Which of the following fractions is the greatest?
\(\tfrac{5}{7}\)
\(\tfrac{5}{6}\)
\(\tfrac{5}{9}\)
\(\tfrac{5}{8}\)
All the fractions have the same numerator: (5).
Rule: When numerators are the same, the fraction with the smaller denominator is larger.
Compare denominators:
(6 < 7 < 8 < 9)
So the order is:
( frac{5}{6} > frac{5}{7} > frac{5}{8} > frac{5}{9})
Therefore, the greatest fraction is ( frac{5}{6}).
Quick check (decimals):