Operator placement — Replace each ‘‘*’’ with the correct mathematical sign so that the equation is true. 24 * 34 * 2 * 5 * 12
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A+ ÷ x =
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B= ÷ + -
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C= ÷ - +
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D+ ÷ = x
Answer
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:= ÷ - +