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GMAT Arithmetic
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Author:  questioner [ Thu Mar 29, 2012 4:40 am ]
Post subject:  GMAT Arithmetic

13/3 + 2 × (52/12) =

A. 13
B. 10.4
C. 10 3/4
D. 10 2/3
E. 7 1/3
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Hi, can you please breakdown this fraction problem step by step? I reviewed the answer key, but I am still confused. Thank you!

Author:  Gennadiy [ Thu Mar 29, 2012 4:51 am ]
Post subject:  Re: a practice question: fractions

13/3 + 2 × (52/12) =
First of all, let's look at the original expression:
13/3 looks ok. So we let it be for now.
2 × (52/12) This term can be simplified at least by dividing the numerator and denominator by 2. So let's do it.

52/12 = 26/6
It's clear that we can simplify further dividing by 2.
26/6 = 13/3
We got the same fraction as the first term of the original expression. So the expression becomes:
13/3 + 2 × (13/3)

Now we can take the common multiplier of the two terms, 13/3, out:
13/3 + 2 × (13/3) = (13/3)(1 + 2)
Note, that 13/3 = (13/3) × 1

The rest is simple:
(13/3)(1 + 2) = (13/3) × 3 = 13
The correct answer is A.

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Another way to simplify 2 × (52/12) is the following:
(2 × 52)/12 = 52/6 = 26/3
Then we just add two fractions with the same denominator:
13/3 + 26/3 = 39/3
And simplify the result dividing the numerator and the denominator by 3:
39/3 = 13/1 = 13

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