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by theCodeToGMAT » Thu Mar 13, 2014 11:29 pm
5/6 +3/2 + 2
--------------
1/3 + 4/9 + 4



= (5+9+12)/6
--------------
(3+4+36)/9


= (26/6) / (43/9)

= (26 * 9) / (6 * 43)

= 26 * 3 / 2 * 43

= 13 * 3 / 43

= 39/43
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by candygal79 » Fri Mar 14, 2014 12:00 am
= (5+9+12)/6
--------------
(3+4+36)/9

Ok why is it /6 and 9 ? I am kind of confused here ...
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by theCodeToGMAT » Fri Mar 14, 2014 12:06 am
candygal79 wrote:= (5+9+12)/6
--------------
(3+4+36)/9

Ok why is it /6 and 9 ? I am kind of confused here ...
5/6 +3/2 + 2
--------------
1/3 + 4/9 + 4

Here, if we consider only Numerator

5/6 +3/2 + 2

So, lets take the LCM considering "6"


= (5 + 9 + 12)/6

= 26/6


Similarly, if we consider only denominator

1/3 + 4/9 + 4

So, lets take the LCM as 9

= (3 + 4 + 36)/9

= 43/9

I hope its better now.
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by GMATGuruNY » Fri Mar 14, 2014 2:13 am
candygal79 wrote:5/6 +3/2 + 2
--------------
1/3 + 4/9 + 4

I tried several times but am not getting 39/43 !
Multiplying a fraction by x/x does not change its value, since x/x = 1.
The least common multiple of the denominators 6, 2, 3 and 9 is 18.
One approach is to multiply the fraction by 18/18:

18 (5/6 + 3/2 + 2) / 18 (1/3 + 4/9 + 4)

= (15 + 27 + 36) / (6 + 8 + 72)

= 78/86

= 39/43.
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