Question : Directions: Which of the following interchanges of signs would make the given equation correct?
5 – 4 ÷ 2 + 7 × 3 = 14
Option 1: ÷ and +
Option 2: × and −
Option 3: − and ÷
Option 4: + and ×
Correct Answer: × and −
Solution :
Given:
5 – 4 ÷ 2 + 7 × 3 = 14
Replace the given symbols in the options one by one with the original symbols in the given equation.
Let's check the options
–
First option:
÷ and +
5 – 4 ÷ 2 + 7 × 3 = 14
⇒ 5 – 4 + 2 ÷ 7 × 3
⇒ 5 – 4 + 0.28 × 3
⇒ 5 – 4 + 0.84
⇒ 1.84 ≠ 14
Second option:
× and −
5 – 4 ÷ 2 + 7 × 3 = 14
⇒ 5 × 4 ÷ 2 + 7 – 3
⇒ 5 × 2 + 7 – 3
⇒ 10 + 7 – 3
⇒ 14
Third option:
− and ÷
5 – 4 ÷ 2 + 7 × 3 = 14
⇒ 5 ÷ 4 – 2 + 7 × 3
⇒ 1.25 – 2 + 7 × 3
⇒ 1.25 – 2 + 21
⇒ 20.25 ≠ 14
Fourth option:
+ and ×
5 – 4 ÷ 2 + 7 × 3 = 14
⇒ 5 – 4 ÷ 2 × 7 + 3
⇒ 5 – 2 × 7 + 3
⇒ 5 – 14 + 3
⇒ –6 ≠ 14
Here, only the second option satisfies the equation. Hence, the second option is correct.
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