Question : Which of the following is correct?
Option 1: $\frac{2}{3}< \frac{3}{5}< \frac{11}{15}$
Option 2: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$
Option 3: $\frac{11}{15}< \frac{3}{5}< \frac{2}{3}$
Option 4: $\frac{3}{5}< \frac{11}{15}< \frac{2}{3}$
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Correct Answer: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$
Solution : Given: The numbers are $\frac{2}{3}, \frac{3}{5}, \frac{11}{15}$. To find the greatest fraction, we have to find the LCM of denominators. LCM of denominators $=$ LCM $(3, 5, 15) = {(3×5)} = 15$ We have to make all denominators the same for comparison, $ ⇒\frac{2}{3}\times \frac{5}{5} = \frac{10}{15} $ $ ⇒\frac{3}{5}\times \frac{3}{3} = \frac{9}{15} $ $ ⇒\frac{11}{15}\times \frac{1}{1} = \frac{11}{15} $ Now, by comparing numerators $(9<10<11)$. So, we can say $\frac{3}{5}< \frac{2}{3}<\frac{11}{15}$. Hence, the correct answer is $\frac{3}{5}< \frac{2}{3}<\frac{11}{15}$.
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