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, mathematicians and mathematics educators have been weighing in on a particular debate rooted in school mathematics that .

The debate, covered by Slate, , and many other outlets, is focused on an equation that went so 鈥溾�� that it, eventually, was lumped with other phenomena that have 鈥溾�� or .

On the off chance you鈥檝e yet to weigh in, now would be a good time to see where you stand. Please answer the following:

8梅2(2+2)=?

If you鈥檙e like most, your answer was 16 and are flabbergasted someone else can find a different answer. Unless, that is, you鈥檙e like most others and your answer was 1 and you鈥檙e equally confused about seeing it another way. Fear not, in what follows, we will explain the definitive answer to this question 鈥� and why the manner in which the equation is written should be banned.

Our interest was piqued because we have on about following 鈥� a sequence of steps taken when faced with a math equation 鈥� and were a bit befuddled with what all the fuss was about.

Clearly, the answer is鈥�

Two viable answers to one math problem? Well, if there鈥檚 one thing we all remember from math class: that can鈥檛 be right!

Many themes emerged from the plethora of articles explaining how and why this 鈥渆quation鈥� broke the internet. Entering the expression on calculators, , was much discussed.

Others, hedging a bit, suggest both (which is ridiculous).

The most dominant theme simply focused on implementation of the order of operations according to different acronyms. Some commentators said people鈥檚 misunderstandings were attributed to like PEMDAS, sometimes used in the United States: PEMDAS refers to applying parentheses, exponents, multiplication, division, addition and subtraction.

A person following this order would have 8梅2(2+2) become 8梅2(4) thanks to starting with parentheses. Then, 8梅2(4) becomes 8梅8 because there are no exponents, and 鈥淢鈥� stands for multiplication, so they multiply 2 by 4. Lastly, according to the 鈥淒鈥� for division, they get 8梅8=1.

By contrast, Canadians may be taught to remember BEDMAS, which stands for applying brackets, exponents, division, multiplication, addition and subtraction. Someone following this order would have 8梅2(2+2) become 8梅2(4) thanks to starting with brackets (the same as parentheses). Then, 8梅2(4) becomes 4(4) because (there are no exponents) and 鈥淒鈥� stands for division. Lastly, according to the 鈥淢鈥� for multiplication, 4(4)=16.

Do not omit multiplication symbol

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

Key to the debate, we contend, 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 脳 x or 3 脳 a. When letters are used for variables or constants, the multiplication sign is omitted. Consider the famous equation e=mc^2, which suggests the computation of energy as e=m脳c^2.

The real reason, then, that 8梅2(2+2) broke the internet stems from the practice of omitting the multiplication symbol, which was inappropriately brought to arithmetic from algebra.

Inappropriate priority

In other words, had the expression been correctly 鈥渟pelled out鈥� that is, presented as 鈥�8 梅 2 脳 (2 + 2) = ? 鈥�, there would be no going viral, no duality, no broken internet, no heated debates. No fun!

Ultimately, omission of the multiplication symbol invites inappropriate priority to multiplication. All commentators agreed that adding the terms in the brackets or parentheses was the appropriate first step. But confusion arose given the proximity of 2 to (4) relative to 8 in 8梅2(4).

We want it known that writing 2(4) to refer to multiplication is inappropriate, but we get that it鈥檚 done all the time and everywhere.

Nice symbol for multiplication

There is a very nice symbol for multiplication, so let鈥檚 use it: 2 脳 4. Should you not be a fan, there are other symbols, such as 2鈥�4. Use either, at your pleasure, but do not omit.

As such, for the record, the debate over one versus 16 is now over! The answer is 16. Case closed. Also, there should have never really been a debate in the first place.

, Professor of Mathematics Education, and , Professor, Faculty of Education,

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