Which sequence of fractions is in descending order (from largest to smallest)?

Introduction / Context:Ordering fractions requires reliable comparison. The goal is to list the given three fractions in strictly descending order (largest first, smallest last).

Given Data / Assumptions:

• Fractions to compare: 7/9, 5/7, 3/5.
• All are positive proper fractions.

Concept / Approach:Use decimal approximations or cross-multiplication. For quick intuition, compare values roughly: 7/9 ≈ 0.777…, 5/7 ≈ 0.714…, 3/5 = 0.6. This suggests 7/9 > 5/7 > 3/5.

Step-by-Step Solution:

Verification / Alternative check:Cross-multiplication: Compare 7/9 and 5/7: 7*7 = 49 vs 5*9 = 45 ⇒ 7/9 > 5/7. Compare 5/7 and 3/5: 5*5 = 25 vs 3*7 = 21 ⇒ 5/7 > 3/5. Chain gives 7/9 > 5/7 > 3/5.

Why Other Options Are Wrong:

• Any sequence not matching 7/9 > 5/7 > 3/5 either reverses one comparison or is fully incorrect.

Common Pitfalls:

• Assuming a larger denominator always means a smaller value without checking the numerator.
• Mixing up descending with ascending order.

Final Answer:7/9, 5/7, 3/5