How to Do Percentages


This note was sent to the HSTUAC home school e-mail discussion list in response to a mother's concern about her son.  He didn't like to "follow the rules" in doing mathematics.  Instead, he liked to find his own way of doing things.



This may not be bad.  I have no problem with letting him use his own method as long as the method is valid.  I'll give you an example.  At one point, if my son was asked to find 32% of 150 he would say 10% is 15 and 1% is 1.5.  So 30% is 45 and 2% is 3.  So 32% is 45 + 3 or 48.  Perfectly valid.  Not the most efficient way but it works.  Of course, if it was 35.68% of 438.976 his method would be a real pain but it is still correct.


Now, if he is reducing the fraction 16/64 to 1/4 by "canceling" the 6's, though the answer is right the method is bogus.


So just look at how he does it.  If it's legitimate, don't stress too much about it.  Show him the other way but don't be too concerned.  I've been showing my son the other way to do percentages and I think he finally sees the advantage but I was pleased that he understood what was going on.


The way I teach people to do percentages is the following:


Every percentage problem can be looked at as an equation with two fractions.


part           PART

---------  =  ------------

whole       WHOLE


For example, what is 32% of 150?


Per cents are fractions over 100 so 32 is a part and 100 is a whole.


32          PART

------  =  ------------

100        WHOLE


The wording of the problem shows that 150 is the "WHOLE" and the "PART" is unknown.  So, we have:


32             x

------  =  --------

100        150




32 (150)     

-------------  =  x



or x = 48.


Doing it this way helps them to see what's really going on and it keeps them from having to memorize how to do 3 different kinds of problems.  Instead of remembering how to do "32 is what percent of 98?" and "32 is 47% of what number?" and "what number is 45% of 68?" all they have to remember is


part           PART

---------  =  ------------

whole       WHOLE