Compute the exact value of the fractional operation: (5/8) * (23/5) ÷ (4/9) = ?

Introduction / Context:
This question checks precision with multiplying and dividing rational numbers. The fastest path is to convert the entire expression to a product by multiplying with the reciprocal of the divisor, then cancel common factors.

Given Data / Assumptions:

• Expression: (5/8) * (23/5) ÷ (4/9).
• All values are exact rational numbers.
• No rounding; simplify by cancellation when possible.

Concept / Approach:
Division by a fraction equals multiplication by its reciprocal. Cancel shared factors before multiplying across to avoid large intermediate numbers.

Step-by-Step Solution:

Verification / Alternative check:
As a decimal: 207/32 = 6.46875. Computing each step numerically also gives 6.46875, confirming the fraction.

Why Other Options Are Wrong:
9/4 and 27/8 reflect partial multiplication errors; 23/32 comes from inverting the wrong factor; 13/10 is unrelated.

Common Pitfalls:
Forgetting to flip the last fraction, canceling across addition (not allowed), or prematurely rounding decimals. Keep everything fractional until the end.

Final Answer:
207/32