Lesson video
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Hello, my name is Mr Clasper and today we're going to be looking at repeated percentage decrease.
Let's have a look at this example.
Decrease 34 by 10%.
If we take a bar and we say the bar is worth 34, at the moment, this is worth 100%.
If we decrease this amount by 10%, this would leave us with 90%.
So that means the remaining part of my bar is worth 90%.
So if we calculate what 90% of 34 is, we'll find our answer.
We should know that 90% is equal to 0.
9.
So if we divide our percentage by 100, we get our decimal equivalent.
And therefore, if we calculate 34 multiplied by 0.
9, we get our final answer of 30.
6.
So decreasing 34 by 10%, would leave us with the answer of 30.
6.
Let's have a look at this example.
We're going to decrease 34 by 10%, then by 20%.
We already know from the previous example that we needed to find 90% of 34 and that gave us 30.
6.
What we now need to do is to take this new amount and decrease this by 20%.
So if we use the same approach, if we start with a hundred percent.
So if we presume that 30.
6 is our new 100% and we decrease this by 20%, that would leave us with 80%.
That means we're going to use the decimal 0.
8, as it is equivalent to 80%.
And our final calculation is our new amount of 30.
6 multiplied by 0.
8, which gave us a value of 24.
48.
Now, a more efficient way to do this is to look carefully at our calculation.
What we could do, we could calculate 34 multiplied by 0.
9, which we know is 30.
6.
And our next step on the previous example was to multiply 30.
6 by 0.
8.
But we know that 30.
6 is equivalent to 34 multiplied by 0.
9.
Therefore we could just calculate, 34 multiplied by 0.
9 as this is the same as 30.
6, then multiply this by 0.
8 and it gives us the same answer of 24.
48.
Let's have a look at this example.
Decrease 325 grammes by 20% then by 30%.
Well, we should know that if we start with 100% and decreased by 20%, this leaves us with 80%.
So one of the decimals we'll be using is 0.
8, as it is equivalent to 80%.
Then we can look at our 30% decrease.
So 100 minus 30 would give us 70% and this is equivalent to 0.
7, which is our second decimal, which we will use in our calculation.
So the final calculation we're going to carry out would be, 325 multiplied by 0.
8.
So this is representative of our 20% decrease, then multiply by 0.
7, which represents our 30% decrease after the initial 20% decrease.
This will give us a final answer of 182.
Therefore the final answer is 182 grammes.
Let's have a look at this question.
Answering A, B, C, or D, can you identify the correct answer? Pause the video to complete your task and click resume once you're finished.
Did you get it? The correct answer was C, 300 multiply by 0.
85.
This is because decreasing by 15% would leave us with 85% and this is equivalent to 0.
85.
For response A, this would be an increase of 15% as we're multiplying by something greater than one.
For part B, this would be equivalent to finding 15% or decreasing by 85%.
And for part D, this would be equivalent to increasing 300 by 85%.
Here's a question for you to try.
Be sure to correct each of the three calculations.
Pause the video to complete your task and click resume once you're finished.
And here are your solutions.
So the first statement was incorrect because we needed to multiply by 0.
9 and 0.
95, as this represents our 90% and 95% that's left when we take away 10% and 5%.
For the second statement, we need to multiply by 0.
8 and then 0.
5.
So again, the 0.
8 represents 80%, which will be left after subtracting 20% from 100.
And our last statement is 92 multiplied by 0.
77, multiplied by 0.
95.
And again, the 0.
95 is our 95%, which will be remaining after we've decreased by 5%.
Here are two questions for you to try.
Pause the video to complete your task and click resume once you're finished.
And here are your answers.
So if we have a look at question two, we needed to decrease by 10%, which leaves 90%, which is 0.
9 as a decimal.
And we then need to decrease by 50%, which is 0.
5.
So if we take 50% from 100, we're left with 50%, which is 0.
5 as a decimal.
And then when we may have a look at question three, decrease 600 by 5%, then 2%, we need to multiply by 0.
95, which is our 100 with 5% taken off, followed by a multiplication of 0.
98, which is our 100% with 2% taken away.
And that leaves us with 558.
6 kilometres as our final answer.
Let's have a look at this example.
A car costs 8,000 pounds and decreases in value by 7% every year.
What will the value of the car be in two years? Well, if we decreased by 7%, we will be left with 93% and 93% as a decimal will be equivalent to 0.
93.
This is the decimal we'll be using in our calculation.
So if we calculate 8,000 multiplied by 0.
93, multiplied by 0.
93, this gives us a final answer of 6,919 pounds and 20 pounds.
However, we could calculate this in a more efficient manner.
So if we take eight thousands, we could multiply by 0.
93 to the power of two, as this is equivalent of two years of a 7% decrease as well.
And obviously this will give us the same response.
Let's have a look at this example.
A forest has 90,000 trees.
The number of trees decreases by 3.
8% every year.
How many trees will be left in the forest in three years? Well, if we decrease by 3.
8%, we would be left with 96.
2% and as a decimal, dividing this percentage by 100 would give us an equivalent of 0.
962.
And for the calculation I could carry out would be 90,000 multiplied by 0.
962, multiplied by 0.
962, multiplied by 0.
962.
And this gives me an answer of approximately 80,125.
If we look closely again, thinking about efficiency, we could calculate 90,000 multiplied by 0.
962 to the power of three, as this is equivalent.
And this will obviously give us the same response.
Here's a question for you to try.
Pause the video to complete your task and click resume once you're finished.
And here is the solution.
So we begin with 120,000, I mean we need to decrease this amount by 2% every month for three months.
So a decrease of 2% would represent a percentage of 98% and as a decimal, this will be 0.
98.
So our calculation was 120,000 multiplied by 0.
98 to the power of three.
And this leaves us with 112,943.
Here are two more questions for you to try.
Pause the video to complete your task and click resume once you're finished.
And here are the solutions.
So if we take a look at question five, we've calculated 20 million multiplied by 0.
97 to the power of two.
So remember that 0.
97 is the 97%, which remains once we've taken away 3% and this gives us our final answer of 18,818,000.
And looking at question six, we've decreased by 5.
3% every year.
So this would leave 94.
7%, which is where our decimals 0.
947 has come from in our calculation.
Let's have a look at this example.
Which has a greater total percentage decrease? So if we take the first example on the left, a decrease by 10%, then by 30%, would be equivalent to multiplying by 0.
9 followed by 0.
7.
And this gives us an answer of 0.
63.
0.
63 is equivalent to 63%, which would be a 37% decrease.
So because we had 63% leftover, that meant we had to decrease by 37% in total.
If we take the second example on the right, a decreased by 15%, then by 25% would be equivalent to a multiplication of 0.
85 followed by 0.
75, which gives us an answer of 0.
6375.
This is equivalent to 63.
75%, which would represent a 36.
25% decrease.
Therefore, the correct answer is the first response.
Here is your last question.
Pause the video to complete your task and click resume once you're finished.
And here is a solution to our final problem.
So Goldwick's, if we calculate 0.
8, multiplied by 0.
85, this would give us 0.
68, which would represent a discount of 32% in total.
And if we look at Silverman's, we're going to calculate 0.
7, multiplied by 0.
95, which gives us 0.
665, which would represent a discount of 33.
5%.
Now Silverman's offers a 33.
5% discount in total and Goldwick's only offers a 32% discount in total.
That leads us to the conclusion that Silverman's had the better discount.
And that brings us nicely to the end of our lesson.
I hope you're feeling comfortable with repeated percentage decrease.
Want to give the exit quiz and go to boost your confidence even further.
I'll hopefully see you soon.
