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Hacker News Comments on
What Is 8÷2(2+2) = ? The Correct Answer Explained

MindYourDecisions · Youtube · 4 HN points · 0 HN comments

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Youtube Summary

What is 8÷2(2+2) = ? Everyone is arguing about this problem, so let's figure out the correct answer! The problem involves the order of operations, historical math notation, and binary expression trees. Glad to see the world is passionate about mathematics!

Here is a 1917 article from "The American Mathematical Monthly" that explains the usage of the division symbol as an exception to the order of operations
http://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents

Google evaluation
https://www.google.com/#q=8÷2(2%2B2)

What is 6÷2(1+2) = ? The Correct Answer Explained
https://youtu.be/URcUvFIUIhQ

9 - 3 ÷ 1/3 + 1 = ? The Correct Answer (Viral Problem In Japan)
https://youtu.be/07Abat5iBbw

Plus Magazine David Linkletter suggests the problem is not well-defined
https://plus.maths.org/content/pemdas-paradox

Harvard's Oliver Knill also says PEMDAS does not resolve the ambiguous problem
http://www.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

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8÷2(2+2) =?

⬐

Aug 02, 2019 · 4 points, 4 comments · submitted by tosh

⬐ tedmiston
To save you the watch...
    8 / 2 (2 + 2)
    = 8 / 2 (4)
    = 4 (4)
    = 16
It's easy to accidentally arrive at a result of 1 by mistake by doing 2 * 4 "bottom up" after the second line instead of applying multiplication & division left to right.
Surprisingly I've seen an older Casio scientific calculator given an incorrect answer of 1.
⬐ simonblack
BODMAS.
is
BRACKETS then OF then DIVISION then MULTIPLICATION Then ADDITION then SUBTRACTION
8 / 2(2 + 2)
8 / 2(4)
8 / 8
= 1
> Surprisingly I've seen an older Casio scientific calculator given an incorrect answer of 1
LOL.
The brackets bind tighter than the division sign. It's a trick question.
What the 16 proponents are seeing is
(8/2) x (2+2)
  (4) x (4)

   (16)
What the brackets are doing though is
(8) / (2 x (2 +2))
(8) / (2 x 4)
(8) / (8)
(1)
⬐ tedmiston
But the extra set of parentheses added here in your reply is not part of the original equation:
    (8) / (2 x (2 +2))
          ^          ^
I don't follow why you don't do the multiplication left to right after the expression inside the parentheses has been evaluated. Once the parentheses (PEMDAS) precedence has been applied to result in 8 / 2 * 4, then it should just be standard multiplication and division left to right, right?
https://www.google.com/search?hl=en&q=%3D%208%20%2F%202%20(2...
⬐ simonblack
The extra set of brackets is an attempt to show that the '2' in front of the bracket is shorthand for '2 x'
i.e 2(...) = (2x(...))
but that '2' is part of the whole brackets expression and should be evaluated as such.
As I mentioned before, this is really a trick question, and meant to be deliberately ambiguous.

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What Is 8÷2(2+2) = ? The Correct Answer Explained