EBITDA wrote:

Which of the following fractions is the largest?

A) 5/6

B) 11/14

C) 12/15

D) 17/21

E) 29/35

Although unlikely to be a general method, I found inverting the fractions and finding the smallest to be useful and fast.

\(\text{(A) }\frac{1}{6} = \frac{3}{18} = 0.1\bar{6}\\

\text{(B) }\frac{3}{14}\\

\text{(C) }\frac{3}{15}\\

\text{(D) }\frac{4}{21}\\

\text{(E) }\frac{6}{35} = \frac{3}{17.5}\)

By setting the numerator to 3, we can eliminate all but one \(\Big(\frac{3}{18} < \frac{3}{17.5} < \frac{3}{15} < \frac{3}{14}\Big)\).

We are left with \(\frac{4}{21}\text{ and }\frac{1}{6}\). \(\frac{1}{6} = \frac{4}{24}\).

Therefore \(\frac{1}{6}\) is the smallest. \(\frac{5}{6}\) is therefore the largest.

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