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The simple reason a viral math equation stumped the internet

September 06, 2022
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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 that it, eventually, was lumped with other phenomena that have or .

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

8繩2(2+2)=?

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

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

Clearly, the answer is

Two viable answers to one math problem? Well, if theres one thing we all remember from math class: that cant be right!

Many themes emerged from the plethora of articles explaining how and why this equation 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 peoples 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繩2(2+2) become 8繩2(4) thanks to starting with parentheses. Then, 8繩2(4) becomes 8繩8 because there are no exponents, and M stands for multiplication, so they multiply 2 by 4. Lastly, according to the D for division, they get 8繩8=1.

Image of the acronym PEMDAS spelled out referring to parentheses, exponents, multiplication, division.
Were different ways of teaching the order of operations responsible for confusion? (Shutterstock)

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繩2(2+2) become 8繩2(4) thanks to starting with brackets (the same as parentheses). Then, 8繩2(4) becomes 4(4) because (there are no exponents) and D stands for division. Lastly, according to the M for multiplication, 4(4)=16.

Do not omit multiplication symbol

For us, the expression 8繩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 x or 3 a. When letters are used for variables or constants, the multiplication sign is omitted. Consider the famous equation e=mc2, which suggests the computation of energy as e=mc2.

The real reason, then, that 8繩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 spelled out that is, presented as 8 繩 2 (2 + 2) = ? , there would be no going viral, no duality, no broken internet, no heated debates. No fun!

The equation 8 繩 2  (2 + 2) = ?
Had the problem been correctly presented as 8 繩 2 (2 + 2) = ?, there would be no heated debate. (Egan J. Chernoff), Author provided

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繩2(4).

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

Nice symbol for multiplication

There is a very nice symbol for multiplication, so lets use it: 2 4. Should you not be a fan, there are other symbols, such as 24. 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.The Conversation

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

This article is republished from under a Creative Commons license. Read the .

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