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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