Q&A #5442

Percentage of change

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Jan 09, 2001 at 20:55:16
Subject: Re: Percentage of change

This may seem simplistic, but most students who have difficulty with percentages seem not to really understand the meaning of percent. You may exchange the word percent, in every application, with the words hundredths or the phrase "divided by 100". The actual Latin meaning of percentum (each hundred) is the origin. To teach percentages, I try to impress upon students this meaning. Problems written as x% * y = z can be restated as x/100 *y = z. They are isomorphic ideas. Now the question above asks about the amount of change, and asks for it to be expressed as a percentage (unstated is that this means a percentage or hundredth of the original amount). In essence then, they are asking you to find the change in price (23.00 - 10.50 = 12.50) and then express this as a percentage of (hundredths of) the original 10.50 price. Since 12.50 /10.50 = appx 1.19 we know that 12.50 is 119 %( hundredths) of 10.50. Another way to get this answer is to ask what is a hundredth (1%) of the original amount (answer .105 or about a dime). How many of these does it take to make the amount of change (how many .105 does it take to make 12.50). A pretty smart kid can recognize that it takes about 125 dimes (remember .105 is about a dime) to make 12.50, so the answer of 119 sounds reasonable. OK applications first is not the way to learn, so to solve 23% of what number is 60 Write 23/100 * x = 60 and solve to solve 23% of 80 is what number, write 23/100 * 80 = ? and evaluate to solve what percentage of 60 is 80? write x/100 * 60 = 80 and solve... Hope this helps.. -Pat Ballew, for the T2T service

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