Finding a Percentage

Date: 01/26/2001 at 17:34:39
From: Wayne Chrisope
Subject: How to arrive at a percentage

How do you arrive at a percentage that a number is of a number? 
Example: what percent of 32000 is 2000?

Date: 01/26/2001 at 19:15:00
From: Doctor Ian
Subject: Re: How to arrive at a percentage

Hi Wayne, 

Every percentage question uses the exact same equation, which looks 
like this:

    part     percentage
   ------- = ----------
    whole       100

Any percentage problem will give you two of the three unknowns, and 
then you just have to rearrange the equation to get the other one.  
And since there are only three unknowns, there are really only three 
kinds of questions that anyone can possibly ask:

  1. What is ___ percent of ___?
     (Given whole and percentage, find part)

  2. ___ is what percent of ___?
     (Given part and whole, find percentage)

  3. ___ is ___ percent of what?
     (Given part and percentage, find whole)

Here is an example:

  36 is what percent of 150?

  I've been given the part and the whole, so I set up my equation:

     36    ?
    --- = ---      
    150   100

  Then I rearrange it, and reduce it:

        100 * 36   2 * 50 * 3 * 12
    ? = -------- = ---------------- = 24
           150          3 * 50

Here is another example:

   25 is 40 percent of what?

   I've been given the part and the percentage, so I set up my equation:

     25    40
     -- = ---
      ?   100

   Then I rearrange it, and reduce it:

          25 * 100   25 * 2 * 5 * 10   125
      ? = -------- = --------------- = --- = 62.5
             40         2 * 2 * 10      2     

Here is another example:

   What is 35 percent of 90?

   I've been given the whole and the percentage, so I set up my equation:

       ?    35
      -- = ---
      90   100

   Then I rearrange it, and reduce it:

           90 * 35   9 * 10 * 7 * 5    63
      ? = -------- = -------------- = ---- = 31.5
             100       2 * 5 * 10       2


Your question, What percent of 32000 is 2000?, is similar to the first 
example above. 

What if you get to the point where you've set up the proportion,
but don't know what to do next?  Take a look at 

  Flipping and Switching Fractions
  http://mathforum.org/library/drmath/view/58193.html

I hope this helps. Write back if you'd like to talk about this some 
more, or if you have any other questions. 

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