how do you find the original price of something that has been changed by a percentage decrease

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Lets say something has been decreased in price by 20% and is now £40. The tempting thing to do here is to find 20% of 40 and add it back on, but this is not okay! The reason we can't do this is that 20% of 40 is different to 20% of the original, bigger number. Instead, think of our original number as 100%. We took away 20% so now we have 80% left, how can we get back? well, if we divide 80% by 4 we get 20%, then multiply it by 5 we get 100%! Do the same to the £40, which is our 80%, and you will get back to the original. I like to draw a grid

80% = £40

divide by 4

20% = £10

multiply by five

100% = £50

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