Fractions in Simplest Form - When?

Date: 11/29/2001 at 12:07:27
From: Krista
Subject: Fractions

Should fractions always be reduced to their simplest form? Why or why 
not?

Date: 11/29/2001 at 12:25:02
From: Doctor Ian
Subject: Re: Fractions

Hi Krista,

Whether you should reduce a fraction to its simplest form depends on 
what you want to do with it.  For example, if you have a bunch of 
lengths, 

  1/2, 3/4, 6/16, 11/32

are they easier to compare if you reduce them, or if you convert them 
all to have a common denominator?

  16/32, 24/32, 12/32, 11/32

You may have noticed that road signs often follow a sequence like 
this:

  1/10 mile
  2/10 mile
  3/10 mile
  4/10 mile
  5/10 mile
   
Would it be clearer if they read like this?

  1/10 mile
  1/5 mile
  3/10 mile
  2/5 mile
  1/2 mile

For the most part, there are two potential advantages to reducing 
fractions:

  1. After you work with some common fractions a lot, you 
     start to remember their decimal equivalents, e.g., 

       1/2 = 0.5      = 50%
       1/3 = 0.333... ~ 33%
       1/4 = 0.25     = 25%
       1/5 = 0.20     = 20%
       1/8 = 0.125    = 12.5%

     So if you end up reducing a fraction to something with one
     of these denominators, it may simplify later steps of whatever
     problem you're trying to solve. 

  2. If you're trying to compare answers with someone else
     (for example, a fellow student, a colleague, a teacher,
     an automatic grading machine), reducing fractions can 
     help avoid miscommunications.  There are infinitely 
     many ways to express any fraction; but there is only 
     one simplest form.  

But as we've seen, these advantages may not apply in a given 
situation. As with most things, there is no hard-and-fast rule that 
you can follow all the time.  You have to use some judgment. 

Does this help? 

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