Which of the following fractions is closest to 1 given that a > b > 1?

In addition to the Alternative approach using numbers shown above, we'll show a Logical approach using fraction properties.

A fraction equals 1 when its numerator is equal to its denominator.
So, we're looking for the answer where the numerator is as close to the denominator as possible.
That is, we'd like to make b 'as close as possilbe' to a.
This happens when a and b become larger for the following reason:
The larger the numbers are, the less of an effect the difference between them makes.
For example, say the difference between a and b is 1.
This has a very large effect if a=3 and b=2 (because 1 is 50% of b), but only a small effect if a=101 and b=100 (because 1 is only 1% of b).
So we'll choose the answer choice that makes the numerator and deonminator as large as possible.
(B) is our answer.