Lesson video

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

We'll be looking at multiplicative relationships, one of my favourites, and that's because it appears so much in real life.

We'll be looking at all these different and wonderful ways on how we can see our multiplicative relationship.

So I hope you enjoy the lesson.

Let's make a start.

Hi, everyone and welcome to this lesson on decrease by percentage and it's under the unit understanding multiplicative relationships percentages and proportionality.

And by the end of the lesson you'll be able to calculate percentage changes.

In this lesson we'll be looking at decrease.

Now proportion is a part to whole, sometimes part to part comparison, and if two things are proportional, then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.

Our lesson will be broken into three parts.

We'll be looking at decreasing an amount by a percentage, using a multiplier, and then mixed percentage change.

So let's have a look at decreasing an amount by a percentage.

Here's a bar model showing 600 pounds.

Now if someone said 10% is lost, how much money would there be in total? Well, first of all, let's divide 100% into 10 equal parts.

From here each part clearly represents 10%, so that means each part is 60 pounds.

Now we're subtracting 10% because we've lost 10%.

So how much do we have left? Well, hopefully you can spot.

We only have 540 pounds left as we lost our 60 pounds.

So decreasing 600 pounds by 10% gives us an answer of 540 pounds.

But what percentage of 600 does 540 represent? Well, 540 is 90% of our 600.

Remember we lost that 10%.

And these two statements represent exactly the same amount.

Find 90% of 600 or decrease 600 by 10%.

So now what I want you to do is have a look at this bar model.

What questions could you write for this bar model? Well, you could say decrease 800 pounds by 40%, or perhaps you could say find 60% of 800 pounds.

Both of these represent exactly the same question and answer.

Now what I want you to do is have a look at a quick check.

What I want you to do is write three questions for each of these bar models.

See if you can give it a go.

Press pause if you need more time.

Great work.

So let's see what you wrote.

Well, you could write decrease 240 pounds by 40%.

You could write find 60% of 240 pounds or what percentage is 144 pounds of 240 pounds? For B, you could say decrease 90 by 20% or maybe find 80% of 90 pounds.

Or perhaps what percentage is 72 pounds of 90 pounds? Well done.

Now what I want you to do is have a look at another check question, but still using our bar models.

We're asked to fill in the missing information and write three questions to represent these bar models.

See if you can give it a go.

Fill in that information and press pause for more time.

Great work.

So let's see how you got on.

Well, hopefully you can spot because 100% is 150 pounds.

This has to be 70%.

So that means we know this has to be 45 pounds.

But what questions did you write? You could say decrease 150 by 70%, find 30% of 150 or maybe what percentage is 45 pounds of 150 pounds? Let's have a look at D.

Hopefully you spotted if you know 160 pounds is 100%, this represents 25%.

So therefore the remaining quantity has to be 120 pounds.

What questions could you write? Well, you could write decrease 160 by 25%.

You could write find 75% of 160, or you could even write what percentage is 120 pounds out of 160 pounds.

Well done if you done those.

So we can use bar models to show a decrease.

So let's do something together.

Firstly, using square gridded paper, I want you to draw a bar using 10 squares, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

From here I'm gonna represent this to be 120 pounds, so I'm gonna indicate this as 100%.

You can press pause at any time if you want to do this a little slowly.

Now from here, what percentage does each of the 10 squares represent? Well, hopefully you can spot each square represents 10%.

So that means how much money is 10%? Well, each square's got to be 12 pounds.

Now what we're going to do is decrease 120 pounds by 20%.

So here's my 20% and I'm simply going to remove this 20% as you can see in my bar model.

Now my question is what amount is a decrease of 120 pounds by 20%? Well, if you work this out, 120 subtract two lots of our 12 gives us 96.

So what does this mean? Well, it means we've decreased 120 by 20%, giving me 96 pounds, or we've worked out 80% of 120, which is 96.

Really well done.

Now what I want you to do is I want you to draw a bar model to work out and represent 20 being decreased by 30%.

Then I want you to draw another bar model to work out and represent 60 being decreased by 45%.

Using squared or gridded paper will help you out.

See if you can give it a go and press pause for more time.

Great work.

So let's see how you got on.

Well, my bar model shows 100% is equal to 20.

So that means 10% is two.

That means I've shown 30% to be three lots of our two.

Now working this out decreasing 20 by 30% gives me 20, subtract my six, which is 14.

Part B, I'm gonna draw my bar model here.

So my 100% represents 60, so 10% is six.

Now given the question wants me to decrease by 45%, you can see 10% is six and 5% has to be three.

So you can see my four lots of 10%, my one lot of 5%, thus giving me a decrease of 45%.

This gives me an answer of 60, subtract my 27, which is 33.

Really well done if you've done this.

So now it's time for your task.

Pair up the equivalent questions, see if you can give it a go.

Press pause one more time.

Well done.

So let's move on to question 2.

You have to fill in the bar model and the missing information.

See if you can give it a go.

Press pause for more time.

Great work.

So let's move on to question three.

Question 3a wants you to draw a bar model to work out and represent 124 pounds being decreased by 40%.

For B, it wants you to draw a bar model and work out and represent 72 pound being decreased by 35%.

See if you can give it a go.

Press pause for more time.

Well done.

Question 4 says both Sam and Aisha are given this question, decreased 300 by 65%, who's correct? And can you explain what the other pupil calculated? See if you can give it a go.

Press pause for more time.

Well done.

Let's go through these answers.

Question 1, hopefully you've got this pairing.

Massive well done if you got this one right.

For question 2, remember we know 400 represents 100%.

So that means we have our 30% represented.

So it's the same as 70% of 400.

Both of these questions are the same, giving us a final answer of 280.

For B, we know 88 represents the 100%.

So the 20% is our two lots of 8.

8.

So that means 88 being decreased by 20% is the same as 80% of 88, giving us an answer of 70.

4.

Now 64 is our 100% and 64 being decreased by 35% is the same as 65% of our 64, thus giving us an answer of 41.

6.

Really well done if you got this one right.

For question 3, hopefully you worked out decreasing 124 pounds by 40%.

Gives us a final answer of 74 pounds 40 pence.

Very good if you got this one right.

Now the next one for drawing our bar model decreasing 72 pounds by 35% gives us this calculation giving us an answer of 46 pounds and 80 pence.

Massive well done if you got this one right.

Question 4, who's correct? Aisha is correct.

She's worked out 35% of 300, which is the same as decreasing 300 by 65%.

Now what Sam worked out? Now Sam is incorrect.

As Sam has worked out, 65% of 300 or Sam has worked out a decrease of 300 by 35%.

Well done if you spotted those.

Great work everybody.

So let's move on to the second part of our lesson, which is using a multiplier.

Now here we have a double number line showing 100% is 450.

What is 10% of our 450? Well hopefully you spot 10% of our 450 is 45, so what's 20%? Well it'd be 90, so on and so forth.

So what does a decrease of 20% to 450 look like in our number line? Well, you could just subtract 20%, giving us 80%.

So if we know 20% is 90, we subtract 90 from our 450.

Now this approach works to find a percentage decrease, but now let's see if we can use our multiplier given that we know there is a multiplicative relationship.

To decrease 450 by 20%, what do you think we multiply 100 by to give 80? Well the multiplier has to be 80 over 100 which is 0.

8.

So if you multiply 100 by 0.

8, that means you get your 80%.

So that means given that multiplicative relationship you have to multiply 450 by 0.

8 giving us 360.

So using a multiplier is a much more efficient way.

It really does use that understanding of the multiplicative relationship in order to decrease an amount by a percentage.

Now this bar model shows 780 is decreased by 21%.

Do you think you can work out what that multiplier is? Well hopefully you've spotted 79 over 100 would give us 79%.

Remember, 79% of a value is the same as decreasing that value by 21%.

So multiplying by 0.

79 gives me my final answer of 616.

2.

It's so important to recognise decreasing 780 by 21% is the same as finding 79% of our 780.

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

Now the double number line shows a decrease of 120 by 52% and you're asked to fill in that missing information.

See if you can give it a go.

Remember, think, if a number's been decreased by 52%, what are you actually finding? Well hopefully you've spotted we are finding 48% as something is decreased by 52%.

So therefore the multiplier must be 0.

48, giving me a final answer of 57.

6.

Great work if you spotted this.

So removing the double number lines, can you work out the multiplier to decrease any amount by 35%? Well to do this, you're simply multiplying by 0.

65 because it's a decrease of 85%.

But what I want you to do is have a little think.

Can you explain how to quickly find this multiplier? Well given 35% as a decimal as 0.

35 and 100% as a decimal as 1, subtracting as it's decrease gives us a 0.

65 multiplier.

Really well done if you got this? It's also important to remember decreasing anything by 35% is the same as working out 65% of a number.

So now it's time for your check.

I want you to identify the multiplier when any number is decreased by 40%, decreased by 34%, so on and so forth.

See if you can give it a go and press pause if you need more time.

Well done.

So let's see how you got on.

Well, decreasing by 40% is the same as finding 60% of something.

So that means your multiplier is 0.

6 or 0.

60.

Decreasing by 34% means you're finding 66% of something.

So that means the multiplier is 0.

66.

Decreasing something by 78% means you're finding 22% of something.

So the multiplier is 0.

22.

Decreasing by 16% means you're finding 84% of the value.

So our multiplier is 0.

84.

Decreasing by 4% means you're finding 96% of something.

So the multiplier is 0.

96.

Decreasing by 8% means you're finding 92% of something.

So you're multiplying by 0.

92.

This is a tough one.

Decreasing by 2.

3% means you're finding 97.

7% of something.

So your multiplier is 0.

977.

Well done if you go this one right.

So using a multiplier and the associative law makes finding the percentage of an amount so much easier without a calculator.

For example, if we're asked to decrease 48 by 68%.

Well we know this is the same as finding 32% of 48.

So that means we need to work out 48 x 0.

32, a decrease of 68%.

Using the associative law we've got 48 x 32 x 0.

01.

Remember, it's easy to multiply by integers.

I'm going to use an area model to work it out.

So I know 48 x 32 is 1,536.

Multiplying this by my 0.

01 gives me an answer of 15.

36.

So decreasing 48 by 68% gives me 15.

36.

Now what I want you to do is a quick check.

I'm want you to work out the amount when 342 pounds has been decreased by 88%.

Show all your working out, press pause for more time.

Great work.

Let's see how you got on.

Well this is the same as working out 12% to 342.

So we need to work out 342 x 0.

12.

Using the associative law just so I've got some integers when I'm multiplying, I'm going to use my area model.

342 x 12 gives me 4,104.

Multiplying by 0.

01 gives me 41.

04.

So 342 decreased by 88% gives me 41.

04.

Fantastic work if you got this one right.

Now it's time for your task.

I want you to match the statements with the calculation.

See if you can give it a go.

Press pause for more time.

Really well done.

So let's move on to question 2.

Question 2 wants you to work out the amount of money when 94 pounds has been decreased by 47%.

And question 3 wants you to work out the amount of money when 162 pounds has been decreased by 28%.

See if you can give it a go.

Press pause one more time.

Great work.

Let's go through question 4 and 5.

Question 4 says, a T-shirt was reduced by 24% in a sale.

How much is the T-shirt now? And question 5 says, Izzy has been running obstacle courses and her time improves each time in practise.

Her last personal best was 134 minutes.

She improved her personal best by 13%.

What's her new personal best? Well done.

Let's see how you got on.

Well matching these questions with our answers, you should have got these.

Huge well done if you got this one right.

For question 2, did you work out these amounts? Well, 94 x 0.

53 shows the decrease of 47%, which is 49.

82.

For question 3, 162 x by 0.

72 shows a decrease of 28%, which is 116.

64.

For question 3, it's reduced by 24%.

So 25 x 0.

76 shows the reduction 24%, which is 19 pounds.

And Izzy improved her time by 13%.

So that means it's 134 x 0.

87.

So Izzy ran her new personal best to be 116.

58 minutes.

Well done Izzy.

Great work everybody.

So let's have a look at the last part of our lesson looking at mixed percentage change.

Now remember, double number lines are excellent visual tools to see percentage increase.

For example, increasing any number by 35%, we multiply by 1.

35 and when we're decreasing a number by 59%, we're simply multiplying by 0.

41.

Now Aisha and Alex are both having a conversation.

When I increase, I add the percentage as a decimal to 1 and then Alex spots, well when I decrease I subtract the percentage as a decimal from 1.

Can you explain why this works? Well, the original amount is always 100% or 1 as a decimal.

So increasing any amount by a percentage simply means you're adding the decimal equivalent to 1.

So let's explain what Alex meant.

Well the original amount is always 100% or 1 is a decimal.

So decreasing any amount by a percentage simply means you're subtracting the decimal equivalent from 1.

So now we've summarised increase and decrease.

What I want you to do is identify the multiplier of the following mixed percentage change questions.

See if you can give it a go and press pause one more time.

Great work.

Let's see how you got on.

Well, increasing by 40% is multiplying by 1.

4 or 1.

40.

Decreasing by 34% is multiplied by 0.

66.

Remember, something's decreased by 34%.

There's only 66% left.

Increasing by 78% is multiplying by 1.

78.

Decreasing by 16% is multiplying by 0.

84.

Increasing by 4% is multiplying by 1.

04.

Increasing by 8% multiplied by 1.

08.

And decreasing by 3.

2% is multiplying by 0.

968.

Really well done if you've got this one right.

Now let's have a look at matching some statements with our understanding of mixed percentage change.

See if you can give these a go and press pause for more time.

Well done.

Let's see how you got on.

Well, increasing 400 by 80% is 400 x by 1.

8 and decreasing 600 by 25% is the same as 600 x 0.

75.

Working out 75% of 600 is exactly the same as decreasing 600 by 25%.

So it's 600 x 0.

75.

Decreasing 400 by 80% is 400 x 0.

2 and working out 20% to 400 is exactly the same as decreasing 400 by 80%.

So we have these equivalent calculations.

Equating them to the answer we should have these.

Really well done if you got this one right.

Excellent work everybody.

So now it's time for your task.

I want you to tick the calculations that correctly represent each statement.

See if you can give it a go.

Press pause for more time.

Well done.

Let's move on to the second question.

Question 2 says, Aisha has 20 pounds to buy a present for her dad and there is a sale on at the shop.

Below some items with their original prices and the discounts to be applied.

Which of the items can she afford? And for B, for those she can't afford, what discounts would she need so she can afford any item in the shop.

See if you can give them a go.

Press pause if you need more time.

Well done.

So let's move on to question 3.

And question 3 says if you increase an amount by 13% and then decrease it by 13%, you get the same value you started with.

Explain whether Laura is correct.

See if you can give it a go.

Press pause one more time.

Great work.

So let's move on to these answers.

Let's see how you got on.

Here are the only correct statements and calculations.

Great work if you've got this one right.

For question 2, hopefully you spotted she can only afford the T-shirt, scarf, or the hat.

For B, Aisha would need these discounts.

A minimum discount of 33.

3% to two decimal places discount for the shorts and the jacket would have to be a minimum discount of 60%.

Well done if you've got this one right.

For question 3, Laura is not correct.

It can be explained in a few different ways.

Increasing an amount by 13% then gives you a new different amount.

And this new different amount is then regarded as 100%.

Thus finding 13% of this new different amount is not the same as 13% of the original amount.

Another way is to use multipliers and an amount increased by 13% and then decreased by 13% is the same as multiplying by 1.

13 and then multiplying by 0.

87.

And using the associative law this is the same as 0.

9831.

In other words, this means the final answer is 98.

31% of its original amount, not 100% of the original amount.

Well done if you spotted this? Great work everybody.

So let's summarise all the wonderful work we did in our lesson.

Well, we've looked at different representations of percentage increase and decrease.

Bar models and double number lines are both really visual helpful approaches to work out increase.

However, using a multiplier is a good approach to work out any percentage increase or decrease.

And it is so important to remember the same question can be asked but in different ways.

For example, decreased 70 by 12% is the same as 88% of 70.

Fantastic work everybody.

It was great learning with you.