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Question

Difficulty: MediumOrder of Operations

Compute the final value of the following fraction by correctly applying the order of operations:

−3(4−7)2+1523−4÷2 \frac{-3(4 - 7)^2 + 15}{2^3 - 4 \div 2}

Which of the following is the correct result?

  1. A
    -6
  2. B
    7
  3. -2Answer
  4. D
    16

Answer

-2
The correct answer is found by evaluating the numerator and denominator independently using the order of operations. In the numerator, the subtraction inside the parentheses is performed first (4 minus 7 is -3), followed by the exponent (-3 squared is 9). Multiplying by -3 gives -27, and adding 15 results in -12. In the denominator, the exponent is evaluated first (2 cubed is 8), followed by the division (4 divided by 2 is 2). Subtracting 2 from 8 gives 6. Finally, dividing the numerator by the denominator (-12 divided by 6) yields -2.

Step-by-Step Solution

1
Simplify the expression inside the parentheses in the numerator.
4 - 7 = -3
According to the order of operations, operations inside grouping symbols must be completed first.
2
Evaluate the exponents in both the numerator and the denominator.
Numerator: (-3)^2 = 9. Denominator: 2^3 = 8.
Exponents are the next highest priority after grouping symbols.
3
Perform multiplication and division operations from left to right.
Numerator: -3 \times 9 = -27. Denominator: 4 \div 2 = 2.
Multiplication and division take precedence over addition and subtraction.
4
Perform the remaining addition and subtraction operations.
Numerator: -27 + 15 = -12. Denominator: 8 - 2 = 6.
Addition and subtraction are the final steps before resolving the main fraction bar.
5
Divide the simplified numerator by the simplified denominator.
−12÷6=−2-12 \div 6 = -2
The fraction bar acts as a final division operation grouping the entire numerator and denominator.

Key Concept

Order of operations with rational expressions and signed numbers
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Topics

Order of Operations

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