Tips on Quickly Converting Fractions to Percents

Date: 02/14/2005 at 08:14:56
From: steve
Subject: Dividing a number by a larger number

I'm reviewing for a recruitment test.  A majority of the math 
questions are percentages, eg. 9 as a percentage of 60.

I know the formula as (9/60) * 100, but I don't know how to calculate 
9/60 without using a calculator.

Date: 02/14/2005 at 10:52:47
From: Doctor Ian
Subject: Re: Dividing a number by a larger number

Hi Steve,

In the most general case, you just use long division.  The fraction
9/60 just means '9 divided by 60', so

        0.1 5
      _______                     
   60 ) 9.0 0      -->  9/60 = 0.15
        6 0
        ---
        3 0 0 
        3 0 0 
         -----
            0

You can simplify your life a little by trying to reduce the fraction,
e.g., 

   9   3 *  3    3   
  -- = ------ = -- 
  60   3 * 20   20   

In this case, you get a denominator that is a divisor of 100, which
means you're golden:

   3   5    15
  -- * - = ---
  20   5   100

which, of course, means the same thing as 0.15.  (If you're not sure
why, let me know, because this is a fairly important thing to 
understand.) 

If you just need to get an approximate answer, there are other things
you can try.  For example, 60 is a little more than half of 100.  And
9 is half of 18, so it's a little more than half of, say, 15 or 16.  So 

   9         15 or 16
  -- = about --------
  60            100

On a multiple choice test, that might get you close enough to be able
to pick out the actual answer. 

Note that it can be helpful to do the multiplication first, since in
made-up problems, you can often get rid of the denominator by reducing it:

   9         900   90   30
  -- * 100 = --- = -- = -- = 15
  60          60    6    2

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 02/14/2005 at 11:29:44
From: steve
Subject: Thank you (Dividing a number by a larger number)

Thank you very much for your reply.  The information you provided me
with was a great help.  I've run through a few test questions, and I
am now comfortably able to answer them using the methods you have
suggested. 

Thanks again.