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:

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 parenthesis which are parenthesis that are "nested" inside another set of parenthesis. In this case, you must always work the inner most parenthesis first. In other words, always work from the inside out. Take a look....

Example 1 - Nested Parenthesis

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.

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