Using PEMDAS to Evaluate Numerical Expressions

Do you remember PEMDAS? In the previous lesson, we discussed the basic rules for evaluating using numerical expressions using the Order of Operations. We looked at the acronym PEMDAS and how it helps us to remember the rules when using the order of operations. In case you've forgotten, let's review:

This explains what PEMDAS means: parentheses, exponents, multiplication, division, addition, subtraction

In the next few examples, we are going to focus on other grouping symbols other than parenthesis. A grouping symbol is used to indicate that operations contained within should be computed separately from other operations in the expression.

First we will take a look at nested parentheses which are parentheses that are "nested" inside another set of parentheses. In this case, you must always work the inner most parentheses first. In other words, always work from the inside out.  In the second example, we will explore the fraction bar, and in the last example, we will explore the radical sign.

Watch the following video for step by step instructions on how to solve examples with nested parentheses and the fraction bar.  If you prefer not to watch the video, keep reading and you'll discover through our print examples how to evaluate these expressions!

Example 1 - Nested Parenthesis

Using PEMDAS to evaluate, the correct solution is 80.

In the next example, we are going to take a look at the fraction bar. The fraction bar is also considered a grouping symbol. The fraction bar groups together the terms that are in the numerator and the terms that are in the denominator. Take a look....

Example 2 - The Fraction Bar

Our last grouping symbol is the radical sign. The radical sign tells us that we want to take the square root of a number. We treat the radical symbol as a grouping symbol, and therefore, we must evaluate the expression (using PEMDAS) inside of the radical before taking the square root.

Example 3 - The Radical Symbol (Taking the Square Root)

Notice how we use the word "parenthesis" in PEMDAS, but we are referring to many other grouping symbols besides just parentheses.

You must begin evaluating any expression by evaluating the innermost grouping symbols first. Then work your way out.

Grouping symbols may refer to: brackets, parentheses, fraction bar, or the radical symbol.

I hope this helps in your study of order of operations.

  1. Home
  2. >
  3. Pre-Algebra
  4. >
  5. Order of operations


We would love to hear what you have to say about this page!

Need More Help With Your Algebra Studies?

Get access to hundreds of video examples and practice problems with your subscription! 

Click here for more information on our affordable subscription options.

Not ready to subscribe?  Register for our FREE Pre-Algebra Refresher course.