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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

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/
```
Associated Topics:
Elementary Fractions

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