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### Fractions Table

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

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
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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