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By Tara Haelle|Posted Tuesday, March 12, 2013, at 1:04 PM
Screenshot courtesy of Facebook
Perhaps you’ve seen the problem on Facebook or another forum:
6 ÷ 2(1+2) = ?
It’s one of several similar math problems popping up on social networks recently. Perhaps you, too, thought, “Duh! That’s easy,” and then, as I did, became embroiled in an epically long comment thread while your blood pressure steadily rose because you could not possibly understand why the others doing this problem could not get the right answer.
Perhaps, if you’re a nerd like me, or you teach math as I do, you even fell asleep thinking about this problem, baffled and frustrated about why you were unable to convince intelligent, educated friends that your calculation of this deceptively simple problem was accurate.
So, did you get 1 or 9? We’ll get to the “correct” answer in a moment.
But first, why do we get so riled up about these problems? People don’t usually get into fistfights at the bar over arithmetic, but these math threads are spectacularly vitriolic. A couple of factors are at work in these math debates, according to Robert Glenn Howard, a social psychologist at the University of Wisconsin–Madison who specializes in Internet communication and folklore.
For one thing, the whole point of Facebook and other forums is to provide a place for discourse and debate. Yes, there are your cousin’s new-baby pictures, and the opportunity to stalk a crush, but really, people go to social sites to say stuff. And argue about it. “People are already primed to engage in pretty intense deliberations, and that can bleed over into the way they play games,” Howard says.
And that’s exactly what these problems are: games. “Humans have used riddles as a form of play since ancient times,” Howard says. “And sometimes people can get competitive and wrapped up in it.” People use puzzles to show off their smarts, make others feel subordinate, and enjoy telling the story of the game later (as I’m doing right now).
Of course, the fervor with which some people debate basic arithmetic may be a proxy: There’s less at stake in a math debate than a potentially friendship-ending political debate. Arguing over multiplication may even be a way to make a subtle political point, using others’ “wrong” answers to reinforce a broader worldview, such as that the United States has poor math education.
But why do the debates often go on so long? One reason is psychological, another mathematical.
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Please tell me am right. my answer is 1 and it must be right!
The answer is 9, but could also be 1. The fun is the discussion on why we disagree on the answer, or more accurately, why people would take a stand on one answer or the other.
how is it 9?
If you start at the left, 6 divided by 2 is 3, times (2+1) which equals 3, equals 9. It is a question of syntax, of language used to express the math.
If you think that everything to the right of the division symbol should be done before dividing into 6, the answer would be 1.
You can alternatively apply PEMDAS as schools do today: Simplify everything inside the parentheses first, then exponents, then all multiplication and division from left to right in the order both operations appear, then all addition and subtraction from left to right in the order both operations appear. (A better acronym would be PEMA, actually, to make it clear that multiplication and division are done together, and addition and subtraction are done together.) By that convention, 6 ÷ 2(1+2) = 6 ÷ 2 × (1+2) = 6 ÷ 2 × 3 = 3 × 3 = 9. If you were taking the ACT, SAT, or GRE (which would probably use parentheses to eliminate confusion), this method would yield the correct answer.
When in doubt, I add parentheses everywhere I can, and go right to left from the inside out.
So I'm a "1" guy. As I do write some code, it's the safe way to go: 6 divided by (2(1+2)).
With the added parenthesis, it becomes a different problem.
I typically don't do that for short equations such as this one but for more complicated stuff I only add valid but unnecessary parentheses to help with the inside-out thing. In scripting you can wind up with things like {[("'x'")]} where "X" is actually spread out on multiple lines.
The parentheses I add usually don't change the problem =)
Some brackets are indirectly implied in mathematics as in the example that led to this discussion thread. That is what Michel did added the implied brackets.
a ÷ b(c+b) = Z multiply out to remove brackets.
a÷ bc+ b x b = Z
now substituting the unknowns with numerical values
a = 6 b =2 c = 1
gives
6 ÷ 2 x 1 + 2 x 2 = Z
6÷ 2+4 = Z Since dividing the 6 by either the 2 or 4 would give two differing answers the common practice is to add the 4 and 2 together before dividing.
6 ÷ 6 = 1.
Algebra is based on the same mathematical operations as when you use numbers instead of characters.
So if 9 is the correct answer to the equation there is a lot of error filled algebraic equations out there in the big wide world of science and technology.
That is my take on it any way.
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