Question

In the given question below, which one of the interchanges in signs and numbers would make the given equation correct? \[ (3 \div 4) + 2 = 2\]

• A. + and ÷, 2 and 3
• B. + and ÷, 2 and 4
• C. + and ÷, 3 and 4
• D. No interchange, 3 and 4

Hint:

In such problems, carefully check each possible option and perform the mathematical operations step-by-step to verify which option satisfies the equation.

Answer 1

The Correct Option is A

Original Equation: \[ (3 \div 4) + 2 = 2 \] Simplify: \[ 0.75 + 2 = 2.75 \neq 2. \] The equation is not correct as written.
Option 1: Interchange \(+\) and \(\div\), and interchange \(2\) and \(3\) The equation becomes:
\[ (2 + 4) \div 3 = 2. \] Simplify: \[ 6 \div 3 = 2. \] \[ 2 = 2. \] This is correct. Option 2: Interchange \(+\) and \(\div\), and interchange \(2\) and \(4\) The equation becomes:
\[ (3 + 2) \div 4 = 2. \] Simplify: \[ 5 \div 4 = 1.25 \neq 2. \] This is not correct. Option 3: Interchange \(+\) and \(\div\), and interchange \(3\) and \(4\) The equation becomes: \[ (4 \div 3) + 2 = 2. \] Simplify: \[ 1.333 + 2 = 3.333 \neq 2. \] This is not correct. Option 4: No interchange, interchange \(3\) and \(4\) The equation becomes: \[ (4 \div 3) + 2 = 2. \] Simplify: \[ 1.333 + 2 = 3.333 \neq 2. \] This is not correct. Conclusion: Only Option 1 makes the equation correct.
Final Answer: \[ \boxed{1} \]