Operator re-mapping – evaluate the expression under new symbol meanings: If "+" means "-", "−" means "×", "×" means "÷" and "÷" means "+", then compute the value of: 16 × 2 ÷ 25 + 7 − 4

Difficulty: Easy

Correct Answer: 5

Explanation:


Introduction / Context:
In operator re-mapping questions, symbols are reassigned new meanings. You must first translate the expression into its true operations and then evaluate with standard operator precedence (× and ÷ before + and −). Careful symbol-by-symbol substitution prevents common mistakes.



Given Data / Assumptions:

  • Mapping: "+" → "−", "−" → "×", "×" → "÷", "÷" → "+".
  • Expression: 16 × 2 ÷ 25 + 7 − 4.


Concept / Approach:
Translate each symbol first, then compute. Do not mix the original symbols with their new meanings during evaluation; complete translation ensures correct precedence and arithmetic.



Step-by-Step Solution:

Translate: "×" → "÷", "÷" → "+", "+" → "−", "−" → "×".So the expression becomes: 16 ÷ 2 + 25 − 7 × 4.Evaluate: 16 ÷ 2 = 8; 7 × 4 = 28; then 8 + 25 − 28 = 5.


Verification / Alternative check:
Re-translate in a second pass to confirm no symbol was missed; recompute to confirm 5.



Why Other Options Are Wrong:

104, 22, and 4 result from misreading precedence or applying the mapping incorrectly (e.g., translating commas of operations inconsistently).


Common Pitfalls:
Attempting to compute while translating on the fly; always finish translation first, then apply normal precedence.



Final Answer:
5

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