M21-01

Official Solution:

Which of the following fractions is the largest?

A. \(\frac{9}{17}\)


B. \(\frac{17}{35}\)


C. \(\frac{31}{61}\)


D. \(\frac{25}{52}\)


E. \(\frac{41}{81}\)


The fractions \(\frac{17}{35}\) and \(\frac{25}{52}\) are both less than \(\frac{1}{2}\), so they can be eliminated.

Comparing the other fractions:

\(\frac{9}{17}\) can be broken down as \(\frac{8.5}{17} + \frac{0.5}{17}\), which equals \(\frac{1}{2} + \frac{0.5}{17}\).

\(\frac{31}{61}\) can be broken down as \(\frac{30.5}{61} + \frac{0.5}{61}\), or \(\frac{1}{2} + \frac{0.5}{61}\).

\(\frac{41}{81}\) can be broken down as \(\frac{40.5}{81} + \frac{0.5}{81}\), equating to \(\frac{1}{2} + \frac{0.5}{81}\).

Since \((\frac{1}{2} + \frac{0.5}{17}) > (\frac{1}{2} + \frac{0.5}{61}) > (\frac{1}{2} + \frac{0.5}{81})\), then option A has the largest value among the given fractions.


Answer: A