Posted on 08/01/2019 4:58:47 AM PDT by Renkluaf
“8÷2(2+2).” Can you solve this math problem? The equation went viral online this week on Twitter causing major confusion over the right answer. Mathematicians and physicists went nuts about it. Mike Breen, the Public Awareness Officer for the American Mathematical Society, told popular Mechanics: “The way it’s written, it’s ambiguous. In math, a lot of times there are ambiguities. Mathematicians try to make rules as precise as possible.” Depending on where in the world you learned math, as Mashable reported, determines how you can solve the problem.
(Excerpt) Read more at nypost.com ...
The is.... It depends ( if you owe me money, it’s 16, if I owe you, then it’s 1). The theory of relativity....
My answer above, citing the standard
“Even if you choose to do operations from left to right, the multiplication or division is against EVERYTHING AFTER THE OPERATION SIGN until you get to addition or subtraction signs outside of brackets or parentheses (or powers)”
is in contrast to the opinion stated in the journal article another poster gave (thank you for that, btw):
https://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents
(all caps added by me, for emphasis):
“In case the signs of multiplication and division occur with no signs of addition and subtraction intervening, and in case no symbols of aggregation are used, then it is likewise agreed (in the theoretical development in the books) that each symbol applies ONLY to the factor (or divisor) IMMEDIATELY FOLLOWING it, and that the operations are to be performed in order from left to right.
That is the crux of the issue, and I disagree with the journal author’s opinion (not how I learned, and have operated for decades; BS Chem and BA Math). That author’s opinion leads to the answer of 16, rather than 1. I don’t know what “books” that journal author is referring to, and why we should adopt his opinion, or any other, for that matter—who is really to say? Who really has the authority to set the modern standards?
That’s why it’s better to be wordy and add “symbols of aggregation” (brackets, parentheses, squiggly brackets, etc.) to make it crystal clear. And that’s the REAL correct answer.
42.
The ultimate answer.
Clarification......
8 / 2 X (2+2) = 4 X 4 = 16.
Otherwise it could have been written as as:
8 / [2(2+2)]
and then would be:
8 / [2x4] or 8/8 = 1.
It didn’t have the brackets so the answer should be 16 by the rule of order of operations.
It is a language problem not a math problem.
You get the answer as one by assuming that the division symbol separates terms. In advanced math please avoid this symbol and avoid the elementary “division” concept, rather understanding it as multiplication by the reciprocal.
You get the answer “sixteen” by assuming that the symbol for division, “÷”, is equivalent to the slash, “/” , which is a grouping symbol. In other words, the entire denominator must be simplified before the entire term is simplified. So what is the denominator? If the entire denominator is 2 , then the result is 16.
Remember that language must depend on context! For example, there are people who delight in asking if a tomato is a fruit, but the question assumes that there is no difference between the kitchen and the laboratory. If you are trying to do a problem in a computer, you must use the parentheses according to the program instructions. In geometry class however, the lesson here is to throw out the whole problem on ambiguity. In physics class, you must make the demonstration experiment turn out right, and all the ambiguity disappears because forces are calculated as they are applied.
My position is neither one nor sixteen is correct without a given context. The computer people who are saying sixteen are assuming a context not given. The ÷ sign people are assuming that the sign separates terms which it does not do outside of an elementary academic context. The people who substituted the slash for the division symbol forgot it’s use as a grouping symbol. The slash does NOT group all things after it; it only groups those things under it as drawn. When a rational coefficient is written not with a slash but as a fraction, then all ambiguity vanishes.
Yes a tomato is a fruit which is why we pour it over ice cream!
Excel says 16 QED
You are correct. I tried to clue my grandson in a couple of years ago by stating “something about Aunt Sally”... he responded with “I dunno, she sell seashells down by the seashore?”. I hurt myself laughing!
This probably explains why space vehicles crash into the moon, or miss their splashdowns... why cruise missiles hit children’s hospitals, etc.
Please excuse my dear aunt sally.
Well, the acronym I learned is used internationally. Maybe it’s just the US trying to be independent and different. There’s nothing wrong with that either heh. We’re all unique, just like everyone else haha.
You are correct.
My point is that the answer one gets, assuming it’s either 16 or 1, and further assuming the answer is based on the accurate application of the method used, has absolutely no bearing on whether one is “good at math”, “bad at math”, or anywhere in between.
BTW, all I ever learned in school was “mdas”. And I made it through vector calculus - div, grad, curl, and all that.
8÷2(2+2) becomes
8÷2(4). The next step is the part that throws you if you're not paying attention. It looks like the 2 should be multiplied to 4 first (because the parenthesis pull our eyes in), instead it should be seen as
8÷2X4, and now you see it's easy to see the operations are left-to-right as
4X4 = 16.
the answer is one
follow the rules.
t
1 is the loneliest number is the answer
Two can be as bad as one.
Only if you prioritize multiplication higher than division. In software, they are equal, so the equation would be processed left-to-right after the parenthetical is done.
The two answers are 16 and 1.
8÷2(2+2)
written out 8 ÷ 2 x 2 + 2 is not what defines the terms.. or the answer would be 10
8 is not divided by 2
8 is divided by 2(2+2)
i will stick to 1 being the answer. the rules are wrong
wha?!
the answer is one.
see post 53
math is hard
Order of operations. I say “1” as well
Well, if an Internet search says 16, the science is settled. After all, the Internet only publishes the truth.
I think the answer is "Trump is a racist". Seems to be the answer for everything nowadays.
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