Reducing Fractions

Date: 5/30/96 at 15:44:39
From: Vivian McCraw
Subject: Reducing fractions

I was placed in ESE from Pre-k through grade 12 and they never had me 
learn to reduce fractions. What is the easiest method of reducing
fractions to lowest terms that you know?

Greg

Date: 5/31/96 at 16:6:3
From: Doctor Byron
Subject: Re: Reducing fractions

Hi Greg,

In order to reduce a fraction, you need to find the biggest number 
that divides into both the numerator (the top number) and the 
denominator (the bottom number).  After some practice, you may find 
that you can do this pretty quickly.  At first, though, it is often 
helpful to list all the factors and simply look to see the biggest one 
shared by both numbers.  

Factors, by the way, are simply any number that divides into another 
number evenly.  Let me give you an example:

Let's look at the fraction - 

       48
     ------
       32

The factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 32 are:
1, 2, 4, 8, 16, 32

If you look at both lists you'll see that 16 is the biggest number 
that is on both lists.  So to reduce the fraction, we divide the top 
and bottom by sixteen.

      48/16        3 
     -------  =  -----
      32/16        2

If you find that there are no numbers (other than one) which are 
shared factors of both, the the fraction is as simple as it can get.

Also, you don't have to simply look for the biggest factor right away.  
If you notice a shared factor quickly, you can go ahead and divide by 
it right away.  You will have to make sure that there aren't any 
factors left, though.  Let's look at the same example again:

You may have noticed that both 48 and 32 are even, so it's pretty 
obvious that they both share two as a factor.  So you could start by 
dividing both by two:

      48/2       24
     ------  =  ----
      32/2       16

Now you might notice that 24 and 16 are both divisible by four, so you 
can go ahead and divide again:

      24/4       6
     ------  =  ---
      16/4       4

Finally, we see that these are even and can be divided by 2 again:

      6/2       3
     -----  =  ---
      4/2       2

I hope this has been helpful.  I would suggest you find a math book 
that has some problems with answers given so that you can practice 
reducing fractions for a while, or maybe you could ask someone who 
knows how to make some problems for you to practice.  Good luck!

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