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In this video we are going to look at how to do percentage increases and decreases, using multipliers. You should already know what percentages are, and how to find them.



Example: A train ticket costing £40 is reduced by 20%. What is the price of the new ticket? 20% of 40 = 20/100 X 40 = £8. £40 - £8 = £32.



We could find a percentage decrease by finding the amount and then subtracting it from the original, like the train ticket example. But there is a much faster way… that is especially great if you have a calculator to hand: using multipliers.



Multipliers are based on decimals, with a slight difference for if you’re doing a percentage increase or a decrease.



For percentage increases, we add the percentage to 100% and then turn it into a decimal. Example: 8% increase = 100% + 8% = 108% as a decimal = 1.08.



The multipliers for percentage increases are always 1 point something if they’re for a 0 to 100% increase.



A 100% increase means double, and will be 2 point something multiplier because 100% + 100% = 200% = 2.0 as a decimal.



But what are multipliers? Why are they 1 point something? We always start with 100% of the item. And then if we want to increase it by 25% we have the starting 100% plus the increased 25%. So that now we have 125%. Which written as a decimal is 1.25. The 1 represents our starting amount and the point 25 represents the percentage increase.



For percentage decreases we subtract the percentage from 100% and then turn it into a decimal. Example: 8% decrease = 100% - 8% = 92% as a decimal = 0.92.



Back to our train ticket example, let’s do it with multipliers this time. A train ticket costing £40 is reduced by 20%. What is the price of the new ticket? It is a percentage decrease, so 100% - 20% = 80% as a decimal = 0.8. £40 X 0.8 = £32

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