Order of Operations (or PEMDAS)

What is Order of Operations, or PEMDAS?

Order of operations is a set of rules, essentially a recipe, for how to simplify an expression. It goes like this. Here is the order in which you simplify an expression:

  1. Parentheses (starting with the innermost, and working out)
  2. Exponents and Roots (from left to right)
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

Let's look at some examples:

Evaluate: LaTeX: 6-3\left(7\right)63(7)

Solution: The tendency is to want to subtract LaTeX: 6-363 first because we are so accustomed to reading things from left to right. Instead, we need to follow the Order of Operations, which clearly says to do the Multiplication BEFORE we do the Subtraction. So,

LaTeX: 6-3\left(7\right)=6-21=-1563(7)=621=15

Next try to evaluate the following expression:

LaTeX: \left(6+2\right)^2\div4\times2-3+1(6+2)2÷4×23+1

You can check your answer by watching this video: