The internet is full of puzzles that leave people debating the right answer. One such case is a viral math problem, similar to the infamous blue and black dress that sparked widespread online discussion.
In 2019, a Twitter user shared a controversial math question: 8 ÷ 2(2 + 2). The post quickly ignited debates across social media, with even workplaces and scientists joining the conversation.
Editors at Popular Mechanics, a lifestyle magazine, couldn’t agree on the solution. They took the debate to their workplace chat, trying to figure out the correct answer.
One editor pointed out the common teaching method using “PEMDAS” (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). According to this rule, equations are solved step by step, starting with parentheses, followed by exponents, and then multiplication or division (from left to right). This method became the center of the debate as people tried to apply it to the problem.
First, the 2 + 2 inside the parentheses is solved, giving 4. This turns the equation into 8 ÷ 2 × 4. According to Mashup Math, the next step is to resolve the operations from left to right. This means solving 8 ÷ 2 first, resulting in 4, and then multiplying by 4, giving a final answer of 16. However, many online disagreed with this approach, including some mathematicians.
The other half of the Popular Mechanics editors argued that the answer is 1. They also used “PEMDAS” but interpreted it differently. While they agreed to solve the parentheses first, they treated the resulting expression as 8 ÷ 2(4), considering the multiplication tied to the parentheses as higher priority. One editor explained that, based on their math education, multiplication attached to parentheses takes precedence over division, regardless of position.
As the debate gained momentum, mathematicians joined the discussion. Mike Breen, from the American Mathematical Society’s Public Awareness Office, weighed in, confirming that 16 is the correct answer according to the standard order of operations. Yet, the debate highlighted how interpretation plays a significant role in solving math problems.
However, Breen acknowledged that the way the equation is written makes it inherently “ambiguous.”
“In math, there are often ambiguities. Mathematicians work to make rules as precise as possible. According to the strict order of operations, the answer is 16, but I wouldn’t fault someone if they said 1,” he explained.
Despite Breen’s reasoning, some remained unconvinced. The other half of the magazine’s editors sought input from Physics Professor Rhett Allain of Southeastern Louisiana University, who offered a new perspective on the debate.
“This is about convention. We have conventions for writing math, just like we have conventions for spelling. Some people write ‘gray,’ others write ‘grey,’ but we still understand the meaning,” Allain noted.
For clarity, Allain suggested the problem should have been written as 8 ÷ (2 × (2 + 2)), which clearly results in 1.
