Operator remapping — If “+” means “÷”, “−” means “×”, “×” means “+”, and “÷” means “−”, evaluate: 90 + 18 − 6 × 30 ÷ 4

Difficulty: Medium

Correct Answer: 56

Explanation:


Introduction / Context:
Translate each symbol to its true operation, then compute with standard precedence rules. Carefully track each mapping to avoid mistakes.


Given Data / Assumptions:

  • “+” → “÷”
  • “−” → “×”
  • “×” → “+”
  • “÷” → “−”


Concept / Approach:
Replace first, then evaluate ×/÷ (i.e., the real operations after mapping), finally do +/−.


Step-by-Step Solution:

Expression becomes: 90 ÷ 18 × 6 + 30 − 4Compute: 90 ÷ 18 = 5; 5 × 6 = 30Then: 30 + 30 − 4 = 56


Verification / Alternative check:
Regrouping as (90 ÷ 18) × 6 + (30 − 4) = 30 + 26 = 56 confirms the result.


Why Other Options Are Wrong:
They come from wrong replacements or ignoring precedence.


Common Pitfalls:

  • Accidentally treating the original symbols’ positions as changing precedence. They do not.


Final Answer:
56

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