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### Percentages to or from Fractions

```
Date: 04/04/97 at 21:13:15
From: Matthew Parkin
Subject: Percentages to/from Fractions

How do you convert between percents and fractions?
```

```
Date: 04/04/97 at 22:22:53
From: Doctor Toby
Subject: Re: Percentages to/from Fractions

The definition of x percent is x divided by 100. So, if you have a
fraction and want to convert it to a percentage, you know that the
fraction equals x percent and you want to find x. Since x percent is x
divided by 100, you will get x by multiplying x percent by 100.
But x percent equals the fraction.  So multiply the fraction by 100.

For example, suppose the fraction is 1/3. If you multiply 1/3 by 100,
you get 33 1/3. Therefore, 1/3 = 33 1/3 percent.

Now, people often want the percentage to be expressed as a decimal.
In this case, you have to take two steps to solve the problem. First,
multiply the fraction by 100 the way I did above. Then, once you get a
fractional percentage (like 33 1/3 in the example above), convert that
fraction into the decimal percentage. In the example, that decimal is
33.333...(repeating forever).

Now you can go one way, from fraction to percentage.

Going from percentage to fraction is even easier. All you have to do
is divide by 100. For example, if someone gives you 60 percent, divide
60 by 100 to get the fraction 60/100. Reduce this to lowest terms, and
you get 3/5.

After all, "60 percent = 3/5" just means that 60 divided by 100 equals
3/5, because "percent" means "divided by 100".

I hope this helps.

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

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