This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To make the given equation correct, we need to interchange two numbers. The original equation is: 18 × 3 ÷ 9 + 5 - 6 = 2 First, let's evaluate the Left Hand Side (LHS) of the original equation: 18 × 3 ÷ 9 + 5 - 6 = 54 ÷ 9 + 5 - 6 = 6 + 5 - 6 = 11 - 6 = 5 Since 5 ≠ 2, the original equation is incorrect. We need to find which interchange makes it correct. Let's test each option: Option 1: Interchange 18 and 6 The equation becomes: 6 × 3 ÷ 9 + 5 - 18 = 2 Evaluate LHS: 6 × 3 ÷ 9 + 5 - 18 = 18 ÷ 9 + 5 - 18 = 2 + 5 - 18 = 7 - 18 = -11 Since -11 ≠ 2, this option is incorrect. Option 2: Interchange 3 and 5 The equation becomes: 18 × 5 ÷ 9 + 3 - 6 = 2 Evaluate LHS: 18 × 5 ÷ 9 + 3 - 6 = 90 ÷ 9 + 3 - 6 = 10 + 3 - 6 = 13 - 6 = 7 Since 7 ≠ 2, this option is incorrect. Option 3: Interchange 2 and 3 This means we replace '3' on the left side with '2', and '2' (the result on the right side) with '3'. The equation becomes: 18 × 2 ÷ 9 + 5 - 6 = 3 Evaluate LHS: 18 × 2 ÷ 9 + 5 - 6 = 36 ÷ 9 + 5 - 6 = 4 + 5 - 6 = 9 - 6 = 3 Since 3 = 3, this equation is correct. This option works. Option 4: Interchange 5 and 9 The equation becomes: 18 × 3 ÷ 5 + 9 - 6 = 2 Evaluate LHS: 18 × 3 ÷ 5 + 9 - 6 = 54 ÷ 5 + 9 - 6 = 10.8 + 9 - 6 = 19.8 - 6 = 13.8 Since 13.8 ≠ 2, this option is incorrect. Therefore, interchanging 2 and 3 makes the equation correct. The final answer is 3