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
Fraction Cancellation Rules
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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)
GMAT assassins aren't born, they're made,
Rich
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)
GMAT assassins aren't born, they're made,
Rich
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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?
https://www.regentsprep.org/Regents/math ... cefrac.htm
Thanks.
That is, you cannot reduce part of a sum or part of a difference. Can you provide me any other links or examples?
https://www.regentsprep.org/Regents/math ... cefrac.htm
Thanks.
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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:
https://isites.harvard.edu/fs/docs/icb.t ... PPEodd.pdf
(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:
https://isites.harvard.edu/fs/docs/icb.t ... PPEodd.pdf
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It's clearly been a while since highschool algebra...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:
https://isites.harvard.edu/fs/docs/icb.t ... PPEodd.pdf
Thanks.