Which of the following sequences of fractions is correctly arranged in descending order of their values (from largest to smallest)?

Introduction / Context:
This question tests your ability to compare fractions and arrange them in descending order. Comparing fractions with different denominators is a core skill in arithmetic and is important for number sense, ratio problems, and probability questions.

Given Data / Assumptions:

• The fractions to be compared are 5/9, 7/11, 8/15, and 11/17.
• We must find the sequence that lists these fractions from largest to smallest.
• All fractions are positive and less than 1.
• The options provide different possible orderings of these four fractions.

Concept / Approach:
There are two standard approaches: convert each fraction into a decimal approximation or compare pairs using cross multiplication. Because the denominators are different and not simple multiples of each other, decimal approximations or careful cross multiplication are convenient. Our goal is to determine which fraction is largest, which is smallest, and the correct order in between.

Step-by-Step Solution:
Approximate each fraction as a decimal.5/9 ≈ 0.5556.7/11 ≈ 0.6364.8/15 ≈ 0.5333.11/17 ≈ 0.6471.Now rank these approximate decimal values from largest to smallest: 0.6471 (11/17), 0.6364 (7/11), 0.5556 (5/9), 0.5333 (8/15).Thus the correct descending order is 11/17, 7/11, 5/9, 8/15.

Verification / Alternative check:
We can also verify using cross multiplication without decimals. To compare 11/17 and 7/11, compute 11 × 11 = 121 and 7 × 17 = 119. Since 121 > 119, 11/17 > 7/11. Compare 7/11 and 5/9: 7 × 9 = 63 and 5 × 11 = 55, so 7/11 > 5/9. Compare 5/9 and 8/15: 5 × 15 = 75 and 8 × 9 = 72, so 5/9 > 8/15. These comparisons confirm the exact same ordering: 11/17 > 7/11 > 5/9 > 8/15.

Why Other Options Are Wrong:
Any option that places a smaller fraction before a larger one is incorrect. For example, options that start with 5/9 or 7/11 ignore that 11/17 is actually greater than both. Options that place 8/15 before 5/9 contradict our comparison showing 5/9 is larger. Only the option listing 11/17, 7/11, 5/9, 8/15 respects all the pairwise comparisons and therefore represents the true descending order.

Common Pitfalls:
Some learners try to compare fractions by looking only at numerators or denominators, which is misleading when denominators differ. Others may attempt to convert only some fractions to decimals and misjudge the relative sizes due to rounding. Using systematic cross multiplication or consistent decimal approximations for all fractions avoids these issues and leads to the correct ordering.

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