Fraction Cancellation Rules

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stevennu Senior | Next Rank: 100 Posts Default Avatar
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Fraction Cancellation Rules

Post Sun Aug 04, 2013 4:42 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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    Post 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 Default Avatar
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    Post Mon Aug 05, 2013 11:24 am
    The latter.

    10X/(5+X)

    stevennu Senior | Next Rank: 100 Posts Default Avatar
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    Post 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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    Post 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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    stevennu Senior | Next Rank: 100 Posts Default Avatar
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    Post 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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