Question : Directions: Which two signs need to be interchanged to make the following equation correct? 2 + 78 ÷ 13 – 4 × 111 = 119
Option 1: + and ÷
Option 2: ÷ and ×
Option 3: + and –
Option 4: + and ×
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Correct Answer: + and ×
Solution : Given: 2 + 78 ÷ 13 – 4 × 111 = 119
Let's check each option – First Option: + and ÷ On interchanging the mathematical signs, we get – 2 ÷ 78 + 13 – 4 × 111 = 119 On solving the L.H.S. of the equation – = 2 ÷ 78 + 13 – 4 × 111 = 0.026 + 13 – 4 × 111 = 0.026 + 13 – 444 = –430.974 ≠ 119 Second Option: ÷ and × On interchanging the mathematical signs, we get – 2 + 78 × 13 – 4 ÷ 111 = 119 On solving the L.H.S. of the equation – = 2 + 78 × 13 – 4 ÷ 111 = 2 + 78 × 13 – 0.036 = 2 + 1014 – 0.036 = 1015.964 ≠ 119 Third Option: + and – On interchanging the mathematical signs, we get – 2 – 78 ÷ 13 + 4 × 111 = 119 On solving the L.H.S. of the equation – = 2 – 78 ÷ 13 + 4 × 111 = 2 – 78 ÷ 13 + 4 × 111 = 2 – 6 + 444 = 440 ≠ 119 Fourth Option: + and × On interchanging the mathematical signs, we get – 2 × 78 ÷ 13 – 4 + 111 = 119 On solving the L.H.S. of the equation – = 2 × 78 ÷ 13 – 4 + 111 = 2 × 6 – 4 + 111 = 12 – 4 + 111 = 119
So, only the fourth option satisfies the equation. Hence, the fourth option is correct.
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