Word Problems/Division

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Question
QUESTION: Hello:

$0.15 can be expressed as 15/100 and as 1/100 X 15.  Where should the dollar sign be placed when the fraction 15/100 is used and when 1/100 X 15 is used?

Which are correct:

($15)/100 or 15/($100)

$1/100 X 15, 1/$100 X 15, or 1/100 X $15?

I thank you for your reply.

ANSWER: Treat units like any other constant or variable. When you are counting apples, you could write 3apples, but not 3/apples.
It's the same with dollars. $0.15 = $(15/100) = ($15)/100.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply.

I am somewhat confused by your reply. Can you explain "Treat units like any other constant or variable."?

-----------
And also, which one of these is correct?

$1/100 X 15, 1/$100 X 15, or 1/100 X $15?

I thank you for your follow-up reply.

Answer
Suppose you have an unknown called α.
The expression 0.15α means "0.15 multiplied by α".
If you convert the number to a fraction, the expression becomes
 (15/100)α
which is the same as
 15α/100
The α stays in the numerator because it started out in the numerator.

Now replace α with $.
 0.15$ = 15$/100 = $15/100
(15$ is the same as $15 because multiplication is commutative.)
=====
Suppose 6 pencils cost $0.50. The price of pencils can be expressed as
 6 pencils/($0.50)
which can also be expressed as
 6 pencils/($·1/2) = 6 pencils·2/($1) = 12 pencils/($1)
The $ started in the denominator and stays in the denominator, even when 0.50 is converted to 1/2.
=====
0.15 can be expressed as
 15/100
or
 1/100 × 15

Therefore, $0.15 = $15/100 = $1/100 × 15

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Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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