Skip to 0 minutes and 8 secondsMICHAEL ANDERSON: So in this step, we're going to increase an amount by a percentage a common example of this is when you purchase an item from a shop. In the UK, most items have VAT, Value Added Tax, of 20% added onto the cost of purchasing them. So if I was to buy a microwave that was worth 140 pounds, I wouldn't necessarily just pay 140 pounds. I'd have to pay some VAT on top of that. Now In order to find the total that I'm going to have to pay at the till, we're going to have to find 20%, and then add it on. So 20% I can think of in two different ways.

Skip to 0 minutes and 46 secondsI could think of it as being a fraction, so 20/100, and then I'm going to multiply that by 140 over 1.

Skip to 0 minutes and 56 secondsPAULA KELLY: That's some quite big numbers to multiply.

Skip to 0 minutes and 58 secondsMICHAEL ANDERSON: It is.

Skip to 0 minutes and 59 secondsPAULA KELLY: Could you simplify anywhere?

Skip to 1 minute and 0 secondsMICHAEL ANDERSON: Yeah, definitely. So 20 and 100, actually, I can cancel that to 2 over 10. And I suppose with 140, I can do that and that, as well. And then I've just got to multiply across. So 1 multiplied by 1 gives us 1. And 2 times 14 is 28. So that 28 represents the 20% that we're going to have to pay on top of the 140 pounds.

Skip to 1 minute and 32 secondsSo 28 pounds worth of VAT, my microwave is going to cost me 168 pounds.

Skip to 1 minute and 42 secondsPAULA KELLY: As well as a fraction, then, could you also use in calculations the decimal?

Skip to 1 minute and 47 secondsMICHAEL ANDERSON: Yeah, so 20% is obviously 20/100 as a fraction. As a decimal, it's 0.2. So I can do 0.2 multiplied by 140.

Skip to 2 minutes and 0 secondsPAULA KELLY: Again, not very nice.

Skip to 2 minutes and 1 secondMICHAEL ANDERSON: Yeah, a little bit tricky. What I can do, I'm pretty good at multiplying by 2. So 140 times 2 is going to give me 280. Now this calculation is going to be 10 times larger than this one, because to go from not 0.2 to 2, I've multiplied by 10. So I'm going to do the opposite and divide by 10 here, to get 0.2 multiplied by 140 is 28 pounds.

Skip to 2 minutes and 27 secondsPAULA KELLY: And that makes sense, because the other method was 28 pounds again. So pretty happy, you got it right.

Skip to 2 minutes and 33 secondsMICHAEL ANDERSON: I'm relieved, yes. Both ways are going to work.

Skip to 2 minutes and 36 secondsPAULA KELLY: So we've just seen how you use a fraction and a decimal. And you found 20% of the cost of your microwave. And then you add added it on. Is there a quicker way of doing this?

Skip to 2 minutes and 47 secondsMICHAEL ANDERSON: There is an alternative approach, which is called the "multiplier method." So if we think of the 140 pounds, the original cost of our microwave, and that being 100% of the value, when we add 20% VAT on, what we're actually paying is 122% of the value of the microwave. So we can find 120%, and that will tell us the cost that we're going to have to pay. Now, 120% we can think of, again, as a fraction. It's 120 over 100. And we're going to multiply that by 140 instead.

Skip to 3 minutes and 22 secondsPAULA KELLY: Again, big numbers. Can we simplify?

Skip to 3 minutes and 25 secondsMICHAEL ANDERSON: Yeah we can do the same trick. So 120 and 100 are both multiples of 10. So I could cancel that down. I can then cancel this down and this down. And then all I have to do is know my 12 times tables to 14, so 12 multiplied by 14. Thankfully, I got 168 pounds as a total cost, which is how much we had to pay in the previous methods.

Skip to 3 minutes and 47 secondsPAULA KELLY: So that's some fractions. Have we also got decimals?

Skip to 3 minutes and 50 secondsMICHAEL ANDERSON: Yeah. So again, because we've increased from 100% to 120%, 120% as a decimal is just 1.2. So if we take our original value, 140 pounds, and multiply that by 1.2, it will also give us the price we have to pay after VAT has been added. Now at this stage, I might get my calculator out. And that will, thankfully, give us the exact same amount of 168 pounds.

Skip to 4 minutes and 19 secondsPAULA KELLY: So you have lots of methods. Slightly quicker, maybe, this one?

Skip to 4 minutes and 23 secondsMICHAEL ANDERSON : I think once you understand the percentage change, actually, there's only one calculation here. So it can be a little bit more efficient.

Skip to 4 minutes and 29 secondsPAULA KELLY: Great.

Increasing by a percentage

A common use for percentages is when amounts are increased, or decreased, by a percentage of that amount. For example, when buying a carton of orange juice, it might say 50% extra free. In that case, the total volume of the juice has been increased by 50% of its original volume.

Before watching the video, consider how you would increase 140 by 20%.

There are two basic ways of increasing an amount by a percentage.

The first is a two stage method which involves finding the percentage and then adding on the answer. The second is using a multiplier which calculates the final answer in one stage.

Whilst the first method is easy to understand, the second method is more efficient and much more useful when working out more complex percentage questions at a later stage.

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This video is from the free online course:

Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre