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### Finding a Percentage

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Date: 01/26/2001 at 17:34:39
From: Wayne Chrisope
Subject: How to arrive at a percentage

How do you arrive at a percentage that a number is of a number?
Example: what percent of 32000 is 2000?
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```
Date: 01/26/2001 at 19:15:00
From: Doctor Ian
Subject: Re: How to arrive at a percentage

Hi Wayne,

Every percentage question uses the exact same equation, which looks
like this:

part     percentage
------- = ----------
whole       100

Any percentage problem will give you two of the three unknowns, and
then you just have to rearrange the equation to get the other one.
And since there are only three unknowns, there are really only three
kinds of questions that anyone can possibly ask:

1. What is ___ percent of ___?
(Given whole and percentage, find part)

2. ___ is what percent of ___?
(Given part and whole, find percentage)

3. ___ is ___ percent of what?
(Given part and percentage, find whole)

Here is an example:

36 is what percent of 150?

I've been given the part and the whole, so I set up my equation:

36    ?
--- = ---
150   100

Then I rearrange it, and reduce it:

100 * 36   2 * 50 * 3 * 12
? = -------- = ---------------- = 24
150          3 * 50

Here is another example:

25 is 40 percent of what?

I've been given the part and the percentage, so I set up my equation:

25    40
-- = ---
?   100

Then I rearrange it, and reduce it:

25 * 100   25 * 2 * 5 * 10   125
? = -------- = --------------- = --- = 62.5
40         2 * 2 * 10      2

Here is another example:

What is 35 percent of 90?

I've been given the whole and the percentage, so I set up my equation:

?    35
-- = ---
90   100

Then I rearrange it, and reduce it:

90 * 35   9 * 10 * 7 * 5    63
? = -------- = -------------- = ---- = 31.5
100       2 * 5 * 10       2

Your question, What percent of 32000 is 2000?, is similar to the first
example above.

What if you get to the point where you've set up the proportion,
but don't know what to do next?  Take a look at

Flipping and Switching Fractions
http://mathforum.org/library/drmath/view/58193.html

more, or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Fractions

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