# 6÷2(2+1), and the shocking errors that people make.

• 1MileCrash
In summary, these "problem"s are floating around facebook and youtube:-There is a confusion regarding multiplication and distribution.-People believe that the 2(3) is somehow of higher precedence than "normal" multiplication, saying that it is "one term" and cannot be separated.-There is also a confusion regarding the order of operations, with the claim being that the 2 must be multiplicatively distributed among (1+2) before doing anything.
1MileCrash

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?

In other words, deliberately ambiguous mathematics creates confusion? Looks like a big troll to me.

I would suspect the quotes supporting an incorrect order of operations were faked up by someone trying to work mischief.

These misunderstandings are completely unimportant, because NOBODY writes equations the way you wrote it. You'll always see it written like this:

$$\frac{6}{2}\left( 2 + 1 \right)$$

Or like this:

$$\frac{6\left( 2 + 1 \right)}{2}$$

Writing it in such an unintuitive and ambiguous manner and then being shocked SHOCKED that people get it wrong is silly.

I agree that the equation is written in a way that is purposely meant to confuse the average person, and that equations are never written that way. I disagree that it is ambiguous.

What shocks me isn't the error with the problem itself - it's the reasoning behind it (besides the simple forgivable order of operations misunderstanding.) This idea that 2(3) and 2*3 are somehow different, by engineers, I do find shocking. These errors have nothing to do with the weird way the equation was written.

No it's correct because the BODMAS rule of math says that brackets need to be opened first. So the answer is definitely 1.

MrWarlock616 said:
No it's correct because the BODMAS rule of math says that brackets need to be opened first. So the answer is definitely 1.

See what I mean?

From http://spikedmath.com/415.html

http://img.spikedmath.com/comics/415-dear-internet.png

And I think it is time that this thread is closed.
We have seen this discussion way too many times already.

Last edited by a moderator:

## What is the correct answer to 6÷2(2+1)?

The correct answer is 9. This is because the order of operations states that multiplication and division should be performed before addition and subtraction. So, 2(2+1) should be solved first, resulting in 6. Then, 6÷2 is solved, resulting in 3. Finally, 3 is multiplied by 2, resulting in the final answer of 9.

## Why do people often get the wrong answer for 6÷2(2+1)?

People commonly get the wrong answer because they do not follow the order of operations. Some may mistakenly think that multiplication should be performed before division, leading them to solve 6÷2 as 3 instead of 6. Others may simply forget to perform the multiplication step at all.

## What is the most common error made when solving 6÷2(2+1)?

The most common error made is forgetting to perform the multiplication step after solving the parentheses. This results in the wrong answer of 3 instead of the correct answer of 9.

## Is it ever acceptable to interpret 6÷2(2+1) as 1?

No, it is not acceptable to interpret 6÷2(2+1) as 1. The order of operations is a universally accepted rule in mathematics and must be followed to arrive at the correct answer. Interpreting the expression as 1 is a violation of this rule and is not mathematically sound.

## Are there any real-life applications of solving 6÷2(2+1) correctly?

Yes, the order of operations is important in many real-life scenarios, such as calculating drug dosages in medicine, solving equations in physics, and creating computer code. In these situations, following the correct order of operations ensures accurate and consistent results.

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