Make the equation true by swapping signs — Which interchange of signs makes the statement correct? (18 ÷ 9) + 3 × 5 = 45

Introduction / Context:Sign-interchange problems ask you to swap two operator symbols everywhere they occur to make a false equation true. Parentheses and operator precedence must still be respected.

Given Data / Assumptions:

• Original: (18 ÷ 9) + 3 × 5 = 17, which is not 45.
• We may interchange a specified pair of signs throughout the expression.
• Standard precedence applies after the swap.

Concept / Approach:Try swapping '+' and '÷' wherever they appear. The division inside parentheses becomes addition, and the addition between terms becomes division, potentially rebalancing the expression.

Step-by-Step Solution:Swap '+' ↔ '÷': Expression becomes (18 + 9) ÷ 3 × 5.Evaluate: 27 ÷ 3 = 9; 9 × 5 = 45.Therefore, after the swap, the equation equals 45 and is correct.

Verification / Alternative check:Check another option: swapping '×' and '÷' yields (18 × 9) + 3 ÷ 5 = 162.6…, not 45.

Why Other Options Are Wrong:

• 'x ÷': makes the value ≫ 45.
• Swapping numbers ('18 and 5' or '3 and 9') does not achieve 45 under precedence.
• 'None of these': unnecessary because '+ ÷' works.

Common Pitfalls:Swapping only one occurrence instead of all occurrences, or discarding parentheses impact when recalculating.

Final Answer:+ ÷