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Difficulty: MediumOrder of Operations and Number Properties

What is the value of the following expression?

−32−16−4×523−10-3^2 - \frac{16 - 4 \times 5}{2^3 - 10}
  1. A
    77
  2. B
    −10-10
  3. −11-11Answer
  4. D
    2121
  5. E
    3939

Answer

−11-11
The correct value is −11-11. By following the standard order of operations, we first evaluate the leading term −32=−9-3^2 = -9. Next, we evaluate the numerator of the fraction (16−4×5=16−20=−416 - 4 \times 5 = 16 - 20 = -4) and the denominator of the fraction (23−10=8−10=−22^3 - 10 = 8 - 10 = -2). Simplifying the fraction gives −4−2=2\frac{-4}{-2} = 2. Finally, subtracting this value from the leading term yields −9−2=−11-9 - 2 = -11.

Step-by-Step Solution

1
Evaluate the exponent term on the left side of the subtraction.
−32=−(3×3)=−9-3^2 = -(3 \times 3) = -9
According to the order of operations, the exponent applies only to the base 33, not the negative sign, unless parentheses are present.
2
Evaluate the numerator of the fraction by performing multiplication before subtraction.
16−4×5=16−20=−416 - 4 \times 5 = 16 - 20 = -4
Multiplication has a higher priority than subtraction in the standard order of operations.
3
Evaluate the denominator of the fraction by evaluating the exponent before subtraction.
23−10=8−10=−22^3 - 10 = 8 - 10 = -2
Exponentiation must be performed before subtraction.
4
Divide the simplified numerator by the simplified denominator to find the value of the fraction.
−4−2=2\frac{-4}{-2} = 2
Dividing a negative number by a negative number yields a positive result.
5
Perform the final subtraction using the values from Step 1 and Step 4.
−9−2=−11-9 - 2 = -11
Subtracting 22 from −9-9 moves further left on the number line, resulting in −11-11.

Key Concept

Order of Operations (PEMDAS/BODMAS)
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Topics

Order of Operations and Number Properties

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