Which of the following sequences of fractions is correctly arranged in descending order (from greatest value to least value)?

Introduction / Context:
Ordering fractions is a common task in aptitude and school mathematics. This question asks you to determine which sequence lists the given fractions in descending order, that is, from the largest value to the smallest. Understanding how to compare fractions is essential to solve such problems accurately.

Given Data / Assumptions:

• Fractions involved: 5/9, 7/11, 8/15, 11/17.
• We must identify the option that lists these fractions from greatest to least.
• No calculators are strictly required; approximate values or cross-multiplication are enough.

Concept / Approach:
There are two main ways to compare these fractions:

• Convert each fraction to a decimal approximation.
• Use cross-multiplication to compare pairs of fractions without explicitly using decimals.

We will use decimal approximations for clarity and then confirm the order.

Step-by-Step Solution:
Step 1: Approximate each fraction as a decimal: 5/9 ≈ 0.5556 7/11 ≈ 0.6364 8/15 ≈ 0.5333 11/17 ≈ 0.6471 Step 2: Arrange these decimal values from largest to smallest: 0.6471 (11/17), 0.6364 (7/11), 0.5556 (5/9), 0.5333 (8/15). Step 3: Convert this back into a sequence of fractions: 11/17, then 7/11, then 5/9, and finally 8/15.

Verification / Alternative check:
We can compare 11/17 and 7/11 by cross-multiplication: 11 × 11 = 121 and 7 × 17 = 119. Since 121 > 119, 11/17 > 7/11. Similarly, compare 7/11 and 5/9: 7 × 9 = 63 and 5 × 11 = 55, so 7/11 > 5/9. Finally, 5/9 and 8/15: 5 × 15 = 75 and 8 × 9 = 72, so 5/9 > 8/15. This confirms the descending order 11/17 > 7/11 > 5/9 > 8/15.

Why Other Options Are Wrong:
Options A, B, and C place at least one fraction out of order when compared carefully using decimals or cross-multiplication.
Option E "None of these" is incorrect because option D provides the correct descending order.

Common Pitfalls:
A frequent mistake is to compare fractions by looking only at numerators or denominators separately, which can be misleading. Another issue is rounding decimals too aggressively, which might reverse the order of close values. Using cross-multiplication is a safe way to avoid these errors.

Final Answer:
The correct descending order is 11/17, 7/11, 5/9, 8/15.