8 ÷ 2 (2+2) = ?

YSU’s latest award-winning mathematician calls BS on viral equation

After all of these years, the question is still often asked, “So, why did you want to be a writer?”

My answer: “It’s not math.”

Well, it’s not that simple. But still, it’s kind of ironic - me writing a story about, of all things, a math equation!

Actually, more to the point, this is the story about award-winning YSU Mathematics Professor Anita O’Mellan, who has this to say about the aforementioned equation: "It’s BS."

The little equation in question is this: 8 ÷ 2 (2+2) = ?

For several days earlier this year, the tricky mathematical problem was all the rage across social media, prompting heated debates, blatant math-shaming and even three articles in the New York Times’ Science section.

“I have two math degrees, and the answer is one,” one Tweeter proclaimed, who promptly got Tweeted back:  “I took 3 calc classes, differential equations and linear algebra, the answer is 16.”

So, to resolve the dispute, we turned to O’Mellan, the winner of the 2019 Kenneth Cummins Award for Exemplary Mathematics Teaching from the Ohio Council of Teachers of Mathematics, which makes her one of Ohio’s top university math teachers.

O’Mellan was a kindergartener in Danville, Ill., when she decided she wanted to be a teacher. (Well, except for a brief time when she thought it’d be cool to be a truck driver like in the hit TV show of the time, “B.J. and the Bear,” about a trucker and his chimpanzee. But we digress...) It was in the fourth grade that she honed in on math, when her teacher told her that she could make up her own numbers for math problems and solve them.

She went on to earn a bachelor’s degree from Southern Illinois University, a master’s from Texas A&M and a PhD from Memphis State, all in Mathematics, before joining the YSU faculty in 1993. She’s won the YSU Distinguished Professor Award, twice, and is the author of a textbook to help educators teach math to pre-K through fourth graders.

Primarily, O’Mellan instructs Education students how to teach math on the pre-K and elementary levels, and many of them suffer a fair share of math anxiety themselves. In fact, nearly half of the 25 students in her math class for future elementary teachers described their feelings about math thusly: hate, terrible, scared, confused.

“Those,” she said, “are my favorite students.”

The key, she said, is not just teaching math rules, but getting students to understand the rules so they make sense.

Speaking of sense, or in O’Mellan’s opinion, nonsense, that brings us back to the viral equation, 8 ÷ 2 (2+2) = ?. Is the answer 1, 16, or something else?

O’Mellan said all of the hubbub is, well, “interesting.”

Here’s what we know. Everyone agrees that you first deal with the 2+2 in parentheses. So, you end up with 8÷2(4). The question then becomes: do we divide first or multiply first? If we do the division first, we get 4×4 = 16. If we multiply first, we get 8÷8 = 1.

So, which one? Let's ask Aunt Sally. You may recall the little ditty - “Please Excuse My Dear Aunt Sally” -  to help remember the order of operations for such equations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Some believe you do the 2(4) part first because Aunt Sally says to do parentheses first. The answer then is 1.

The other camp says, no, no, no! The parentheses around the (4) is there to only indicate multiplication, and since Aunt Sally tells us multiplication and division are equal, we default to solving the problem starting from the left and working right. Thus, the answer is 16.

For what it’s worth, Twitter took a poll: 60 percent of respondents went with 1, and 40 went with 16.

O’Mellan says it’s neither.

When all is said and done, it’s a vaguely-written, ambiguous and faulty equation intentionally designed to confound and stew internet chaos, similar to the viral black-and-blue dress and the Laurel vs. Yanny phenomenon. Remember those?

“No mathematician would write this equation this way,” O’Mellan said.

So, there it is: There is no definitive answer. As Steven Strogatz, a professor of Mathematics at Cornell, wrote in the Times: “You say tomayto, I say tomahto.”

Throw in some lettuce and a slice of bacon, and you’ve got lunch.