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What will come in place of the ‘?’ in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 231 ÷ 61 × 427 − 321 + 217 = ?
137
317
173
117
137
Apply the BODMAS rule strictly after swapping signs: replace divide with multiply, multiply with divide, plus with minus, and minus with plus before solving.
Apply the BODMAS rule strictly after swapping signs: replace divide with multiply, multiply with divide, plus with minus, and minus with plus before solving.
Symbol Interchange
Original equation: 231 / 61 * 427 - 321 + 217. According to instructions, exchange signs: / becomes *, * becomes /, - becomes +, and + becomes -. New equation: 231 * 61 / 427 + 321 - 217.
Arithmetic Simplification
First, perform division/multiplication (BODMAS): 231 * (61 / 427). Simplifying 61/427: 427 divided by 61 is 7. So, the term becomes 231 * (1 / 7) = 231 / 7 = 33.
Final Calculation
Now substitute the result back: 33 + 321 - 217. Performing addition and subtraction: 33 + 321 = 354, and 354 - 217 = 137.
B: 317 is incorrect as it results from calculation errors; C: 173 is incorrect as it results from neglecting BODMAS priority; D: 117 is incorrect due to arithmetic errors in subtraction.
A is correct because applying the sign changes 231 * 61 / 427 + 321 - 217 yields 33 + 321 - 217, which equals 137.
Always solve the division part of the equation first after sign conversion, as this often leads to a whole number that simplifies the rest of the calculation.
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