Which of the following are in descending order of their values?

### Concept & Strategy To arrange fractions in descending order, convert them into decimals or use cross-multiplication to compare their relative values. ### Step-by-Step Solution Let's convert each fraction into its approximate decimal value: * $$\frac{5}{9} \approx 0.555$$ * $$\frac{7}{11} \approx 0.636$$ * $$\frac{8}{15} \approx 0.533$$ * $$\frac{11}{17} \approx 0.647$$ Comparing the decimal values: $$0.647 > 0.636 > 0.555 > 0.533$$ Arranging the corresponding fractions in descending order: $$\frac{11}{17} > \frac{7}{11} > \frac{5}{9} > \frac{8}{15}$$ ### Exam Strategy & Shortcut **Approximation & Native Division:** Instead of fully dividing, look at the values relative to half ($$0.5$$). All are slightly greater than $$0.5$$. Quickly compute just two decimal places for the closest ones: $$\frac{11}{17} \approx 0.64$$ and $$\frac{7}{11} \approx 0.63$$. Since $$\frac{11}{17}$$ is the largest, options (c) and (d) are the only candidates. Next, compare $$\frac{5}{9} \approx 0.55$$ and $$\frac{8}{15} \approx 0.53$$, confirming option (d) is correct. ### Common Pitfall Confusing ascending order (smallest to largest) with descending order (largest to smallest). Always double-check the requested order before marking the answer. ### Final Answer **Therefore, the correct answer is option (d).**