 # 8÷2(2+2) viral math question

## 8÷2(2+2)

The above is a link to an article on Lew Rockwell.

8÷2(2+2)

This is a recent viral math problem.

There are two claimed answers, 16 & 1.

You start with the portion of the equation in the parentheses first, than multiple that by the number adjoining the parentheses. Then finally you do the division.

2+2=4*2=8 8/8=1.

What throws most people is that the correct order goes right to left, rather than the more intuitive left to right.

(8÷2)(2+2) would be equal to 16.
8÷2(2+2) is equal to 1.

Yep - I can always tell who knows their order of operations really well when I see those types of math posts.

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To be clear, the order of operations is not driven by direction, left or right. It is an established order based on a set of rule, it just happens that the order of operations in this case occurs from right to left in the equation.

Another interesting math question: Sum of all natural positive numbers: Infinity or -1/12???

These type of things are clickbait.

PEMDAS

Learned that in elementary

It depends. Modern interpretation of the order of operations considers the implicit multiplication of 2(4) to be considered in normal left to right order. So it’s essentially: 8 / 2 * (4) = 16. The 2(4) product doesn’t take precedence over 8 / 2. In other words, the P in PEMDAS only applies to the result inside the parentheses.

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Hence, wise people don’t rely on order of operations to communicate. Parenthesis make one’s meaning clear.

Divide and Multiply rank equally (and go left to right).

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I can live with this kind of clickbait.

It’s an ambiguously written equation.

It could be

8

2(2+2)

Or 8/2(2+2)

The world is screwed if we cant agree on this

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Used to have a great time with this when I taught classes in Excel. Used it as kind of an ice breaker on constructing formulas.

I’d ask them for a series of numbers which I’d include in a formula purposely incorporating PEMDAS signs in a left to right order that made a difference as I went on and put them on the board. Most didn’t realize that the numbers they gave were irrelevant, it was to placement of the numbers in what I had in mind that changed the outcome.

Then I’d ask them to solve the problem themselves and keep their answer to themselves. Then we’d enter the formula in Excel and hit enter. Probably 75-80% of the time the answer they wrote down and the answer they got in Excel was different.

Usually worked out as a pretty effective tool.

(NOTE: Classes consisted mostly of manufacturing floor assemblers and clerical staff without college degrees looking to expand skill sets.)
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.^^^^

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PEMDAS

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Correct I shall fix typo

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Click bait, yes. Fun, also yes. These are referred to as a “badly written equations”.

It’s not really ambiguous - there is only one correct answer following proper order of operations and you can get to that answer as it is written. However, it could be written more clearly so folks don’t have to think about it as much.

@Safiel I have never seen order of operations taught as right-to-left. Equal operations (division/multiplication and addition/subtraction) are properly dealt with left-to-right. So in this case it is parentheses, then division, the multiplication giving you 8/2(2+2) > 8/2(4) > 4(4) > 16.

I wish people would straighten out spelling, grammar and correct apostrophe usage.