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### Two Ways to Change Percents to Fractions

```
Date: 02/21/98 at 08:36:46
From: Tiffany
Subject: Percents to fractions

It is easy until I get to a problem like 10 1/4% and I can't change it
into a fraction. Please send me info.
```

```
Date: 02/23/98 at 11:08:01
From: Doctor Schwenoha
Subject: Re: Percents to fractions

There are several approaches to deal with this problem.  I think it's
important for my students to know two of them.

The first is probably the easiest in this case.  Change the 1/4 to
decimal form so that you get 10.25% and now just follow your rules for
changing from percent to fraction.  The percent sign can be broken
down into two parts: per means divided by and cent means 100.
Replacing the % sign with this information gives us 10.25/100.

Generally we don't like having decimals mixed into fractions (it is
not considered "simplest form") so we could multiply this fraction by
100/100 to eliminate the decimal and end up with 1025/10000.  We still
need to reduce this fraction to be in simplest form and we can divide
both the top and the bottom by 25 to get 41/400.

10.25     100      1025
-----  x  ---   =  -----
100      100      10000

1025       25        41
-----  /   --   =   ---
10000      25       400

The other method I would want my students to know how to do is to go
straight to the definition of the percent sign we just looked at, and
make a complex fraction which needs to be simplified. Do you know how
to make a whole number into fraction form (just put a fraction bar and
a 1 under it)? Do you know how to divide by fractions (multiply by the
reciprocal of the divisor)?  Here's what it looks like:

41
--
10 1/4       4       41      1       41
------  =  -----  =  --  x  ---  =  ---
100       100       4     100     400
---
1

We get the same answer either way.  I think it's important to know
both methods so that we can choose the method that works best for the
problem we encounter. I prefer the fraction method (2nd one we looked
at) because I think it builds ability in working with any numbers in
fraction form.

-Doctor Schwenoha,  The Math Forum
Check out our web site http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions

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