Bracketed fractional simplification — nested division and “of” as multiplication Evaluate 3 ÷ [(8 − 5) ÷ {(4 − 2) ÷ (2 + 8/13)}] carefully using left-to-right precedence for × and ÷.

Introduction / Context:
Complex fractional expressions with nested parentheses test precision with order of operations. Here, “of” means multiplication, and division and multiplication share the same precedence, evaluated left to right. The main skill is systematic simplification from the innermost bracket outward.

Given Data / Assumptions:

• Expression: 3 ÷ [(8 − 5) ÷ {(4 − 2) ÷ (2 + 8/13)}].
• Interpret “of” (if present) as multiplication.
• Perform operations in the structured bracket order.

Concept / Approach:
Compute from the deepest inner group: first (2 + 8/13), then (4 − 2), then form the division (4 − 2)/(2 + 8/13). Next, evaluate (8 − 5) ÷ {previous result}. Finally, divide 3 by that outcome.

Step-by-Step Solution:
Compute inner sum: 2 + 8/13 = 34/13.Compute 4 − 2 = 2.Form ratio: (4 − 2)/(2 + 8/13) = 2 / (34/13) = 2 * 13/34 = 26/34 = 13/17.Compute 8 − 5 = 3.Now 3 ÷ (13/17) = 3 * 17/13 = 51/13.Finally, 3 ÷ [51/13] = 3 * 13/51 = 39/51 = 13/17.

Verification / Alternative check:
Convert intermediate numbers to decimals to sanity-check: 13/17 ≈ 0.7647. The inner ratio 2/(2.615...) ≈ 0.7647; the outer sequence returns to the same exact fraction.

Why Other Options Are Wrong:
68/13 and 17/13 invert or misplace a division; 13/68 is an over-inversion; 51/13 is an intermediate value, not the final result.

Common Pitfalls:
Reversing the order of division; dropping the final division by 3; mishandling the conversion of mixed fractions to improper fractions.

Final Answer:
13/17