Of all the explanations I read, I feel the below one is the best one.

Since we need to find out what's closest to 1/2, just subtract that from each of the options.

(A) 4/7 - 1/2 = 1/7
(B) 5/9 - 1/2 = 1/18
(C) 6/11 - 1/2 = 1/22
(D) 7/13 - 1/2 = 1/26
(E) 9/16 - 1/2 = 2/32 => 1/16

From the above since 1/26 is the lowest number, (D) is the correct answer.
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ScottTargetTestPrep /VeritasKarishma. Kindly help. If the Options include the following three:

1. 5/11
2. 50/99
3. 50/101.

Then with the above approach I am getting two negative values (For 1 and 3). Should I ignore the negative sign and focus on largest denominator ? So that the largest denominator can be the ans.

In the original example, all the given answer choices were greater than 1/2; that’s why we didn’t bother with absolute values and just subtracted 1/2 from each answer choice. In reality, if some of the answer choices were greater than 1/2 and some were less, we would compare the absolute value of the difference of the numbers and 1/2. The reason for that has to do with distances on the real number line; the distance between two real numbers is the absolute value of their difference. So, for the numbers you provided, you should compare the absolute values of the distances and take the one closest to zero. Another way of saying that is for the ones greater than 1/2, subtract 1/2 and for the ones less than 1/2, subtract those numbers from 1/2.
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I solved this by % method.
If we know a few fractions --> percentages conversions, it will be easier.
The Question asks - fraction closest to \(\frac{1}{2}\)--> 50%

Let analyze the options
A) \(\frac{4}{7}\) -- \(4*\frac{1}{7}\) = \(14.28 * 4\) = \(57.something%\) (Since, we know \(\frac{1}{7}\) = 14.28%) - 57.14% to be precise

B) \(\frac{5}{9}\) -- \(5*\frac{1}{9}\) = \(11.11 * 5\) = \(55.something%\) (Since, we know \(\frac{1}{9}\) = 11.11%) - 55.55% to be precise

C) \(\frac{6}{11}\) -- \(6*\frac{1}{11}\) = \(9.09 * 6\) = \(54.something%\) (Since, we know \(\frac{1}{11}\) = 09.09%) - 54.54% to be precise

D) \(\frac{7}{13}\) -- \(7*\frac{1}{13}\) = \(7.67 * 7\) = \(53.something%\) (Since, we know \(\frac{1}{13}\) = 07.67%) - 53.80% to be precise

E) \(\frac{9}{16}\) -- \(9*\frac{1}{16}\) = \(6.25 * 9\) = \(56.something%\) (Since, we know \(\frac{1}{16}\) = 06.25%) - 56.25% to be precise

Clearly, Option A to Option E ranges from - 57, 55, 54, 53, 56 % respectively with 53% being the closest to 50%
Hence, our answer Option D \(\frac{7}{13}\)

Just for info below are some basic fraction to a percentage conversion
\(\frac{1}{1} = 100\)% ------ \(\frac{1}{2} = 50\)%

\(\frac{1}{3} = 33.33\)% ------ \(\frac{1}{4} = 25\)%

\(\frac{1}{5} = 20\)% ------ \(\frac{1}{6} = 16.67\)%

\(\frac{1}{7} = 14.28\)% ------ \(\frac{1}{8} = 12.25\)%

\(\frac{1}{9} = 11.11\)% ------ \(\frac{1}{10} = 10\)%

\(\frac{1}{11} = 09.09\)% ------ \(\frac{1}{12} = 8.33\)%

\(\frac{1}{13} = 7.67\)% ------ \(\frac{1}{14} = 7.14\)%

\(\frac{1}{15} = 7.33\)% ------ \(\frac{1}{16} = 6.25\)%

\(\frac{2}{5} = 40\)% ------ \(\frac{3}{5} = 60\)%

\(\frac{3}{4} = 75\)% ------ \(\frac{4}{5} = 80\)%