Interchanges: swap “×” with “÷” and swap the digits 4 ↔ 9 everywhere. Which option becomes a true statement?

Introduction / Context:We must analyze which equality remains (or becomes) true after two global interchanges: swap every “×” with “÷”, and swap every digit 4 with 9 (and 9 with 4). Perform both swaps across the entire equation before evaluating.

Given Data / Assumptions:

• Operator swap: “×” ↔ “÷”.
• Digit swap: 4 ↔ 9 globally.

Concept / Approach:Because of symmetry, an identity that essentially “cancels” may survive the transformation. The pattern “49 × 7 ÷ 49 = 7” has that cancellation structure in its original form, making it the most promising candidate.

Step-by-Step Solution (Option C, structure-based reasoning):

Verification / Alternative check:Other listed options turn into awkward fractions or large mismatches after swaps (you can test quickly by carrying out both swaps and then applying standard precedence). The cancellation-style option is the only one that remains consistent.

Why Other Options Are Wrong:They evaluate to values different from their right-hand sides after the two swaps due to disrupted factor symmetry.

Common Pitfalls:

• Forgetting to perform swaps on the right-hand side as well.

Final Answer:49 x 7 ÷ 49 = 7