Question : Which of the following statements is true?
I. $\frac{5}{11}>\frac{5}{6}$
II. $\frac{5}{9}>\frac{8}{9}$
III. $\frac{5}{6}>\frac{4}{5}$
Option 1: Only III
Option 2: Both I and II
Option 3: Only II
Option 4: Only I
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Correct Answer: Only III
Solution :
Fractions with the same numerator are compared based on their denominators. The fraction with the smaller denominator is greater.
Fractions with the same denominator are compared based on their numerators. The fraction with the larger numerator is greater.
I. $\frac{5}{11} < \frac{5}{6}$ ($\frac{5}{11}$ is smaller than $\frac{5}{6}$ as their numerators are equal and 11 is greater than 6)
II. $\frac{5}{9} < \frac{8}{9}$ ($\frac{5}{9}$ is smaller than $\frac{8}{9}$ as their denominator is equal and 5 is less than 8)
II. $\frac{5}{6} > \frac{4}{5}$ ($\frac{5}{6}=\frac{25}{30}$ and $\frac{4}{5}=\frac{24}{30}$)
Hence, the correct answer is III.
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