Simplify the expression [2(3 + 5 X 3)] / (12 ÷ 2)

Rationale

The simplified form of the expression [2(3 + 5 X 3)] / (12 ÷ 2) is 6.

This correct answer can be obtained by first performing operations within parentheses, following the mathematical order of operations (BIDMAS/BODMAS/PEDMAS): Brackets, Indices (exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

A (12) YOUR ANSWER

This is incorrect because the operations within the parentheses are not performed correctly. If we compute the expression without following the correct order of operations and perform the multiplication before the addition, we would get 12 which is not the correct result.

B (1) YOUR ANSWER

This answer would be the result if the entire expression was divided by itself. However, the operations within the parentheses must be performed first, yielding a different result. Hence, this option is not correct.

C (8) YOUR ANSWER

This is incorrect because it seems to involve incorrectly dividing the total of the numerator (24) by the total of the denominator (6) before completing the operations within the parentheses. The correct procedure is to perform the operations within parentheses first, then divide.

D (6) CORRECT

This is the correct answer. The operations within the parentheses are performed first, so the expression simplifies to [2(3 + 15)] / 6, then to [2(18)] / 6, then to 36 / 6, and finally to 6.

Conclusion

The mathematical expression [2(3 + 5 X 3)] / (12 ÷ 2) simplifies to 6 when correctly following the order of operations, which states that operations within parentheses should be performed first, followed by multiplication and division from left to right, and finally addition and subtraction from left to right. The incorrect choices result from not correctly applying this rule.

Simplify the expression [2(3 + 5 X 3)] / (12 ÷ 2)

The simplified form of the expression [2(3 + 5 X 3)] / (12 ÷ 2) is 6.

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