By interchanging the given two signs which of the following equation will NOT be correct?
$+$ and $\div$
I. $27 \div 3 - 18 \times 3 + 9 = 24$
II. $12 \div 8 \times 12 + 16 - 7 = 19$
Interchanging Signs: Equation Analysis
The question asks us to swap the mathematical signs '+' and '÷' in the given equations (I and II) and determine which equation becomes incorrect after the swap. We will use the standard order of operations (BODMAS/PEMDAS) to evaluate the equations.
Equation I Analysis
Original Equation I: $27 \div 3 - 18 \times 3 + 9 = 24$
Interchange '+' and '÷':
- The equation becomes: $27 + 3 - 18 \times 3 \div 9$
- Applying BODMAS/PEMDAS:
- Multiplication first: $18 \times 3 = 54$
- Division next: $54 \div 9 = 6$
- The expression simplifies to: $27 + 3 - 6$
- Addition: $27 + 3 = 30$
- Subtraction: $30 - 6 = 24$
The resulting value is $24$, which matches the right-hand side of the original equation. Therefore, Equation I is correct after interchanging the signs.
Equation II Analysis
Original Equation II: $12 \div 8 \times 12 + 16 - 7 = 19$
Interchange '+' and '÷':
- The equation becomes: $12 + 8 \times 12 \div 16 - 7$
- Applying BODMAS/PEMDAS:
- Multiplication first: $8 \times 12 = 96$
- Division next: $96 \div 16 = 6$
- The expression simplifies to: $12 + 6 - 7$
- Addition: $12 + 6 = 18$
- Subtraction: $18 - 7 = 11$
The resulting value is $11$. The original right-hand side was $19$. Since $11 \neq 19$, Equation II is NOT correct after interchanging the signs.
Conclusion
Based on the analysis, only Equation II becomes incorrect when the signs '+' and '÷' are interchanged.
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