For about a decade, mathematicians and mathematics educators have been engaged in a particular debate that is rooted in school mathematics and shows no signs of abating.

The debate, covered by *slate*, *Popular mechanics*, *The New York Times* and many other outlets, focuses on an equation that went so “viral” that it was eventually lumped together with other phenomena that have “broken” or “divided” the Internet.

In case you’re still weighing things up, now would be a good time to see where you stand. Please answer the following:

**8÷2(2+2)=?**

If you’re like most, your answer was 16 and you’re amazed that someone else can come up with a different answer. Unless you’re like most and your answer was 1 and you’re just as confused about seeing it any other way. Don’t worry, below we explain the definitive answer to this question – and why the notation of the equation should be banned.

Our interest was piqued because we were delving into conventions for following the order of operations – a sequence of steps performed when faced with a mathematical equation – and were a little confused as to what all the fuss was about went.

### Clearly, the answer is…

Two viable answers to a math problem? Well, if we all remember one thing from math class: That can’t be right!

Many topics emerged from the plethora of articles explaining how and why this “equation” destroyed the internet. Entering the expression on calculators, some of which are programmed to follow a specific sequence of operations, has been the subject of much debate.

Others, backing up a bit, suggest both answers are correct (which is ridiculous).

The dominant theme simply focused on the implementation of the order of operations according to different acronyms. Some commenters said people’s misunderstandings were due to a misinterpretation of the memorized acronym taught in various countries to remember the order of operations, such as PEMDAS, sometimes used in the United States: PEMDAS refers focuses on the use of parentheses, exponents, multiplication, division, addition and subtraction.

A person following this order would make 8÷2(2+2) 8÷2(4) thanks to the beginning with parentheses. Then 8÷2(4) becomes 8÷8 because there are no exponents and “M” stands for multiplication, so you multiply 2 by 4. Finally, according to the “D” for division, you get 8÷8= 1.

In contrast, Canadians can be taught to memorize BEDMAS, which stands for the use of parentheses, exponents, division, multiplication, addition, and subtraction. Someone following this order would make 8÷2(2+2) 8÷2(4) since it starts with parentheses (same as parentheses). Then 8÷2(4) becomes 4(4) because (there are no exponents) and “D” stands for division. Finally, according to the “M” for multiplication, 4(4)=16.

### Don’t omit the multiplication sign

For us, the expression 8÷2(2+2) is syntactically wrong.

We contend that the key to the debate is that the multiplication symbol before the parentheses is omitted.

Such an omission is a convention in algebra. For example, in algebra we write 2x or 3a, which means 2 × x or 3 × a. When using letters for variables or constants, the multiplication sign is omitted. Consider the famous equation e=mc2, which suggests calculating the energy as e=m×c2.

The real reason 8÷2(2+2) destroyed the internet is because of the practice of omitting the multiplication symbol, which was inappropriately brought into arithmetic from algebra.

### Inappropriate Priority

In other words, was the expression “spelled” correctly, ie represented as “8 ÷ 2 × (2 + 2) = ? ‘, there would be no going viral, no duality, no broken internet, no heated debates. No fun!

Finally, the omission of the multiplication symbol invites an undue priority for multiplication. All commentators agreed that adding the terms in parentheses or parentheses was the appropriate first step. However, confusion arose because of the closeness of 2 to (4) relative to 8 in 8÷2(4).

We want it known that it’s inappropriate to write 2(4) to refer to multiplication, but we know that’s how it’s always done.

### Beautiful symbol for multiplication

There is a very nice symbol for multiplication, so let’s use it: 2 × 4. If you are not a fan, there are other symbols, e.g. e.g. 2•4. Use both as you like, but don’t skip it.

As such, for the record, the 1v16 debate is now closed! The answer is 16. Case closed. Besides, there really shouldn’t have been a debate at all.

*Egan J. Chernoff is Professor of Mathematics Education at the University of Saskatchewan. **Rina Zazkis is a Professor in the School of Education at Simon Fraser University.*

*This article first appeared on The Conversation.*

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