Without Order, There’s Chaos!

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Have you ever seen a problem similar to this on social media sites?

               5 - 1 x 0 + 3 ÷ 3 = ?

Is the answer 1 or is it 6?* Or did you get something completely different?
Here’s another example.

               6 ÷ 2(1+2) = ?

Is the answer 1 or is it 9?* Or once did you get something completely different.
Here’s another simpler example.

               8 - 5 + 3 = ?

Is the answer 0 or 6?*

As a math teacher, I’m always intrigued by the numerous answers given in the comments. Some people will explain how they reached their answer, and some will not. But it never fails that some are adamant about an incorrect answer. So let’s set the record straight.

The key to simplifying these three expressions is the order of operations. The order of operations is a set of rules or steps that ensures everyone arrives at the same answer given an expression with multiple operations. Have you heard the sentence Please Excuse My Dear Aunt Sally? This has been passed down for years as a way to remember the acronym PEMDAS. Although the sentence may help students remember the acronym, the acronym alone is a bit misleading. PEMDAS tells us to simplify expressions in this order:

  1. Parentheses
  2. Exponents
  3. Multiplication & Division
  4. Addition & Subtraction

Let’s look back at the 3rd example,  8 - 5 + 3 = ? If you answered 0, then you added 5 and 3 and then subtracted from 8.

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If you answered 6, then you subtracted 5 from 8 and then added 3.

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This is where you may have been misled. Addition and subtraction must be simplified from left to right. Therefore, 6 is the correct answer.

Now let’s look at the 2nd example, Here’s how to correctly simplify the expression. First, simplify within the parentheses. But as with addition and subtraction, multiplication and division must be performed from left to right.

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And finally, the 1st example After reviewing the order of operations, are you confident in your original answer? Here’s how to simplify the expression.

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So the next time you see one of these posts on social media, remember, without order, there’s chaos!

*Answers:
5 - 1 x 0 + 3 ÷ 3 = 6
6 ÷ 2(1+2) = 9
8 - 5 + 3 = 6

Need more practice with the order of operations? Check out Simplifying Expressions Using Order of Operations.

 

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About Author

Staci Lyon

Staci Lyon is a mathematics curriculum specialist with Curriculum Pathways. She taught high school mathematics for 12 years in Wake County and Granville County. She also taught with North Carolina Virtual Public School. She received both a M.Ed. degree in Instructional Technology and a B. S. degree in Mathematics Education from North Carolina State University. Working alongside a team, she enjoys developing the award winning online math resources for Curriculum Pathways that allow teachers to integrate technology into their classrooms. Outside of work, she enjoys traveling and spending time with family and friends.

1 Comment

  1. Chris Hemedinger
    Chris Hemedinger on

    Please Excuse My Dear Aunt Sally -- all of my kids know that! Good reminder on the left-to-right simplifying though. Order of operations, rules!

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