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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.

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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