Question : The greatest fraction among $\frac{2}{3}, \frac{5}{6}, \frac{11}{15} \text{ and } \frac{7}{8} \text{ is:}$
Option 1: $\frac{7}{8}$
Option 2: $\frac{11}{15}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{2}{3}$
Correct Answer: $\frac{7}{8}$
Solution :
Given numbers are = $\frac{2}{3},\frac{5}{6},\frac{11}{15},\frac{7}{8}$
LCM of denominators (3, 6, 15, 8) = ${3×2×5×4} = 120$
Making all denominators the same for comparison,
$⇒ \frac{2}{3}\times \frac{40}{40} = \frac{80}{120} $
$⇒ \frac{5}{6}\times \frac{20}{20} = \frac{100}{120} $
$⇒ \frac{11}{15}\times \frac{8}{8} = \frac{88}{120} $
$⇒ \frac{7}{8}\times \frac{15}{15} =\frac{105}{120} $
Now, compare the numerators (105 > 100 > 88 > 80)
So, $\frac{7}{8}$ is the greatest fraction.
Hence, the correct answer is $\frac{7}{8}$.
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