Order Of Operations

The Four Rules of Order of Operations

  • General Overview: Follow the sequence to get consistent answers:

    1. Operations in parentheses and brackets.

    2. Exponents.

    3. Multiplication and division (from left to right).

    4. Addition and subtraction (from left to right).

Rule 1: Parentheses and Brackets

Rule 2: Exponents

  • Definition: Exponents represent repeated multiplications, indicating how many times to multiply a number.

  • Example: In 5²:

    • 5 squared means 5 × 5 = 25.

  • Exponents in Parentheses: In 3² + 4, process inside parentheses FIRST:

    • 3² = 9, then add: 9 + 4 = 13.

Rule 3: Multiplication and Division

  • Operation Priority: Do multiplication and division before addition and subtraction.

  • Example Problems:

    • 2 + 5 + 4 (2 + 20 = 22).

    • 3 × 5 − 1 (3 × 5 = 15, then 15 − 1 = 14).

    • 20 − 10 ÷ 5 (0 − 2 = 18).

    • 12 ÷ 6 + 5 (2 + 5 = 7).

  • Order with Ties: When multiplication and division occur together:

    • Resolve from left to right. E.g. 40 ÷ 4 × 5 should be computed as:

      • 40 ÷ 4 = 10, then 10 × 5 = 50.

Rule 4: Addition and Subtraction

  • Operation Priority: Follow the same left-to-right rule for addition and subtraction as with multiplication and division.

  • Example with Ties: In 18 − 12 + 10:

    • Solve left to right: 18 − 12 = 6, then 6 + 10 = 16.

Summary of the Rules for Order of Operations

  • FIRST: Parentheses/brackets go first.

  • NEXT: Solve exponents next.

  • THEN: Resolve multiplication and division left to right.

  • LAST: Handle addition and subtraction left to right.