Expert: Ahmed Salami - 11/17/2004

Question
Hello:

I want to thank you for the reply.

6 pens/1/2 dozen pens can be simplified to 1 by converting units or to 12 pens/1 dozen by dividing both denominator and numerator by 1/2.
Under what circumstances should 6 pens/1/2 dozen be change to 1 and under what circumstances should 6 pens/1/2 dozen be changed to 12 pens/1 dozen?

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Followup To
Question -
Hello:

I thank you for the reply.
Yes, I am merely stating that 6 pens = 1/2 dozen pens.  How can it be expressed so that (6 pens/1/2 dozen pens) is not confusing and that it indicates that 6 pens equals 1/2 dozen pens?
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Followup To
Question -
Hello:

I thank you for the reply.  I am curious to know how 6 pens/1/2 dozen pens equals 1.  Can you demonstrate how this equals 1?

I placed the 1/2 dozen pens under the 6 pens because 6 pens represents 1/2 dozen pens.  I did not know how adding the 1/2 dozen pens under the 6 pens would change the answer.

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Followup To
Question -
Hello:

I want to thank you for the reply.

If 3 pens cost $0.30, then 6 pens will cost $0.60.  The calculation should equal $0.60. I added the (1/2 dozen pens) as a denominator for 6 pens. I thought that it would not change the calculation.
Compare 3 pens/6 pens = $0.30/$? to 3 pens/(6 pens/1/2 dozen pens) = $0.30/$?
$0.60 should be the correct answer.

After cross multiplication, the calculation should appear as follows: (6 pens/1/2 dozen pens) X $0.30 = 3 pens X $?

Solve for $?

I thank you for your follow-up reply.

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Followup To
Question -
Hello:

Can you solve the following?

(6 pens/1/2 dozen pens) X $0.30 = 3 pens X $?

Answer: $0.60

Divide both sides by 3 pens. However, when I divide the left side by 3 pens, the result is one of the following, either divide $0.30 by 3 pens or divide (6 pens/1/2 dozen pens) by 3 pens.
Dividing $0.30 by 3 pens equals $0.10/1 pen, $0.30/3 pens.
Dividing (6 pens/1/2 dozen pens) by 3 pens equals 1/3 pens, (6 pens/1/2 dozen pens)/3 pens

Can you demonstrate how the answer becomes $0.60 by dividing $0.30 by 3 pens and by dividing (6 pens/1/2 dozen pens) by 3 pens?

I thank you for your reply



Answer -
Hi,
Are you sure the answer is $0.60?
From what I can see here, you're right about the answer being $0.10.
Regards.
Answer -
Hi,
Sorry for the lateness.
(6 pens/1/2 dozen pens) is simply 1.
So, (6 pens/1/2 dozen pens) X $0.30 = 3 pens X $?
is simply 1 X $0.30 = 3 pens X $?
which would still give $0.10
I don't understand why you added the (1/2 dozen pens) as a denominator for 6 pens and still expected that it would not change the calculation.
Regards.





Answer -
Hi,
If you were dividing 6 pens by 1/2 dozen pens, then it would be 1 but if you were merely stating that 6 pens = 1/2 dozen pens, your answer of $0.60 would then be right.
But then your notation of stating that 6 pens = 1/2 dozen pens by writing 6 pens/ 1/2dozen pens is very confusing.
Regards.
Answer -
Hi,
Its not even a necessity that you try to show that 6 pens equals 1/2 dozen pens. But if you insist on showing it, you could write it as 6 pens(i.e 1/2 dozen pens)which seems better.
Regards.

Answer
Hi,
There are actually no rules concerning that. It all comes down to the situation, you have to adjust things to suit you. In a particular situation, you might even need to convert 6/1/2 dozen to 3/1/4 dozen. It all depends on the situation.
Regards.