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6.9

## National STEM Learning Centre

Skip to 0 minutes and 7 secondsPAULA KELLY: So now let's have a look at how we calculate a loss as a percentage. So, for example, if I bought a car for 8,000 pounds, some time later, I sell it for 6,200 pounds, I know I've made a loss. But what what is that as a percentage?

Skip to 0 minutes and 23 secondsMICHAEL ANDERSON: OK. So what we need to do is, first of all, figure out the loss, which, unfortunately this time, is 1,800 pounds. And then we're going to divide that by the original amount that you paid for the car.

Skip to 0 minutes and 35 secondsMICHAEL ANDERSON: So you made a loss of 1,800 pounds. And we're going to divide that by the 8,000 pounds that you originally paid. So I could try and work this out, simplify it down as a fraction, but what I'm going to do is do a division on the calculator. And that will give me 0.225 as a decimal.

Skip to 0 minutes and 54 secondsMICHAEL ANDERSON: So to convert this to a percentage, the percentage loss, well, that's just going to be 22.5%.

Skip to 1 minute and 1 secondPAULA KELLY: So as a decimal, you multiply it by 100 to get your percentage. So my percentage loss was 22.5%?

Skip to 1 minute and 7 secondsMICHAEL ANDERSON: Yep, of the original amount.

Skip to 1 minute and 17 secondsSo that's one method of working out. Is there an alternative strategy we could use?

Skip to 1 minute and 21 secondsMICHAEL ANDERSON: Yeah, so we've already visited the multiply methods. In this case, it's going to be a decrease. So we went from 8,000 pounds. And we sold the car for 6,200 pounds.

Skip to 1 minute and 34 secondsMICHAEL ANDERSON: So we're going to look for a multiplier that takes us from 8,000 to 6,200. So we're going to multiply this 8,000 to give us 6,200.

Skip to 1 minute and 44 secondsMICHAEL ANDERSON: So what I'm going to do is divide both sides by 8,000. So m is going to stay the same. We'll end up with 6,200 divided by 8,000. Now, again, I'm going to use a calculator to work this out. And it will give me a value of 0.775.

Skip to 2 minutes and 1 secondPAULA KELLY: So that's quite a value to what we had earlier. So why is that?

Skip to 2 minutes and 5 secondsMICHAEL ANDERSON: Yeah, well, this 0.775 could be thought of as a percentage, the 77.5%. And that represents the value that the car has retained. So out of your 8,000 pounds, it's still worth 77.5% of the value that you paid originally. So what that means as a loss, well, we have to figure out what we go from 77.5, what we have to add to that to make 100. So in this case, our percentage loss is 22.5%.

# Finding a percentage decrease

In this video we build upon the last step and consider two similar methods of finding a percentage decrease. When finding a percentage decrease we are asking the question: “by what percentage we have to decrease the original amount by to find the new amount?”

The first method uses the equation:

$\frac{loss}{original\ amount} \times 100$

As with percentage increase, if students are to learn through understanding and creating connections between mathematical topics as demanded by the English National Curriculum, it is important, when using this method, to explore how the equation is derived.

The ‘loss’ is the amount which has been subtracted from the original amount. The answer then represents this loss amount as a percentage of the original amount. The second method uses a multiplier

The equation:

$original\ amount \times M = new\ amount$

is again used as with percentage increase. The answer again has to be interpreted correctly.

When M is a decimal number between 0 and 1 tells us that it is a percentage decrease.

The decimal part indicates the magnitude of the percentage we have left. The percentage lost still has to be calculated.

For example, a value of M of 0.65 indicates that 65% of the original value remains so the percentage of the original value we have lost is 35% (the difference between 65% and 100% of the original value).

Another way of thinking about this is using decimals. A value of M equals 0.65 so the percentage decrease is 1 – 0.65 = 0.35 which represents a 35% decrease.

## Problem worksheet

Now complete questions 12 and 13 from this week’s worksheet.

## Share

Earlier in the course we asked you to share your examples of percentages being used in real-life situations. This week, we’d like you to find more complex examples, for example in finance, engineering or other industries. Where are percentage increases and decreases used, or percentages used to indicate a proportion above or below an amount?