Operation Hierarchy Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Evaluate \(2 + 3^2 \times (4 - 1) \div 9\).

Solution

  1. 1
    Parentheses first: \(4 - 1 = 3\). Expression: \(2 + 3^2 \times 3 \div 9\).
  2. 2
    Exponents: \(3^2 = 9\). Expression: \(2 + 9 \times 3 \div 9\).
  3. 3
    Left-to-right multiplication/division: \(9 \times 3 = 27\), then \(27 \div 9 = 3\).
  4. 4
    Addition: \(2 + 3 = 5\).

Answer

5
Follow PEMDAS: Parentheses (4−1=3), Exponents (3²=9), Multiply then Divide left-to-right (9×3÷9=3), then Add (2+3=5).

About Operation Hierarchy

The layered relationship between arithmetic operations, where each is built from the previous: multiplication from addition, exponentiation from multiplication.

Learn more about Operation Hierarchy →

More Operation Hierarchy Examples

Example 1 easy

Evaluate (3 + 4 times 2) using the correct order of operations.

Example 3 easy

Evaluate (10 - 2 times 3 + 1).

Example 4 medium

Evaluate ((5 + 3)^2 div 4 - 6).

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