1MileCrash
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This "problem" is floating around facebook & youtube:
6÷2(2+1)
Now, we all know the answer is 9. The other common answer, 1, was often due to a mistake in thinking that multiplication is of higher precedence than division in order of operations, which was probably the problem's intended way to "trick" people. This is an easily forgivable error in my opinion.
However, I'm also seeing people that believe, almost as commonly, that the multiplication 2(3) is somehow of higher precedence than "normal" multiplication, saying that it is "one term" and cannot be separated. I find this very strange and am not sure where the idea arises.
There is also a confusion regarding distribution, with the claim being that the 2 must be multiplicatively distributed among (1+2) before doing anything. This is the same error, but what's shocking about this is that people call "distribution" a separate operation entirely that is "above" the order of operations when it's still just multiplication, and thus comes after the division of 6÷2 (and therefore you would be distributing a 3.)
These are very grave misunderstandings about simple arithmetic, in my opinion. Of course, some people just aren't "math people" and that's okay, but it's things like this that scare me:
"I was an A+ student as well. My brother is a Mechanical Engineer, my sister in law has her PHD in Chemical Engineering and my math teacher graduated in the top 5% of his class at MIT and he has his PHD. They all agree that it is 1. Not to mention the other 8 friends of mine that are a combination of Mechanical Engineers, Electrical Engineers, Computer Programers and Computer Scientists."
"I am an engineer as well. The answer is 1. There is no argument. Only uneducated responses."
"Um, have we all forgotten about distribution? The 2 being placed directly in front of the parentheses makes it part of that equation, separate from the 6. To use your explanation, putting it in terms of a fraction from the very beginning would show 6 on top and 2(2+1) on bottom. The 2 can not be separated from the parentheses until distributed."
Why do these misunderstandings exist? How can they exist, in people that (if their claims of mathematical experience is truthful) have been doing math as part of their career for years, possibly decades?
6÷2(2+1)
Now, we all know the answer is 9. The other common answer, 1, was often due to a mistake in thinking that multiplication is of higher precedence than division in order of operations, which was probably the problem's intended way to "trick" people. This is an easily forgivable error in my opinion.
However, I'm also seeing people that believe, almost as commonly, that the multiplication 2(3) is somehow of higher precedence than "normal" multiplication, saying that it is "one term" and cannot be separated. I find this very strange and am not sure where the idea arises.
There is also a confusion regarding distribution, with the claim being that the 2 must be multiplicatively distributed among (1+2) before doing anything. This is the same error, but what's shocking about this is that people call "distribution" a separate operation entirely that is "above" the order of operations when it's still just multiplication, and thus comes after the division of 6÷2 (and therefore you would be distributing a 3.)
These are very grave misunderstandings about simple arithmetic, in my opinion. Of course, some people just aren't "math people" and that's okay, but it's things like this that scare me:
"I was an A+ student as well. My brother is a Mechanical Engineer, my sister in law has her PHD in Chemical Engineering and my math teacher graduated in the top 5% of his class at MIT and he has his PHD. They all agree that it is 1. Not to mention the other 8 friends of mine that are a combination of Mechanical Engineers, Electrical Engineers, Computer Programers and Computer Scientists."
"I am an engineer as well. The answer is 1. There is no argument. Only uneducated responses."
"Um, have we all forgotten about distribution? The 2 being placed directly in front of the parentheses makes it part of that equation, separate from the 6. To use your explanation, putting it in terms of a fraction from the very beginning would show 6 on top and 2(2+1) on bottom. The 2 can not be separated from the parentheses until distributed."
Why do these misunderstandings exist? How can they exist, in people that (if their claims of mathematical experience is truthful) have been doing math as part of their career for years, possibly decades?