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Arithmetic

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Re: Arithmetic

by srawat_itpro » Thu Dec 20, 2007 11:26 pm
Anonymous wrote:Can someone explain why multiplying both sides of the equation is incorrect if you want to remove the fraction in the denominator.

R = [24F/N]/[P+A/12]

I saw the following question on the GMAT Prep Software exam, and the question stated "Which of the following is an equivalent form of the formula?" My first step was to remove the fraction from the denominator by multiplying each expression by 12. When I did that I also mutliplied the equation on the left side, R, by 12. However, the final solution did not involve this step. The final solution only involved multiplying the numerator and denominator by 12. I always thought in order to maintain equality in any equation, whatever you did to one side of the equation you must do to the other side.

Any thoughts or ideas? Thanks again for sharing.
Hi

I believe its like this
R = [X]/[Y/Z]

What you are doing by multiplying each side with Z is something like:

ZR = [Z][[X]/[Y/Z]]
=> ZR = [Z][[XZ]/[Y]]
=> ZR = [XZ^2]/[Y]

So you see that what you are doing is actually not eliminating Z, but only further multiplying it.

Rgds
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by Suyog » Sat Dec 22, 2007 9:53 am
all the options are given for R...so just consider the R.H.S..

given - R = [24F/N]/[P+A/12]

= 24F / N * 12 / P+A

= 24F(12) / N(P + A)

= [288F]/ [PN+AN]

Ans D.
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by bacardi_blast » Sat Dec 22, 2007 9:58 pm
IMO answer is E

R = [24F/N] /[P + (A/12)]
= [24F/ N] /[12p + A]/ 12
= 24F *12 / N[12P + A]
= 288F/ 12PN + 12AN
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by giambi » Thu Jun 23, 2011 5:48 am
Actually the answer doesn't have a 12 in the last AN.

R = [24F / N] / [P/1(12)+A/12] <=>
[24F/N]/[12P+A]/12 <=>
24F*12 / N (12P + A) <=>
288F / 12PN + AN

Hope this helps.
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by PencilNerd » Sat Jun 25, 2011 6:07 am
The answer is D. This is just testing the rule that when you have one fraction divided by another fraction you change the problem to multiplication and flip the second fraction. So instead of:
R = [24F/N] / [P+A/12], on the right side flip the second fraction and multiply:
R = [24F/N] * [12/P+A]

To multiply fractions just do top times top and bottom times bottom, so the above becomes:

R = [24F * 12] / [N * P+A] which simplifies to choice D:
R = 288F/[NP+NA]
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by Tani » Sat Jun 25, 2011 7:29 am
When you multiply both the top and bottom of a fraction by x, you are essentially multiplying by x/x, which equals one. Therefore, you don't have to do anything to the other side since you haven't changed the value of the first side.
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