Operator placement — Replace each ‘‘*’’ with the correct mathematical sign so that the equation is true. 24 * 34 * 2 * 5 * 12

Difficulty: Medium

Correct Answer: = ÷ - +

Explanation:


Introduction / Context:
These problems test whether you can place arithmetic symbols so that both sides of an equation balance. You must respect standard precedence (× and ÷ before + and −) on each side of the equality, and the single “=” must split the statement into a left-hand side (LHS) and a right-hand side (RHS).


Given Data / Assumptions:

  • Template: 24 {s1} 34 {s2} 2 {s3} 5 {s4} 12
  • Exactly one of {s1..s4} is “=”; the rest are chosen from +, −, ×, ÷.
  • Usual operator precedence applies on each side of “=”.


Concept / Approach:
Try options that place “=” where the remaining three operators can naturally form a simple calculation. Check each option with clean arithmetic to avoid precedence mistakes.


Step-by-Step Solution:

Test Option C: s1 = “=”, s2 = “÷”, s3 = “−”, s4 = “+”.This yields: 24 = 34 ÷ 2 − 5 + 12.Compute RHS with precedence: 34 ÷ 2 = 17; then 17 − 5 + 12 = 12 + 12 = 24.Hence LHS 24 equals RHS 24 → true.


Verification / Alternative check:
Briefly test other choices: they evaluate to values different from 24 (e.g., 24 + 34 ÷ 2 × 5 = 109; 24 = 34 ÷ 2 + 5 − 12 gives 10). Thus only Option C balances.


Why Other Options Are Wrong:

  • They either misplace the equality or produce incorrect totals due to precedence.


Common Pitfalls:

  • Forgetting that division happens before addition/subtraction.
  • Trying to evaluate left-to-right across the equality instead of evaluating each side independently.


Final Answer:
= ÷ - +

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