Question : Directions: Which two signs should be interchanged to make the following equation correct? 6 ÷ 24 + 6 × 7 – 5 = 29
Option 1: ÷ and ×
Option 2: ÷ and +
Option 3: ÷ and –
Option 4: × and +
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Correct Answer: ÷ and +
Solution : Given: 6 ÷ 24 + 6 × 7 – 5 = 29
Let's check each option – First Option: ÷ and × On interchanging the mathematical signs, we get – 6 × 24 + 6 ÷ 7 – 5 = 29 On solving the L.H.S. of the equation – = 6 × 24 + 6 ÷ 7 – 5 = 6 × 24 + 0.857 – 5 = 144 + 0.857 – 5 = 139.857 ≠ 29 Second Option: ÷ and + On interchanging the mathematical signs, we get – 6 + 24 ÷ 6 × 7 – 5 = 29 On solving the L.H.S. of the equation – = 6 + 24 ÷ 6 × 7 – 5 = 6 + 4 × 7 – 5 = 6 + 28 – 5 = 29 Third Option: ÷ and – On interchanging the mathematical signs, we get – 6 – 24 + 6 × 7 ÷ 5 = 29 On solving the L.H.S. of the equation – = 6 – 24 + 6 × 7 ÷ 5 = 6 – 24 + 6 × 1.4 = 6 – 24 + 8.4 = –9.6 ≠ 29 Fourth Option: × and + On interchanging the mathematical signs, we get – 6 ÷ 24 × 6 + 7 – 5 = 29 On solving the L.H.S. of the equation – = 6 ÷ 24 × 6 + 7 – 5 = 0.25 × 6 + 7 – 5 = 1.5 + 7 – 5 = 3.5 ≠ 29
So, only the second option satisfies the equation. Hence, the second option is correct.
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