Question : Directions: Which two signs need to be interchanged to make the following equation correct?
9 + 3 – 4 ÷ 5 × 2 = 9
Option 1: – and ×
Option 2: + and ×
Option 3: + and ÷
Option 4: – and +
Correct Answer: + and ÷
Solution :
Given:
9 + 3 – 4 ÷ 5 × 2 = 9
Let's check each option –
First option:
– and ×
On interchanging the mathematical signs, we get –
9 + 3 × 4 ÷ 5 – 2 = 9
On solving the L.H.S. of the equation –
= 9 + 3 × 4 ÷ 5 – 2
= 9 + 2.4 – 2
= 9.4 ≠ 9
Second option:
+ and ×
On interchanging the mathematical signs, we get –
9 × 3 – 4 ÷ 5 + 2 = 9
On solving the L.H.S. of the equation –
= 9 × 3 – 4 ÷ 5 + 2
= 9 × 3 – 0.8 + 2
= 27 – 0.8 + 2
= 28.2 ≠ 9
Third option:
+ and ÷
On interchanging the mathematical signs, we get –
9 ÷ 3 – 4 + 5 × 2 = 9
On solving the L.H.S. of the equation –
= 9 ÷ 3 – 4 + 5 × 2
= 3 – 4 + 5 × 2
= 3 – 4 + 10
= 9
Fourth option:
– and +
On interchanging the mathematical signs, we get –
9 – 3 + 4 ÷ 5 × 2 = 9
On solving the L.H.S. of the equation –
= 9 – 3 + 4 ÷ 5 × 2
= 9 – 3 + 0.8 × 2
= 9 – 3 + 1.6
= 7.6 ≠ 9
So, only the third option satisfies the equation. Hence, the third option is correct.
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