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# Word Problems/Division

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?

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

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And also, which one of these is correct?

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

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.)
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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
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 6 Politeness = 7 Comment Thanks for the follow-up reply!

Word Problems

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#### Janet Yang

##### Expertise

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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