Order of Operations

To ensure that arithmetic calculations are performed consistently, we must follow the order of operations.

If an arithmetic expression contains brackets, exponents, multiplication, division, addition, and subtraction, we use the following procedure:

  1. Perform all operations inside a bracket first (the operations inside the bracket must be performed in proper order).
    • ( ) are called parentheses
    • [ ] are called brackets
    • { } are called braces
    • If a set of brackets are within another, these different bracket styles maintain the order in which the content within should be evaluated first, i.e. {4 + [7 – (3 + 2)]}.
  2. Perform exponents.
  3. Perform multiplication and division in order as they appear from left to right.
  4. Perform addition and subtraction in order as they appear from left to right.

Several examples are explained below: