It’s surprising to see such intense disagreement about a mathematical problem at a time when divisive discussions are common on social media. One particular equation, nevertheless, managed to do this.
In 2019, a seemingly straightforward math problem went viral on social media, leading to what some referred to as a “civil war” within Popular Mechanics’ corporate offices.
This scenario transcended basic math and became a cultural event that illustrated the range of legal interpretations and passionate arguments people make to support their beliefs.
Let’s look at the details and identify the reasons behind the controversy around this mathematical problem.
Sometimes math can be a little difficult.
Consider the following issue: 8 ÷ 2(2 + 2)
At first glance, it seems simple, yet it could be misleading. Depending on how you apply the order of operations, the answer could be either 1 or 16.
The rationale behind 16
According to the PEMDAS/BODMAS rule (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction), we should approach the equation in the sequence indicated by the acronym, starting with parentheses, followed by exponents, and working our way through the remaining operations from left to right.
This means that by first solving the 2 + 2 in the parenthesis, we obtain 8 ÷ 2 x 4. Next, we focus on the left-hand operation, handling 8 ÷ 2 before moving on to 2 x 4.
Given that this produces 4, we obtain 4 x 4, or 16.
8 ÷ 4 = 4; 4 x 4 = 16; 2 + 2 = 4.
However, many people in the online community, including some very skilled mathematicians, disagree with this viewpoint.
Mike Breen of the Public Awareness Office of the American Mathematical Society said the language is unclear.
While collaborating with Popular Mechanics to answer this equation, Breen remarked, “In mathematics, ambiguities often arise.” The provision of clear rules is the aim of mathematicians. I wouldn’t reprimand someone for saying 1, but the strict order of operations would indicate that the answer would be 16.
The case for one
How did they decide that 1 was the correct response?
Despite adhering to the PEMDAS standard, the team’s interpretation differed. The total that resulted should be regarded as though it were in parenthesis, they said, even though they agreed that the 2 + 2 in the parentheses should be calculated first. As a result, the equation is essentially rewritten as 8 ÷ 2(4), leading to 1.
Southeastern Louisiana University associate professor of physics Rhett Allain, Ph.D., remarks on this significant conversation by drawing a comparison to the famous question, “What color is this dress? Blue and black or gold and white?
Rhett says that 16 is the correct answer.
It’s not just algebra; conventions are involved. The same rules that apply to writing also apply to mathematical expressions. However, there are distinctions. Some spell it “gray,” while others prefer “grey.” He continues, “We still understand the meaning.” In my opinion, this should be explained more clearly to avoid any misconceptions. That way, nobody can mistake it.
Whether you support team 16 or team 1, there’s no doubting that math has never been more challenging or fascinating. So, which side are you on? Share your thoughts in a comment!
