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What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘-’ are interchanged and ‘x’ and ‘÷’ are interchanged? 3 ÷ 5 + 16 x 8 - 8 = ?
21
18
17
20
21
Apply BODMAS rules strictly after replacing symbols based on the given conversion instructions.
Apply BODMAS rules strictly after replacing symbols based on the given conversion instructions.
Symbol Replacement
Original equation: 3 ÷ 5 + 16 x 8 - 8. Replace symbols as per instructions: ÷ becomes x, + becomes -, x becomes ÷, and - becomes +. New equation: 3 x 5 - 16 ÷ 8 + 8.
Applying BODMAS
Solve by order: Division first, then Multiplication, then Addition/Subtraction. Division: 16 ÷ 8 = 2. Equation becomes: 3 x 5 - 2 + 8. Multiplication: 3 x 5 = 15. Equation becomes: 15 - 2 + 8.
Final Calculation
Perform Addition and Subtraction from left to right: 15 - 2 = 13. Then 13 + 8 = 21.
B: 18 is incorrect because it fails to correctly apply the division and order of operations. C: 17 is incorrect as it results from improper grouping of operators. D: 20 is incorrect as it arises from ignoring the priority of division over addition.
A is correct because substituting the operators yields 3 x 5 - 16 ÷ 8 + 8, which simplifies to 15 - 2 + 8, totaling 21.
Always write down the new equation clearly before calculating, as mental swapping often leads to sign errors.
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