Converting a Long Decimal to a Fraction

Date: 04/11/2002 at 12:22:02
From: Linda Popovich
Subject: Converting long decimal to fraction

If I have 74/13 and I want to reduce it to a mixed number, I know 
that when I divide 74 by 13 I get a long mixed decimal, 5.6923076.  My 
answer book says that the answer is 5 9/13. How do I get from 
5.6923076 to 5 9/13?  

Thanks.

Date: 04/11/2002 at 13:09:54
From: Doctor Peterson
Subject: Re: Converting long decimal to fraction

Hi, Linda.

It's better to avoid the decimals if you are just converting to a 
mixed number. Instead of dividing to get a decimal answer, divide to 
get a whole quotient and remainder:

       ___5_r_9
    13 ) 74
         65
         --
          9

The remainder is the number of extra 13ths that don't form a whole, so 
the answer is 5 9/13.

Now, if you are doing this with a calculator, you have to use 
decimals, because most calculators don't know about fractions. To get 
the remainder, just multiply the decimal part by the denominator:

    13 * .6923076 = 9

(Your calculator may give a number very close to 9 because it's 
missing digits, and you will have to round to the nearest whole 
number.)

This tells you how many 13ths there are in .6923076. This is a special 
kind of decimal-to-fraction conversion that you can use when you know 
the denominator you want.

On my Windows calculator in Scientific mode, there is a "mod" key 
which finds the remainder. If I press "74 mod 13" I get 9, which is 
the numerator for the fractional part.

For more on converting improper fractions to mixed numbers, see our 
archives:

   Fractions - Elementary Level
   http://mathforum.org/library/drmath/sets/elem_fractions.html 

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