4.2 Order of Operations

Did you know that when an expression includes some combination of addition, subtraction, multiplication, and division, order matters? In other words, the order in which you perform the operations makes a difference in the answer you get. That’s right: Certain operations take priority over others. Since many everyday problems that we encounter require the use of more than one operation, we need to make sure we know how to correctly proceed, write, and carry out the calculation.

The five operations we have looked at so far are joined by parentheses when considering order of operation.

Parentheses indicate the highest priority, so you need to work out anything in parentheses first, followed by any exponents (powers). Then, carry out the multiplication and division, and finally any addition and subtraction. If part of the calculation involves only multiplication and division or only addition and subtraction, work through from left to right.

The correct order to carry out the operations can be summarized by using the mnemonic PEMDAS, where the letters stand for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. A saying that may help you remember PEMDAS is: “Please excuse my dear Aunt Sally.”

Let’s watch this quick video, which puts the order of operations to a quick song that might help you remember better!

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Let’s look now at an everyday problem involving more than one operation.

4.1 3 Further Investigation of Exponents on the Calculator

4.2.1 An Everyday Problem