The equation below is incorrect if we follow the standard order of operations (BODMAS/PEMDAS): 4 × 3 − 6 ÷ 2 + 7 = 8 By interchanging (swapping) exactly two operation signs among ×, −, ÷ and +, which pair of signs should be swapped so that the equation becomes correct?

Introduction / Context: This question tests operator precedence and careful checking. You must swap exactly two operator symbols in the expression so that, after applying the standard order of operations, the left-hand side becomes 8.

Given Data / Assumptions:

• Original (incorrect) equation: 4 × 3 − 6 ÷ 2 + 7 = 8 • Swap exactly two operators (their positions) • Use standard precedence: × and ÷ before + and −

Concept / Approach: Try swapping candidate operator pairs and re-evaluate the left-hand side using the correct precedence rules. Because only one swap is allowed, we look for the unique pair that makes the value exactly 8.

Step-by-Step Solution: 1) Evaluate original to confirm it is wrong: 4 × 3 = 12 and 6 ÷ 2 = 3 LHS = 12 − 3 + 7 = 16 (not 8) 2) Swap the positions of − and +, giving: 4 × 3 + 6 ÷ 2 − 7 3) Apply precedence again: 4 × 3 = 12 6 ÷ 2 = 3 4) Now combine with + and −: LHS = 12 + 3 − 7 = 8 5) This matches the required RHS (8), so the swap is correct.

Verification / Alternative check: The corrected equation is: 4 × 3 + 6 ÷ 2 − 7 = 8 Since 12 + 3 − 7 = 8 exactly, the fix is valid without ambiguity.

Why Other Options Are Wrong: • × and +: changes the structure but does not yield 8 with precedence. • ÷ and ×: produces a different multiplication/division pattern, not 8. • × and −, or − and ÷: similarly fail to produce 8 after precedence.

Common Pitfalls: • Evaluating strictly left-to-right and ignoring precedence. • Swapping operator meanings instead of swapping their positions.

Final Answer: − and +