seeking assistance because I'm genuinely curious...as to who is right and who isn't.

Okay so basically I was on Reddit today and a viral math problem appeared in r/YoungPeopleYouTube. It was quite literally written as 8÷2(2+2). Now me and a fellow redditor are at an impasse: they say the answer is verifyably 1, and I say it is verifyably 16.

When I plug in the equation into Mathway or Wolfram Alpha (as it is written, so literally typing it out in order and not changing how I type it or any extra key commands, etc), both services change it into this: (8)/(2(2+2)) where 2(2+2) is the whole bottom of the fraction. If we were to solve the equation this way, naturally it would equal 1. 2+2=4 (parentheses first), then 4*2 (because with fractions you take care of the denominator first if you have nothing on top to do, correct?) which equals 8, 8/8=1.

But how I am understanding the equation as it is written (which I fully understand is a poor example, but it is just a meme after all) is rather that the it needs to be processed through (or thought through) our minds as if it was written like this: (8/2)*(2+2). To my understanding, you do the parentheses first (which would equal 4), then you do the division because it comes first in the problem (M or D, A or S, left to right), so that gets you 8/2=4, then you're left with 4(4), which naturally gets you the result of 16.

Who is right here? And why? Are these calculators inputting it wrong simply due to machine error? Or am I wrong in my thinking? Any help would be greatly appreciated! Thanks!

Hi, Julia.

This problem, or others like it, have been viral literally for decades. We have discussed the issue in our blog here:

Order of Operations: Implicit Multiplication?

As explained there, both approaches to evaluating mixed division and multiplication are taught, in different places. Yours, which treats all multiplications alike, with the same precedence as division, is commonly taught in America, as a rigid version of PEMDAS. The other, which evaluates multiplication written without a symbol first, seems to be common in other places, and among actual users of math. I explain in the following post why I half-heartedly support the latter; but my overall advice is never to write such an expression. (On the other hand, I am troubled by the idea that inserting the multiplication symbol where it was previously only implied would change the value of an expression; that's why it's only half-hearted!)

People who post such questions likely know it will cause arguments, and enjoy doing so. You should just ignore it. It's like arguing over British vs American spelling, only worse.

By the way, when I type the expression into Google, it gives the answer as 16 (along with various explanations of the issue, not necessarily correct!). And when I enter it into Wolfram Alpha in "natural language" format using either the obelus, 8÷2(2+2) or the slash,  8/2(2+2), it gives 16, translating it as (8/2)(2+2); but if I enter it as 8/2(2+2) in "math input" format, it translates it as a fraction with only 8 in the numerator, and gives the answer 1. This appears to be due only to how the math input works (as it makes this change within the input field), and not necessarily how they interpret the symbols. Using the obelus in "math input", it still gives 16.

Clearly, this is just something that isn't fully agreed upon, even after decades of debate.

-- Doctor Peterson

Thank you! That was such a fascinating response! I really appreciate you taking the time to answer this!