Linear Equations and Inequalities: Background You’ll Need 2

  • Use the order of operations – PEMDAS

Order of Operations

You may or may not recall the order of operations for applying several mathematical operations to one expression. Just as it is a social convention for us to drive on the right-hand side of the road, the order of operations is a set of conventions used to provide order when you are required to use several mathematical operations for one expression.

How to: Perform the Order of Operations

  1. Perform all operations within grouping symbols first. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and fraction bars.
  2. Evaluate exponents or square roots.
  3. Multiply or divide, from left to right.
  4. Add or subtract, from left to right.

This order of operations is true for all real numbers.

Some people use a saying to help them remember the order of operations. This saying is called PEMDAS or Please Excuse My Dear Aunt Sally. The first letter of each word begins with the same letter of an arithmetic operation.

  • Please [latex]\displaystyle \Rightarrow[/latex] Parentheses (and other grouping symbols)
  • Excuse [latex]\displaystyle \Rightarrow[/latex] Exponents
  • My Dear [latex]\displaystyle \Rightarrow[/latex] Multiplication and Division (from left to right)
  • Aunt Sally [latex]\displaystyle \Rightarrow[/latex] Addition and Subtraction (from left to right)

Even though multiplication comes before division in the saying, division could be performed first. Which is performed first, between multiplication and division, is determined by which comes first when reading from left to right. The same is true of addition and subtraction. Don’t let the saying confuse you about this!

Simplify the following:

[latex]7–5+3\cdot8[/latex]