Examkin

Question

Difficulty: HardOrder of Operations

Consider the mathematical expression below:

−42−36÷(−3)×2∣1−4∣ -4^2 - \frac{36 \div (-3) \times 2}{|1 - 4|}

What is the exact evaluated value of this expression?

Answer: -8

Answer

-8
The correct answer is derived by carefully following the order of operations (PEMDAS/BODMAS). First, the denominator's absolute value evaluates to 3. Second, evaluating the numerator strictly from left to right gives 36÷(−3)=−1236 \div (-3) = -12, and −12×2=−24-12 \times 2 = -24. The entire fraction therefore simplifies to −24÷3=−8-24 \div 3 = -8. Next, the exponent −42-4^2 evaluates to −16-16 because the negative sign is not inside parentheses. Finally, subtracting the fraction's value yields −16−(−8)-16 - (-8), which simplifies to −16+8=−8-16 + 8 = -8.

Step-by-Step Solution

1
Evaluate the absolute value grouping in the denominator.
∣1−4∣=∣−3∣=3|1 - 4| = |-3| = 3
Absolute value bars act as grouping symbols and must be evaluated first. Absolute value always returns a non-negative distance.
2
Evaluate the numerator from left to right.
36÷(−3)×2=−12×2=−2436 \div (-3) \times 2 = -12 \times 2 = -24
Multiplication and division have equal precedence, so they must be evaluated strictly from left to right.
3
Simplify the fraction by dividing the numerator by the denominator.
−243=−8\frac{-24}{3} = -8
The fraction bar acts as a grouping symbol separating the numerator and denominator.
4
Evaluate the exponent term.
−42=−16-4^2 = -16
Without parentheses around the base, the exponent applies only to the 4, not the negative sign.
5
Perform the final subtraction.
−16−(−8)=−16+8=−8-16 - (-8) = -16 + 8 = -8
Subtracting a negative number is equivalent to adding its positive value.

Key Concept

Applying the order of operations (PEMDAS), specifically evaluating multiplication/division from left to right, processing absolute values, and understanding how exponents apply to negative bases without parentheses.
Rate this question

Topics

Order of Operations

More questions from this topic