Originally published at: Twitter users brawl over simple equation | Boing Boing
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PEMDAS for the win! Wait a minute…
parenthesis, exponent, multiply OR divide, add OR subtract
So both twits are wrong. The equation is invalid.
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It’s not ambiguous at all. Multiplication and division are performed left to right, meaning the answer can only be 16.
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It seems ambiguous because two different notation schemes are being used together
Usually the “just write the factors next to each other and multiplication is implied” form goes with the “division is indicated by a horizontal line with the dividend above and the divisor below”
If the expression were written that way then we could tell which numerals were intended to be part of the divisor by where they were written
OTOH the “÷” symbol generally goes with the “×” symbol and if there were an “×” after the first “2” then left-to-right would be more clearly implied
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I disagree with Chat-GPT on where the ambiguity lies. There are no implied parentheses but instead there is the hidden/implied multiplication between the 2 and the open parenthesis.
Written out: 8 / 2 * (2 + 2)
That’s just straightforward PEMDAS or 8 / 2 * (2 + 2) = 8 / 2 * 4 = 4 * 4 = 16.
But… I will admit that I’ve heard many times that it would still be 1 since the order is Parentheses Exponents Multiplication Division Addition Subtraction and thus you should do the “2 * 4” multiplication before the “8 /” division. That’s just a misunderstanding of the PEMDAS ordering.
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It’s a very nicely constructed trolley. Which is, I admit, mildly unusual since most trollies don’t work that hard.
(edit: what’s with the seeming autocorrect here?)
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Boing Boing likes trolleys
ALL ABOARD 
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I don’t know that implicit multiplication is really part of PEMDAS rules, and you for sure don’t see it used for multiple symbols at a time like that. If someone wrote 8 / 2(2 + 2) I wouldn’t assume the (2 + 2) was meant to be part of the numerator, because if it were anyone sensible would write (8 / 2)(2 + 2).
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Indeed PEMDAS, or some prior agreed alternative, is the answer. If one isn’t explicit of the ordering than the result won’t be either, (and internet(z) warfare is likely)
and, as i’m sure you know and are just pulling our leg, implied multiplication gets 'puter inserted as a ‘*’, and resisting adding any additional parenthesis from the original:
echo “8 / 2 *(2 + 2)” | bc -l
16.00000
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~ $ bc -l<<<'8÷2(2+2)'
(standard_in) 1: illegal character: \303
(standard_in) 1: illegal character: \267
(standard_in) 1: syntax error
~ $
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From said article:
Which even gives this as an example, and explains why so many people with math backgrounds will read it as 1 instead. There the implicit multiplication doesn’t have the same role as saying × or * or whatever.
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They’re both wrong. As written, ?=16. 
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…and once again, unto tedium: implied multiplication is translated into computer-land with a ‘*’ and
÷ becomes ‘/’
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I’ve always hated implied multiplication and all the other shortcuts that mathematicians get up to. I’m sure I would feel differently if I were using a chalkboard instead of a keyboard, but it just seems lazy and unnecessarily vague. Doesn’t make any difference for the result here, but it’s still annoying.
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… when you rewrite the question you can make the answer anything you want
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PEMDAS does say parentheses get evaluated first, so this simplifies to 8/2*4, but at that point it’s ambiguous because PEMDAS gives no official rules for this (whether a left-to-right rule or a prioritization of either multiplication or division). However, as chenille pointed out above, the wiki article on order of operations does note in this section that a number of scientific textbooks and journals have adopted the convention that multiplication comes before division, so for example 1/2n is interpreted as 1/(2n) rather than (1/2)n.
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Well there’s “rewrite” and there’s “translate” (or ‘transliterate’), you must grant there’s a difference there. i didn’t rewrite the question to: “what color shirt am i wearing now?” (blue-ish)
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Or is it gold-ish?
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I don’t necessarily mind people provoking internet strangers for sport. For instance, announcing that (1+2+3…) = -1/12 can spark interesting conversations and lure jerks to reveal themselves.
But this is mere obnox.
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