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What will come in place of the question mark (?) in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 4 ÷ 5 + 21 × 3 − 2= ?
14
15
12
17
15
Apply BODMAS strictly after substituting the signs and remember that division (÷) always comes before multiplication, addition, and subtraction.
Apply BODMAS strictly after substituting the signs and remember that division (÷) always comes before multiplication, addition, and subtraction.
Substitute the signs
Given equation: 4 ÷ 5 + 21 × 3 − 2. Applying the rule: + becomes -, - becomes +, ÷ becomes ×, × becomes ÷. The new equation is: 4 × 5 - 21 ÷ 3 + 2.
Solve using BODMAS
Following BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction): First divide (21 ÷ 3 = 7), then multiply (4 × 5 = 20). The expression becomes: 20 - 7 + 2.
Final Calculation
Perform addition and subtraction: 20 - 7 = 13, and 13 + 2 = 15.
A: 14 is incorrect because the result of the calculation is 15; C: 12 is incorrect as it fails to follow the BODMAS rule correctly during the division step; D: 17 is incorrect because it ignores the correct order of operations.
B is correct because replacing the symbols and applying BODMAS (4 * 5 - 21 / 3 + 2) results in 20 - 7 + 2, which equals 15.
In mathematical operations, always check the sign interchange twice before calculating, as a single sign misplacement will lead to an incorrect option.
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