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Difficulty: MediumOrder of Operations and Number Properties

What is the value of the mathematical expression below?

−32+4×[18−3×(8−4)]÷2 -3^2 + 4 \times [18 - 3 \times (8 - 4)] \div 2

Answer: 3

Answer

The correct value of the expression is 3.
Following the standard order of operations, we first simplify the nested parentheses (8−4)=4(8 - 4) = 4. Next, we evaluate the expression inside the brackets [18−3×4]=[18−12]=6[18 - 3 \times 4] = [18 - 12] = 6. We then evaluate the exponent −32=−9-3^2 = -9. We perform the multiplication and division from left to right: 4×6÷2=124 \times 6 \div 2 = 12. Finally, adding −9+12-9 + 12 yields the correct result of 3.

Step-by-Step Solution

1
Simplify the innermost parentheses.
−32+4×[18−3×4]÷2-3^2 + 4 \times [18 - 3 \times 4] \div 2
According to the order of operations (PEMDAS), operations inside parentheses or grouping symbols must be performed first.
2
Simplify the expression inside the square brackets by performing multiplication before subtraction.
−32+4×6÷2-3^2 + 4 \times 6 \div 2
Multiplication has a higher precedence than subtraction.
3
Evaluate the exponent −32-3^2.
−9+4×6÷2-9 + 4 \times 6 \div 2
The exponent applies only to the base 3, not to the negative sign, because there are no parentheses around −3-3.
4
Perform multiplication and division from left to right.
−9+12-9 + 12
Multiplication and division have the same precedence and must be evaluated in order from left to right.
5
Add the remaining values.
33
Addition is the final operation to perform.

Key Concept

Order of operations (PEMDAS) dictates the sequence in which operations must be performed to evaluate an expression: Parentheses/Brackets, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
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Topics

Order of Operations and Number Properties

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