Auburn professors offer explanation for viral math equation

Published: August 01, 2019
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It’s the math equation that has gone viral on social media: 8 ÷ 2(2+2) = ?

People are divided on the answer—is it 1 or 16? Or something else? Two Auburn University math professors weigh in and give us what they say is the correct answer. Luke Oeding, associate professor and associate chair of the Department of Mathematics and Statistics, and Ash Abebe, professor and graduate program officer in the department, offered an explanation of the equation and how to get the right answer.

“The standard order of operations is what's important here,” Oeding said. “Everyone agrees that PEMDAS with a left to right convention is the golden rule.”

PEMDAS is an acronym for parentheses, exponents, multiplication or division, addition or subtraction—with an implicit left to right convention when all doing the same operation.

Using the PEMDAS rule, Oeding explains the first step of the equation.

  1. We do parentheses first: 8 ÷ 2(2+2) = 8 ÷ 2(4)
  2. Now that the expression inside the parentheses is simplified we write the equation as: 8 ÷ 2 × 4
  3. There are no exponents so we go to division or multiplication, and we go from left to right simplifying: 8 ÷ 2 × 4 = 4 × 4 = 16

“The thing that throws lots of people, I think, is that some calculators might have a different convention built in, which is very confusing,” Oeding said.

To further help people understand, Oeding said you can add parentheses to the last step of the equation.

8 ÷ 2 × 4 = (8 ÷ 2) × 4

“We have mostly been raised under the PEMDAS convention and often take it for granted,” Abebe said. “The solution, which is also emphasized in computer science, is to be redundant with your parentheses. There would have been no ambiguity if the question had been written as (8 ÷ 2) × (2 + 2) = ?”