see how you got on.

Well, using multipliers, we know the proportion of 260 is 143.

Working out the value of p, we know it's 0.

55.

So that means as a percentage, it is 55%.

So what is our percentage loss? The percentage loss is 45%, because 55% of 260 is 143.

So that means it's a 45% loss.

Now what I'm going to do, I'm gonna use the formula.

And the formula states the new amount, subtract the original amount over the original.

The new amount is 143, subtract on 260 over the 260.

This gives us negative 117 over 260, and then it shows me my percentage as negative 45%.

This negative indicates a percentage loss.

So we have a percentage loss of 45%.

So which method do you prefer now? Both again, have their advantages and disadvantages.

Using multipliers allows you to work the percentage as a decimal quickly, but with the percentage loss, it is important to remember to subtract this from 100.

Now using the formula might take a little bit longer, but there is no need to subtract as the final answer is negative, showing that it is a percentage loss.

Great work.

Let's have a look at a check.

Four puzzle shops bought and sold the same puzzle box for different prices.

Put the puzzle shops in ascending order according to profit.

See if you can give it a go.

Press pause if you need more time.

Great work.

Let's see how you got on.

Well, the percentage profit for Puzzle Me is 25%.

The percentage profit for Puzzlemania is 30%.

The percentage profit for Brainiac is 50%.

And the percentage profit for Puzzle Shop is 10%.

So, in ascending order we have Puzzle Shop, Puzzle Me, Puzzlemania, and Brainiac.

Really well done if you got this right.

Next, let's have a look at another check.

Which of the following has a percentage loss greater than 20%? So you can give it a go.

Press pause if you need more time.

Well done.

A.

had a percentage loss of 25%, so that means it made a greater loss than 20%.

For B.

they had a percentage loss of 12.

5%, so the percentage loss is not greater than 20%.

For C.

the percentage loss was 10%.

This does not have a percentage loss greater than 20%.

And lastly, for D.

has a percentage loss of 21%.

That percentage loss is greater than 20%.

Well done if you got these right.

Now, it's time for your task.

I want you to work out the percentage profit or percentage loss for each of the following items. See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question 2.

A shop manager uses a spreadsheet to work out the profit or loss she's made for each item.

She has to reprice the teddy bear so that her overall percentage profit of all items is 10%.

How much must she reprice the teddy bear for? And what integer profit must she make on the teddy bear? See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question 2C.

Would increasing the sale price of each item by 50p give a greater overall percentage profit than increasing each selling price by 10%? I'd like you to explain your answer.

See if you can give it a go.

Press pause if you need more time.

Great work.

Let's see how you got on.

Well, for question 1, you should have had all of these different percentage profits or loss.

Press pause if you need more time to mark.

Well done.

Move on to question 2.

We should have worked out that the total purchase price is 19.

70 pounds, and if we were to multiply by 1.

1, in other words, an increase of 10%, we need our total selling price to be 21.

67 pounds.

So that means she must price the teddy bear at 6.

64 pounds.

Now, working down that percentage profit from the teddy bear, well, it has to be a 15% profit.

Well done if you got this one right.

Well, for question 2C, "Would increasing the selling price of each item by 50p give a greater overall percentage profit than increasing each selling price by 10%?" Now, there are only five items. So increasing each item by 50p, means an overall increase of 2.

50 pounds.

Now, given the fact that we know the total purchase price is 19.

70 pounds, so that would give us a percentage profit of 12.

7%, to one decimal place.

Increasing all the items by 10% gives us a percentage profit of 10%.

So, therefore, increasing all the items by 50p is better profit.

Great work, everybody.

So, in summary, we found percentage changes, percentage profit, and percentage loss using double number lines, ratio tables, multipliers, and a formula for percentage change.

All have their advantages and disadvantages.

For example, when using the formula, the negative percentage clearly indicates a percentage loss.

Make sure you use an efficient approach when using a calculator and non-calculator questions.

Great work, everybody.

It was wonderful learning with you.