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## Fraction Cancellation Rules

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stevennu Senior | Next Rank: 100 Posts
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#### Fraction Cancellation Rules

Sun Aug 04, 2013 4:42 pm
I'm working through the Manhattan GMAT quant books and came across the following question.

Simplify: 10X / 5 + X

Why can't we simplify by cancelation? I know there are rules that regulate when we can and cannot cancel but I cannot seem to find a concise set of rules anywhere. Can someone shed some light?

Thanks

stevennu Senior | Next Rank: 100 Posts
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Tue Aug 06, 2013 8:25 am
Matt@VeritasPrep wrote:
One way of thinking about it:

(10X + 8)/2 = (10X)/2 + 8/2 = 5x + 4

Since you can break the sum into two fractions, you can break them up, then reduce each one individually.

But (10X)/(8+2) is NOT (10x)/8 + (10x)/2, or (5/4)x + 5x ... it's (10X)/10, or x.

So you CAN'T break these up into two fractions and reduce each part individually.

As for fraction rules, how about:

http://isites.harvard.edu/fs/docs/icb.topic760749.files/webAPPEodd.pdf
It's clearly been a while since highschool algebra...

Thanks.

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Matt@VeritasPrep GMAT Instructor
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Mon Aug 05, 2013 6:44 pm
One way of thinking about it:

(10X + 8)/2 = (10X)/2 + 8/2 = 5x + 4

Since you can break the sum into two fractions, you can break them up, then reduce each one individually.

But (10X)/(8+2) is NOT (10x)/8 + (10x)/2, or (5/4)x + 5x ... it's (10X)/10, or x.

So you CAN'T break these up into two fractions and reduce each part individually.

As for fraction rules, how about:

http://isites.harvard.edu/fs/docs/icb.topic760749.files/webAPPEodd.pdf

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Aug 05, 2013 12:08 am
Hi stevennu,

What you've typed in your post needs some clarification.

The fraction that you want to simplify...is it this:

10X/5 + X

or is it this:

10X / (5 + X)

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stevennu Senior | Next Rank: 100 Posts
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Mon Aug 05, 2013 11:24 am
The latter.

10X/(5+X)

stevennu Senior | Next Rank: 100 Posts
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Mon Aug 05, 2013 11:53 am
I think the following link pretty much spells out the rule I was looking for.

That is, you cannot reduce part of a sum or part of a difference. Can you provide me any other links or examples?

http://www.regentsprep.org/Regents/math/ALGEBRA/AV5/reducefrac.htm

Thanks.

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