If the fractions $$\frac{2}{5}, \frac{3}{8}, \frac{4}{9}, \frac{5}{13}$$ and $$\frac{6}{11}$$ are arranged in ascending order of their values, which one will be the fourth?

### Concept & Strategy Ascending order means arranging items from smallest to largest. To find the fourth fraction out of five, we are looking for the second-largest fraction. ### Step-by-Step Solution Convert each fraction into its decimal representation: * $$\frac{2}{5} = 0.400$$ * $$\frac{3}{8} = 0.375$$ * $$\frac{4}{9} = 0.444$$ * $$\frac{5}{13} \approx 0.384$$ * $$\frac{6}{11} \approx 0.545$$ Now, arrange these decimal values in ascending order: $$0.375 < 0.384 < 0.400 < 0.444 < 0.545$$ Replacing them with their original fractions: $$\frac{3}{8} < \frac{5}{13} < \frac{2}{5} < \frac{4}{9} < \frac{6}{11}$$ The $$4^{\text{th}}$$ fraction in ascending order is $$\frac{4}{9}$$. ### Exam Strategy & Shortcut **Targeting the Second-Largest:** The question asks for the $$4^{\text{th}}$$ position out of $$5$$ elements in ascending order, which is equivalent to the $$2^{\text{nd}}$$ largest overall. Clearly, $$\frac{6}{11} > 0.5$$ is the largest. Among the remaining fractions (which are all less than $$0.5$$), $$\frac{4}{9}$$ ($$0.44$$) is obviously greater than $$\frac{2}{5}$$ ($$0.40$$), $$\frac{3}{8}$$ ($$0.375$$), and $$\frac{5}{13}$$ ($$0.38$$). Thus, $$\frac{4}{9}$$ takes the second-highest spot easily. ### Common Pitfall Miscounting the index from the wrong side (e.g., finding the fourth largest instead of the fourth smallest). Always write out the sequence or map "4th in ascending order" directly to "2nd largest". ### Final Answer **Therefore, the correct answer is option (c).**