Operator substitution — If “+” means minus, “−” means multiply, “÷” means plus, and “×” means divide, evaluate: 10 × 5 ÷ 3 − 2 + 3

Difficulty: Medium

Correct Answer: 5

Explanation:


Introduction / Context:
This is a symbol-redefinition puzzle. Each symbol is reassigned to a different arithmetic operation. After replacing symbols, evaluate respecting normal precedence (× and ÷ before + and −) unless brackets dictate otherwise.


Given Data / Assumptions:

  • “+” → minus (−)
  • “−” → multiply (×)
  • “÷” → plus (+)
  • “×” → divide (÷)


Concept / Approach:
Rewrite the expression with the true operations, then compute with standard precedence.


Step-by-Step Solution:

Original: 10 × 5 ÷ 3 − 2 + 3Swap: 10 ÷ 5 + 3 × 2 − 3Compute ×/÷ first: 10 ÷ 5 = 2; 3 × 2 = 6.Then +/−: 2 + 6 − 3 = 5.


Verification / Alternative check:
Evaluate left-to-right but still honoring precedence: same result 5.


Why Other Options Are Wrong:

  • 53/3, 21, 36 arise from misapplying precedence or incorrect replacements.


Common Pitfalls:

  • Treating the redefined symbols with altered precedence; precedence stays the same as the actual operation.


Final Answer:
5

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