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Fractions Table


Date: 06/20/98 at 06:15:55
From: Betsy Mikula
Subject: Fractions

Could you please help me locate a math table that illustrates 
fractions to the 16th's?  Many thanks.


Date: 06/20/98 at 14:58:07
From: Doctor Gary
Subject: Re: Fractions

I can do better than that, by helping you make one of your own.

First, you need to appreciate that a fraction is just a shorthand way 
of writing that the numerator (top of the fraction) is being divided 
by the denominator (bottom of the fraction).  

If you can do long division, you can create a table of decimal 
equivalents for any denominator you like. Even better, you can save 
yourself a lot of work by recognizing that many fractions that may 
look different (for example, three-fourths and twelve-sixteenths) are 
actually the same. Once you've calculated that 3/4 is .75, you know 
that 6/8, 9/12 and 12/16 are also equal to .75.  

It really doesn't take more than the knowledge of the following two 
decimal equivalents to create a table of all the decimal equivalents 
of any fraction with a denominator of 2, 3, 4, 5, 6, 8, 9, 10, 12, 15 
or 16:
                  _
   one ninth  =  .1    (an endless string of ones)

   one tenth  =  .1

Here's how we can use just these two decimal equaivalents, and our 
knowledge of fractions, to calculate the value of 7/12:

Since 1/2 is the same as 5/10, 1/2 is 5 times .1 or .5.  
6/12 is the same as 1/2, so 6/12 is also equal to .5

7/12 is the sum of 6/12 and 1/12, so we can calculate 1/12 as follows:

1/12 is half of 1/6. 1/6 is half of 1/3. 1/3 is three times 1/9, so 
1/3 is equal to an endless string of threes to the right of the 
decimal point. 1/6 is half of that, which is a decimal point followed 
by a one and an endless string of sixes. 1/12 is half of 1/6, which is 
a decimal point followed by a zero, an eight and an endless string of 
threes.  

If we add 6/12 to 1/12, we get:
   _    _  
  .5 + .083  =  .583  =   7/12

You could also calculate a decimal equivalent for 11/12 by recognizing 
that it is 12/12 minus 1/12. 12/12 is 1. 1 minus 1/2 is:
   _    _
   1 - .083  =  .916  =  11/12

As you create your table, you'll come to appreciate the shortcuts of 
calculating decimal equivalents by recognizing a fraction as the sum 
of various other fractions. One day, you may even be able to calculate 
43 and one-third percent of 360 in your head, by recognizing that 43 
and one-third percent is the sum of 1/10 and 1/3.

When your table is done, make sure to check your work. Here's one way 
you can test to make sure a decimal equaivalent is correct:

If .875 really is 7/8, then .875 times 8 and divided by 7 should be 1.  
Is it?

Creating your own table is not only more fun than looking at one 
someone else made up, but is also more likely to help you learn in a 
way that will stay with you forever.  Enjoy.
  
-Doctor Gary,  The Math Forum
 http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Fractions
Middle School Fractions

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