Simplify the expression (2(3 + 5 - 3)) / (12 + 2). Which of the following is correct?
The simplified form of the expression (2(3 + 5 - 3)) / (12 + 2) is 8.
This is determined by following the order of operations, also known as BIDMAS: Brackets, Indices, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
This answer could be obtained by incorrectly performing the operations inside the brackets first, adding 3 + 5 to get 8, then subtracting 3 to get 5, doubling it to get 10, and then dividing by the incorrect sum of 12 + 2 which is 16, instead of 14. However, this is incorrect because the order of operations within the brackets should be followed - the subtraction should be done before the addition.
This is the correct answer. Following the correct order of operations, in the bracket, 3 - 3 is 0, and 0 + 5 is 5. Multiplying this by 2 gives 10. Then, 12 + 2 is 14. Dividing 10 by 14 gives a simplified result of 8.
This answer could be obtained by incorrectly performing the division before the addition in the denominator, dividing 12 by 2 to get 6, and then adding this to the incorrect result of the numerator, which is also 6. However, this is incorrect because the order of operations states that addition should be done before division.
This answer could be obtained by incorrectly simplifying the entire expression to be 1, possibly by misunderstanding the order of operations and treating the entire numerator and denominator as single entities without breaking them down further. However, this is incorrect because the order of operations states that the operations inside the brackets should be performed first, followed by the division.
By following the order of operations (BIDMAS), the expression (2(3 + 5 - 3)) / (12 + 2) simplifies to 8. The operations inside the brackets are performed first, then the result is multiplied by 2. Meanwhile, the denominator is simplified by addition. The resulting numerator and denominator are then divided to obtain the final simplified expression. Incorrect answers may stem from misunderstandings or mistakes in applying the order of operations.
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