Evaluate the compound fraction: (5/8) × (2 3/5) ÷ (4/9). Convert the mixed number to an improper fraction and simplify to an exact fractional result.

Introduction / Context:
This question checks fluency with mixed numbers, improper fractions, and division of fractions. Success depends on consistent conversion and careful cancellation to avoid arithmetic bloat.

Given Data / Assumptions:

• Expression: (5/8) × (2 3/5) ÷ (4/9).
• 2 3/5 is a mixed number, not a product of integers.
• Goal: Produce the exact simplified fraction.

Concept / Approach:
Convert 2 3/5 to an improper fraction: 2 3/5 = 13/5. Division by 4/9 is multiplication by its reciprocal 9/4. Multiply numerators and denominators and simplify if possible.

Step-by-Step Solution:

Verification / Alternative check:
As a decimal, 117/32 = 3.65625. Back-multiplying confirms the same decimal from the original sequence, indicating no cancellation mistakes.

Why Other Options Are Wrong:
213/27, 111/27, 223/32, and 321/32 arise from mixing the divide-by-reciprocal step or misapplying cancellation. None reduce to the correct value 117/32.

Common Pitfalls:
Forgetting to invert 4/9 during division, leaving the mixed number unconverted, or dropping factors during cancellation.

Final Answer:
117/32