Interchange all signs as specified and evaluate the value: Mapping of interchanges: '−' → '+', '+' → '÷', '×' → '−', '÷' → '×'. Find the value of: 6 ÷ 8 + 2 × 5 − 8

Introduction / Context: All operator symbols are to be replaced by new ones according to a fixed mapping. After substituting, evaluate using standard precedence (× and ÷ before + and −).

Given Data / Assumptions:

• Interchanges: −→+, +→÷, ×→−, ÷→×
• Expression: 6 ÷ 8 + 2 × 5 − 8
• Use standard precedence; ×/÷ are left-associative.

Concept / Approach: Apply the mapping to each symbol first; then compute. Do not mix old and new meanings in the same step and do not change numeric order.

Step-by-Step Solution: 1) Substitute: 6 ÷ 8 + 2 × 5 − 8 → 6 × 8 ÷ 2 − 5 + 8 2) ×/÷ left→right: 6 × 8 = 48; 48 ÷ 2 = 24 3) +/−: 24 − 5 = 19; 19 + 8 = 27

Verification / Alternative check: Parenthesized view: ((6 × 8) ÷ 2) − 5 + 8 = (48 ÷ 2) − 5 + 8 = 24 − 5 + 8 = 27.

Why Other Options Are Wrong: 18, 28, and 32 result from common errors such as reversing the ×/÷ left-to-right order or forgetting the +→÷ substitution in the middle of the expression.

Common Pitfalls: Performing +/− before finishing ×/÷ or accidentally keeping an original operator’s meaning after substitution.

Final Answer: 27