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What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘×’ are interchanged and ‘÷’ and ‘−’ are interchanged? 18 − 6 + 3 × 20 ÷ 9 = ?
18
12
6
20
20
Rewrite the expression immediately after applying the sign interchanges, then strictly follow the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction).
Rewrite the expression immediately after applying the sign interchanges, then strictly follow the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction).
Apply Sign Interchange
Original: 18 - 6 + 3 * 20 / 9. Given: '-' becomes '/', '+' becomes '', '' becomes '+', '/' becomes '-'. New expression: 18 / 6 * 3 + 20 - 9.
Evaluate using BODMAS
First division: 18 / 6 = 3. Expression becomes 3 * 3 + 20 - 9. Next multiplication: 3 * 3 = 9. Expression becomes 9 + 20 - 9.
Final Addition and Subtraction
Calculate: 9 + 20 = 29. Then: 29 - 9 = 20.
A: 18 is the result of incorrect BODMAS sequence application, B: 12 is the result of adding before multiplying, C: 6 is the result of ignoring the division order.
D is correct because applying the sign changes 18 / 6 * 3 + 20 - 9 correctly results in 3 * 3 + 20 - 9 = 29 - 9 = 20.
Always write the new expression clearly before performing any calculations to avoid mixing up the interchanged signs; BODMAS failure is the most common reason for errors in this topic.
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