Given : \(\frac{1}{2}\) ÷ \(\frac{1}{32}\) - 5 + 50 × 80 = 50
According to the question, after interchanging the signs:
Option 1) ÷ and ×
\(\frac{1}{2}\) ÷ \(\frac{1}{32}\) - 5 + 50 × 80 = 50 ⇒ \(\frac{1}{2}\) × \(\frac{1}{32}\) - 5 + 50 ÷ 80 = 50
⇒ \(\frac{1}{2}\) × \(\frac{1}{32}\) - 5 + 50 ÷ 80 = 50
⇒ \(\frac{1}{2}\) × \(\frac{1}{32}\) - 5 + 0.625 = 50
⇒ \(\frac{1}{64}\) + 0.625 - 5 = 50
⇒ \(\frac{11}{64}\) - 5 = 50
⇒ -4.82 ≠ 50 (LHS ≠ RHS)
Option 2) × and -
\(\frac{1}{2}\) ÷ \(\frac{1}{32}\) - 5 + 50 × 80 = 50 ⇒ \(\frac{1}{2}\) ÷ \(\frac{1}{32}\) × 5 + 50 - 80 = 50
⇒ \(\frac{1}{2}\) ÷ \(\frac{1}{32}\) × 5 + 50 - 80 = 50
⇒ 16 × 5 + 50 - 80 = 50
⇒ 80 + 50 - 80 = 50
⇒ 130 - 80 = 50
⇒ 50 = 50 (LHS = RHS)
Option 3) + and −
\(\frac{1}{2}\) ÷ \(\frac{1}{32}\) - 5 + 50 × 80 = 50 ⇒ \(\frac{1}{2}\) ÷ \(\frac{1}{32}\) + 5 - 50 × 80 = 50
⇒ \(\frac{1}{2}\) ÷ \(\frac{1}{32}\) + 5 - 50 × 80 = 50
⇒ 16 + 5 - 50 × 80 = 50
⇒ 16 + 5 - 4000 = 50
⇒ 21 - 4000 = 50
⇒ -3979 ≠ 50 (LHS ≠ RHS)
Option 4) + and ×
\(\frac{1}{2}\) ÷ \(\frac{1}{32}\) - 5 + 50 × 80 = 50 ⇒ \(\frac{1}{2}\) ÷ \(\frac{1}{32}\) - 5 × 50 + 80 = 50
⇒ \(\frac{1}{2}\) ÷ \(\frac{1}{32}\) - 5 × 50 + 80 = 50
⇒ 16 - 5 × 50 + 80 = 50
⇒ 16 + 80 - 250 = 50
⇒ 96 - 250 = 50
⇒ -154 ≠ 50 (LHS ≠ RHS)
Hence, "Option 2" is the correct answer.