Order of Operations

Our Pre-Algebra tutorial software program contains over 60 topic areas. One of them is Order of Operations, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor pre-algebra software program.

General Explanation

Mathematical expressions can have numbers, operations ( + - x / ), exponents, and parentheses. There is a set of rules called the Order of Operations that specifies the order in which these operations should be performed.
The basic rules of the order of operations are:
  1. Do all operations within grouping symbols first. Start with the innermost grouping symbols and work outward. Note: grouping symbols may be parentheses () and brackets [].
  2. Next, evaluate all exponents, from left to right.
  3. Next, do multiplication and division, working from left to right.
  4. Finally, do addition and subtraction working from left to right.
Sample Problem

5 x 6 + 3 = ?


Since there are no grouping symbols, we jump to step 2. And since there are no exponents, we jump to step 3. Let's perform the multiplication.
5 x 6 = 30
Our expression is now 30 + 3. Let's perform step 4.
30 + 3 = 33
We have found our answer. 5 x 6 + 3 = 33