Hi, I'm Dr. Shah. I was the National Lecture Competition winner in 1989 and I'm the maths master at Mathscool. Now, ready for a new way of doing maths? The method we're going to use is the scale factor method and it's going to make it very easy for us to do percentage increases and decreases, also very useful for a wide variety of other topics in math such as ratios, proportions, inverse proportion, length, area, volume and scale factors and so on. So, one method is going to make it easy for us to do loads of different things in math which is always very good. To start with an example, I put a thousand pounds into a bank account and it pays 20% interest. How much do I have in total after 1 year? Okay, so, a very easy question to ask with but it's going to help us get the method right and once we've got the method right, even very complicated questions are going to become very straightforward. So, the thousand pounds is what we've put into a bank account to start with, so that's our original amount. So, a thousand pounds is the original amount and the original amount is always assigned a percentage of 100%. So, the original amount of 1,000 pounds is 100%. Now, the bank is going to add 20% to that, so at the end of it, we're going to have the hundred percent of the original amount we had plus the 20% on top. So, we don't want to calculate the 20%, we want to calculate the total amount, so we want to work out 120% and we want to work out what that becomes. Now, this is the clever trick which is going to help us through all of this. To get from here to here, the scale factor is times 120 over 100, the bottom one over the top one and it's always that way, the bottom one over the top one. And so, on the other side, we're going to use exactly the same scale factor, times 120 over 100, and so our answer here is going to be found by 1,000 pounds x 120/100 and so that gives our answer, stick it in the calculator, £1200, and so there's our final answer. Okay, that's a straightforward example, and now we move on to a slightly more involved example. Okay, so we move on to our second example, a laptop computer costs 200 pounds excluding sales tax. We want to know if the sales tax is 17 and half percent, what is the total price going to be of that computer? So I start off by saying £200 goes to 100%. Hundred percent is the original price which indicates the sales tax means the price before any taxes have been added on. So in this case, £200 is before any tax have been added on, so that's assigned 100%. I would now 17.5% to it, so I want the original price plus another 17.5%, so I want to work out 117.5% and now again, that same trick. The scale factor on this side is times 117.5 over 100 and so we're going to use the same scale factor on this side, times 117.5 over 100, and so our answer which goes here will be found by following this calculation. £200 x 117.5/100 and that gives us, again stick it in the calculator, our answer is being £235. Okay, so that's again another example where we're doing a percentage increase. The questions become more difficult when somebody's already made the percentage increase and we need to remove it and so that's the next example we're going to do. Our next example, a TV costs 376 pounds including 17.5% sales tax. We want to know how much was the sales tax on that purchase. This is a much more difficult question but because we're going to use exactly the same method, we're not going to find it that much more difficult as I want you to assign the numbers correctly. The £376 is not a hundred percent. Because it already includes the 17.5%, remember a hundred percent would be the original price before any tax has been added on. This includes 17.5% tax, so this is 117.5%, it's the 100% original price and that 17.5% tax already included on that. We want to work out the tax, we know the tax is just 17.5%, and so using our scale factor method, times 17.5 over 11

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