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Hi everyone, My name is Ms Koo, and I'm really happy to be learning with you today.
In today's lesson we'll be looking at percentages and percentages are so important as they appear so much in everyday life.
I really hope you enjoy the lesson, so let's make a start.
Welcome to this lesson on checking and securing understanding of percentage decrease.
It's under the unit percentages.
And by the end of the lesson, you'll be able to decrease an amount by a given percentage.
Now for the key words, we'll be looking at the word proportion and proportion is a part to whole, sometimes part to part comparison.
And if two things are proportional, then the ratio of the part to whole is maintained and that multiplicative relationship between the parts is also maintained.
Our lesson will be broken into three parts.
First we'll be looking at decreasing by a percentage, non-calculator.
Then we'll be looking at decreasing by a percentage with a calculator and finally, finding the original amount after a decrease.
So let's make a start.
Here is a bar model showing 600 pounds and if 10% is taken away, how much money would there be in total? Well first of all, let's divide our bar model into 10 equal parts.
Remember, 100% divided by 10 gives us our 10%, so we know each part is 10%.
Now in doing so, we also know each part is 60 pounds, so subtracting 10%, because we're taking away 10%, means we have 540 pounds left over because we've taken away that 10%, which we know is 60 pounds.
So how much money do we have left over? Well it's 540 pounds.
So decreasing 600 pounds by 10% gives us 540 pounds.
But what percentage of 600 pounds does 540 pounds represent? Have a little think.
Well, 540 pounds is 90% of 600 pounds.
These two statements represent exactly the same amount.
If somebody were to ask you to find 90% of 600 pounds, it's exactly the same as decreasing 600 pounds by 10%.
So what question do you think we should write for this bar model? Here, you can see originally 100% was 800 pounds.
What question do you think it would be? Well it could possibly be decrease 800 pounds by 40%, or the question could be find 60% of 800 pounds, both of them would equate to the same answer.
Now using this knowledge, let's check.
I want to check your understanding by asking you to match together the equivalent questions.
See if you can give it a go.
Press pause for more time.
Great work, let's see how you got on.
Well, decreasing 50 by 30% is the same as working out 70% of 50.
And working out 97% of 50 is the same as decreasing 50 by 3%.
And decreasing 50 by 20% is the same as working out 80% of 50.
Working out 145% of 50 is the same as increasing 50 by 45%.
Really good if you got this.
Now this approach can be applied to any percentage.
For example, here's a bar model showing 240 pounds.
I want you to think, how can we find 1% of 240 pounds in one calculation? Well, we'd simply divide 240 by 100 and this will give us our 1%.
So that means our 1% of 240 pounds is 240.
So decreasing 240 pounds by 3%, what do you think that would look like? Well it would mean identifying our 3% from our 100% and then simply subtracting it.
So what do you think the answer would be if you were to decrease 240 pounds by 3%? Have a little think.
Well, it would mean that we'd need to find what the quantity of 3% is.
So if we know 1% is 2.
40 pounds, 43% must be 2.
40 times by three, which is 7.
20 pound, then the decrease of 3% simply means we subtract 7.
20 pounds from our 240 pounds, thus giving us 232.
80.
So now we've decreased 240 pounds by 3%.
But what percentage is remaining when 100% is decreased by 3%? Have a little think and look at that bar model.
Well hopefully you can spot it's 97%, because subtracting 3% from 100% gives us 97%.
All I'm gonna do now is transfer exactly the same information from our bar model into our ratio table.
We know 100% is 240 pounds.
1% is found by dividing by 100 and we know that to be 2.
40 pound, and we are asked to work out 3%, remember ratio tables use that multiplicative relationship.
So that means 3% can be found by multiplying one by three to give me 7.
20 pounds.
So now we know 3% is 7.
20 pounds.
We can do exactly as we did before to work out a decrease of 3% by subtracting our 3% from 100%.
So subtracting 7.
20 pounds from our 240 pounds, giving us 232.
80 pounds as our 97%.
So you can use either a bar model or ratio table to help you decrease an amount by a percentage.
Now what I want you to do is have a look at this check question.
Jacob represents a decrease with a bar model and Aisha represents the same decrease with a ratio table.
Write the question they were answering using their working out and answer.
So even give it a go, press pause for more time.
Well done, let's see how you got on.
Well some possible questions could be decrease 640 by 11%.
You can see the 100% there was represented as the 640 pounds in Aisha's ratio table.
Another question could be find 89% of 640.
Same again, you can see this represented on either the ratio table or the bar model.
Really well done if you got this one right.
So if you were asked to decrease 640 by 0.
5%, which approach do you think is the most efficient, bar model or ratio table? I want you to explain why.
Because showing 1% on a bar model is really tricky to see, so showing 0.
5% on a bar model will be really hard to construct and hard to see, a ratio table is much more concise and efficient.
Now let's have a look at another check using our ratio table.
If we know 100% is 880, can you work out the following percentages? Remember that multiplicative relationship, press pause if you need more time.
Now there are lots of ways to work out these missing amounts, here's just one example.
Well, to work out 10% I'm going to divide 100% by 10.
To work out 5%, I'm going to divide my 10% by two.
To work out 1%, I'm choosing to divide my 10% by 10.
You can divide your 5% by five.
For me, I think it's just a little bit easier to divide by 10.
Then to work out 0.
5%, I'm going to divide my 5% by 10 to gimme 0.
5% and dividing my 1% by 10 gives me my 0.
1%.
So ratio tables are amazing because you can easily and efficiently work out an amount as a percentage and a percentage as an amount.
So now using our completed ratio table, do you think you can decrease 880 by 6.
5% and then decrease 880 by 3.
6? Well done, let's see how you got on.
Well decreasing 880 by 6.
5% can be done in a number of ways.
For me, I'm going to sum 5%, 1%, 0.
5% and then subtract it from 880.
So 6.
5% would be 44, add our 8.
8, add our 4.
4, giving me 57.
2 and then I'm going to subtract that from our 100%, which is 880, giving me 822.
8.
Alternatively, you can show it in one calculation.
880 subtract our 44, take away our 8.
8, take away our 4.
4, gives us exactly the same answer.
It's always nice to show a calculation written in a different way for understanding the reasons behind the calculation.
Well done if you got this.
For B, to decrease 880 by 3.
6%.
I'm going to multiply my 1% by three and then sum 0.
5% and 0.
1% and then I'm gonna subtract it from 880.
So 3.
6% can be worked out by three times 8.
8, add 4.
4, add 0.
88, gives me 31.
68.
Subtracting that from my 100%, which I know is 880, gives us the final answer of 848.
32.
Alternatively, you can do it in one straightforward calculation, 100 subtract three, multiply by 8.
8, subtract the 4.
4, subtract the 0.
88, gives you exactly the same answer.
Well done if you got this one right.
Great work everybody, so now it's time for your task.
I want you to fill in the ratio table and work out the following.
See if you can give it a go.
Press pause for more time.
Well done, let's move on to question two.
Jacob and Jun are answering the same question.
Jacob writes this calculation and Jun writes this calculation, what question do you think they were asked and I want you to explain their working out.
Can you also complete that ratio table to help you? See if you can give it a go.
Press pause for more time.
Great work, so let's move on to these answers.
Well, for question one filling in our ratio table, you could do it all sorts of different ways but you still would've had these amounts.
Well done, have you got this? From here, you can work out the following.
Press pause if you need more time to mark.
Well done.
For question two, well, let's have a look at each calculation.
Filling in that ratio table first, you should have these amounts.
So let's have a look at what question Jacob could have been asked.
Well we know 100% is 84 and 42 is clearly 50%.
So 100% subtract 50%.
Now the 0.
84 from our ratio table is 1%, and then we've got three lots of our 0.
1%, which is 0.
3%.
So therefore the question is asking Jacob to decrease our 84 by 51.
3%.
The next calculation from Jun, we know we have 40% illustrated by the four times the 8.
4, then we're adding 8% because it's eight lots of our 0.
84.
Then we're adding our 0.
5%, our 0.
2%, which gives us 48.
7% of 84.
So that could be a question which is being asked.
Hopefully, you realised decreasing 84 by 51.
3% is exactly the same as working out 48.
7% of 84.
So one question could be decrease 84 by 51.
3% or find 48.
7% of 84.
Really well done if you've got this.
Great work everybody, so now let's move on to decreasing by a percentage but using a calculator.
Now here we have a double number line and it shows 100% of 450.
So what do you think 10% would look like on our number line? Well, 10% would be right here and it would be 45.
So what do you think 20% would look like? 20% would be here and we know it to be 90.
Now what does a decrease of 20% of 450 look like on our number line? Well, we know a decrease of 20% means we're subtracting 20%, thus giving us 80%.
Given the fact that we know 20% is 90, we're subtracting 90 from 450, giving us 360.
This approach works to find percentage decrease.
But now let's see if we can use a multiplier, given we know there is always a multiplicative relationship with double number lines.
So to decrease 450 by 20%, what do you think we multiply 100 by to give 80? Well the multiplier would be 80 over 100, which is 0.
8.
So if you multiply 100 by 0.
8, you would get your 80%.
So because of that multiplicative relationship we're going to do the same with 450.
450 multiplied by 0.
8 gives us the exact same answer as before, 360, we've just used multipliers because of that multiplicative relationship.
This double number line shows 780 decreased by 21% and what I want you to do is identify what that missing multiplier would be and what the missing percentage and amount would be.
See if you can give it a go, press pause for more time.
Well done, let's see how you got on.
Well to decrease by 21%, that means the multiplier has to be 79 over 100, which is 0.
79.
So that means a decrease of 21% gives me 79%, so the multiplier's 0.
79.
So if I multiply 780 by 0.
79, I have my quantity or my amount, which is 616.
2.
Really well done if you spotted this.
So now it's time for your check, using the double number line, I want you to show a decrease of 120 by 52% and then I want you to fill in the missing information, see if you can give it a go.
Press pause for more time.
Great work, so let's see how you got on.
Well, to decrease 120 by 52%, that means the percentage would have to be 40% because if you decrease by 52%, there is only 48% left over, so the multiplier must be 0.
48.
So multiplying 120 by 0.
48 gives me 57.
6.
Well done if you got this.
So removing the double number lines, can you work out the multiplier to decrease any amount by 35%? I want you to have a little think.
Well the multiplier would be 0.
65, but can you quickly explain how to find this multiplier? Well, given the fact that 35% as a decimal is 0.
35 and we know 100% as a decimal is one, subtracting, because it's a decrease, gives us 0.
65 and that's a really nifty way to work out that multiplier when decreasing.
Another way to think about it is decreasing a number by 35% is the same as working out 65% of that number.
Well done, so let's have a look at a quick check.
I want you to identify the multiplier when any number is decreased by 22%, decreased by 45%, decreased by 89.
5%, decreased by 4.
1%, and decreased by 0.
23%.
That last one's a bit tricky.
See if you can give it a go, press pause for more time.
Great work, let's see how you got on.
Well, decreasing by 22% has a multiplier of 0.
78.
Think about it.
If you decrease something by 22%, there's only 78% left over.
Decreasing by 45% is the multiplier of 0.
55.
Decreasing by 89.
5% has a multiplier of 0.
105.
Decreasing by 4.
1% has a multiplier of 0.
959.
This is a great one well done, if you at this one, decreasing by 0.
23% has a multiplier of 0.
9977.
Great work if you've got this one right.
Now, let's move one step further, I want you to match each statement to the correct calculation.
See if you can give it a go, press pause for more time.
Well done, decreasing 16 by 61% is the same as 16 multiplied by 0.
39.
Decreasing 600 by 14% is the same as 600 multiplied by 0.
86.
Decreasing 400 by 14% is the same as 400 multiplied by 0.
86.
Decreasing 14 by 16% is 14 multiplied by 0.
84.
And decreasing 400 by 16% is 400 times 0.
84.
Great work if you've got this.
Now let's have a look at another check question, but in a real life context, an Oak teacher currently pays 156 pound per month to his electricity and gas supplier.
Now 78 pounds per month is also paid to a water supplier and he sees this advertisement.
All4One, we provide electricity, gas and water and we guarantee to save you 2.
45% from your current bills.
How much money will the Oak teacher save if he swaps to All4One supplier? Take your time, show your working out, you have a calculator, and press pause if you need.
Well done, let's see how you got on.
Well first of all, we know he pays a total of 234 pounds.
Now if he's guaranteed a discount of 2.
45%, let's see what that multiplier must be.
The multiplier to decrease by 2.
45% is 0.
9755.
So multiplying 234 by 0.
9755 gives him 228.
27 pounds, rounded to two decimal places.
Then we're gonna subtract it from what he currently pays.
So he makes a saving of 5.
73 pounds.
Great work if you've got this one.
Excellent work everybody.
So now it's time for your task.
For question one, you simply need to identify the multiplier given these decreases.
See if you can give it a go.
Press pause for more time.
Well done, question two wants you to use your calculator and to work out the following and I do want you to show your working out.
In other words, write the calculation that you've inputted into your calculator.
See if you can give it a go.
Press pause for more time.
Well done, let's move on to question three.
Question three shows a shop and it has a sale and all the items are reduced.
Andeep has 40 pounds.
Which three items can he buy with his 40 pounds and find as many answers as you can.
See if you can give it a go.
Press pause for more time.
Well done, let's see how you got on.
Well for question one, here are our multipliers.
Massive well done if you got this right, press pause if you need more time to mark.
For question two, here are all our working out and our answers.
Same again, press pause if you need more time.
Very well done if you got this one right.
Question three, well let's work out how much each item is after the discount.
Well the new price of our shorts would be 11.
40 pounds.
The new price of our T-shirt would be 17.
50 pounds.
The new price of our jacket is 39 pounds.
The new price of the hat is 7.
80 pounds.
and the new price of the scarf is 4.
75 pounds.
So what three items can he afford? Well he can buy any three items excluding the jacket, for example, shorts, t-shirt and scarf, shorts, scarf, and hat, any three items, but you just must not include the jacket.
Well done if you got this one right.
Great work everybody, so let's have a look at the last part of our lesson, finding the original amount after a decrease.
Now I'm thinking of a number and I decrease it by 15% and my new number is 55.
25, what was my original number? Well let's first of all think about what this represents.
My new number includes the original number, which was 100% and then a decrease of 15%.
So that means my new number is 85% of the number I first thought of.
So as a calculation, 85% of the number I first thought of is 55.
25.
Now I'm going to do is exchange this word of for multiplication.
So 85% times the number I first thought of is equal to 55.
25.
Now what I'm gonna do is use my percentage and decimal equivalents.
I know 85% is equivalent to 0.
85.
I'm gonna multiply this again by the number I first thought of to give me 55.
25.
Now I'm going to rearrange.
I'm going to rearrange so to work out what my value of N is.
55.
25 divided by 0.
85 gives me 65 was the first number I was thinking of.
This is a really important process.
To find the original amount after a decrease can be easily found by using the inverse of multiplication.
In other words, division.
And knowing the multiplier for a percentage decrease means you can undo the multiplication using division.
So now what I want you to do is match the question with the working out and then I'd like you to work out the answer.
See if you can give it a go, press pause for more time.
Well done, let's see how you got on.
Well, an amount has been decreased by 20% and is now 99 pounds.
How do we show that as a calculation? Well, it would be here, A multiplied by 0.
8 because it's a decrease of 20% is equal to 99.
An amount has been decreased by 45% and is now 99 pounds.
How do we work out the original amount? Well, it's A multiplied by 0.
55.
0.
55 shows you that 55% is remaining, in other words, a 45% discount.
Lastly, it says an amount which has been decreased by 55% is now 99 pounds, what is that original amount? Well it has to be A multiplied by 0.
45 is equal to 99.
So if something's decreased by 55%, that means there's only 45% left over.
Working this out and rearranging using that inverse of multiplication, for our first one we have A is equal to 99 divided by 0.
45.
The second one we have A is equal to 99 divided by 0.
55 and the third one is A equals 99 divided by 0.
8.
Working these out, we have 180, 220, and 123.
75.
Amazing work if you got this one.
Let's have a look at another real life check question.
With a calculator, a shop decreases its prices of chocolate by 2.
5% and they're now 1.
95 pounds per bar.
How much were the bars originally? And a hotel wants to encourage more customers during the off peak season.
So has a 11.
3% sale for a room and the room now costs 177.
40 pounds.
How much was the room before the decrease? See if you can give these questions a go and show your working out.
Great work, let's see how you got on.
Well, we know the calculation would be our original amount multiplied by 0.
975 because it's a decrease of 2.
5%, gives my 1.
95 pounds.
Rearranging, that means 1.
95 pounds divided by 0.
975 gives me the original price of the chocolate bar.
It was two pounds.
Now for the hotel, we don't know what the original amount was, but we do know it was reduced by 11.
3%.
So the multiplier was 0.
887 and that gave us the new price of the room, which is 177.
40 pounds.
Now I'm going to rearrange to find A, which is 177.
40 pounds divided by 0.
887.
So the original price of the room was 200 pounds.
Well done if got these right.
Great work everybody, now it's time for your task.
I want you to work out the missing information from the table and the first row has been done for you.
See if you can give it a go, press pause for more time.
Well done, let's move on to question two.
Read the question carefully here and see what you can do.
Press pause for more time.
Great work everybody, so let's go through these answers.
For question one, here are all our answers.
Massive well done if you've got these right.
Press pause if you need more time to mark.
Great work, let's have a look at question two.
Question two was a tricky question, so a huge well done if you've got this one right.
We have percentages and ratio in here.
So working out the answer, we have all of this wonderful working out and this is our correct answer.
Massive well done if you got this one right.
Excellent work everybody.
So in summary, we've looked at decreasing an amount by a percentage using double number lines, bar models, ratio tables, and even using a decimal multiplier.
We've also looked at different ways a percentage decrease question can be written.
For example, decrease 70 by 12% is exactly the same as finding 88% of 70.
Using a decimal multiplier is efficient when using a calculator.
It also allows you to easily calculate the original amount using the inverse of multiplication.
Massive well done today everybody, it was tough, but it was great learning with you.
