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Order Of Operations: Definition, Problems & Examples

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  • 0:04 What is Order of Operations?
  • 1:22 Memorization Tricks
  • 2:18 Examples
  • 4:19 Lesson Summary
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Lesson Transcript
Instructor: Tara Quinn
In this lesson, we'll discuss order of operations. We'll look at what the order is, how some people remember it, and one of the most common misconceptions people have regarding it.

What Is Order of Operations?

Let's say you see a problem with lots of numbers and operations. There's addition, multiplication, parentheses, exponents, etc. all mixed into the problem. How do you know where to begin? Does it matter what you do first, second, or last? These are the questions that order of operations will help you answer.

Order of operations is the hierarchy of mathematical operations. It is the set of rules that determines which operations should be done before or after others. Operations should be done in this order:

  1. Parentheses
  2. Exponents
  3. Multiplication or division (from left to right, as found in the problem)
  4. Addition or subtraction (from left to right, as found in the problem)

Note that multiplication and division as well as addition and subtraction do not have a set order. There is a common misconception that multiplication must be done before division and addition must be done before subtraction; however, this is not true.

After you solve any parentheses and exponents in a problem, then you'll solve any multiplication or division problems that remain, moving from left to right in the equation. Similarly, after completing all the other operations, you should complete all addition or subtraction problems, moving from left to right in the equation.

Memorization Tricks

One way people try to remember the order of operations is with the acronym PEMDAS. Here, each letter stands for one of the operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Alternatively, some people will use the sentence: ''Please Excuse My Dear Aunt Sally'' to help them remember the order. Here, the first letter of each word in the sentence refers to one of the operations.

These are both helpful mnemonic devices, but there is one significant draw back. Both of these memory devices can imply that multiplication is always done before division and that addition is always done before subtraction. In truth, as we've discussed, multiplication and division are at the same importance level; you should do whichever comes first in the problem as you read from left to right. Addition and subtraction work the same way.

Examples

Example 1: Evaluate: (11 - 5) x 2 - 3 + 1

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