Two Ways to Change Percents to Fractions

Date: 02/21/98 at 08:36:46
From: Tiffany
Subject: Percents to fractions

It is easy until I get to a problem like 10 1/4% and I can't change it 
into a fraction. Please send me info.

Date: 02/23/98 at 11:08:01
From: Doctor Schwenoha
Subject: Re: Percents to fractions

There are several approaches to deal with this problem.  I think it's 
important for my students to know two of them.  

The first is probably the easiest in this case.  Change the 1/4 to 
decimal form so that you get 10.25% and now just follow your rules for 
changing from percent to fraction.  The percent sign can be broken 
down into two parts: per means divided by and cent means 100.  
Replacing the % sign with this information gives us 10.25/100.  

Generally we don't like having decimals mixed into fractions (it is 
not considered "simplest form") so we could multiply this fraction by 
100/100 to eliminate the decimal and end up with 1025/10000.  We still 
need to reduce this fraction to be in simplest form and we can divide 
both the top and the bottom by 25 to get 41/400.
 
      10.25     100      1025
      -----  x  ---   =  -----
       100      100      10000


      1025       25        41
      -----  /   --   =   ---
      10000      25       400


The other method I would want my students to know how to do is to go 
straight to the definition of the percent sign we just looked at, and 
make a complex fraction which needs to be simplified. Do you know how 
to make a whole number into fraction form (just put a fraction bar and 
a 1 under it)? Do you know how to divide by fractions (multiply by the 
reciprocal of the divisor)?  Here's what it looks like:

                41                      
                --
    10 1/4       4       41      1       41
    ------  =  -----  =  --  x  ---  =  ---
      100       100       4     100     400
                ---
                 1

We get the same answer either way.  I think it's important to know 
both methods so that we can choose the method that works best for the 
problem we encounter. I prefer the fraction method (2nd one we looked 
at) because I think it builds ability in working with any numbers in 
fraction form.

-Doctor Schwenoha,  The Math Forum
 Check out our web site http://mathforum.org/dr.math/