Which two signs and two numbers should be interchanged to make the given equation correct?
64−4×2÷8+7=19
- A4 and 8, ÷ and −
- B64 and 8, ÷ and −
- C4 and 8, + and ÷
- D7 and 8, + and ×
Solution & Step-by-step Explanation
Let's test the options using the BODMAS rule to find the one that balances the equation to 19.
Test Option A: Interchange 4 and 8, and interchange ÷ and −
The original equation is: 64−4×2÷8+7=19
After swapping (4 ↔ 8) and (− ↔ ÷):
64÷8×2−4+7
Applying BODMAS:
Division: 64÷8=8
Substitution back: 8×2−4+7
Multiplication: 8×2=16
Substitution back: 16−4+7
Addition and Subtraction: 12+7=19
Since 19=19, Option A satisfies the equation.
Test Option A: Interchange 4 and 8, and interchange ÷ and −
The original equation is: 64−4×2÷8+7=19
After swapping (4 ↔ 8) and (− ↔ ÷):
64÷8×2−4+7
Applying BODMAS:
Division: 64÷8=8
Substitution back: 8×2−4+7
Multiplication: 8×2=16
Substitution back: 16−4+7
Addition and Subtraction: 12+7=19
Since 19=19, Option A satisfies the equation.