6÷2(2+1), the answer is actually 9. For the people who used this principle x/2y, 2y is obviously together in a group. Polynomials is a simpliest form of an equation the doesn't need parentheses. for example, if the problem is written as 6÷[2(2+1)], in algebraic expression it can easily written as 6÷2y or 6/2y with y=2+1. For the people who said that we should use the distribution, using distribution in 2(2+1) is actually a multiplication method which means you break the rule of PEMDAS that Multiplication and Division are tied in priority which who comes first from left to right should be solve first. 1st step: 6÷2(2+1), Inside the parentheses, 6÷2(3), the parentheses sign is indicate a multiplication, eq. of multiplication signs [x, *, ()] 2nd Step: 6÷2(3), since () is indicate a multiplication, you can rewrite the problem as 6÷2x3, since Division comes first, used Left to Right rule, solve 6÷2=3 3(3) or 3x3 or 3*3 3rd Step 3(3)=3x3= ****9****.

Thank you all!

All things considered would an appropriate answer be "Need more information to solve" since the author gave no context clues to assist?

It all depends on what they call the precedence of the operators. For Mathematica (Wolfram Language) the Divide has a higher precedence than Times. So it will first do divisions then multiplications:

Precedence[Divide]
Precedence[Times]
470
400

But in other cases you also have to look at how it groups:

6/2/3

could be 6/(2/3) or (6/2)/3, giving different answers.

have a look here:

https://reference.wolfram.com/language/tutorial/OperatorInputForms.html

To sum up: the author of that equation is just sloppy; you have to assume something in order to solve it, and depending on the conventions... so therefore always add extra parenthesis to rules out those cases...

Thank you for your response Gianluca,

For my own edification, what context clues would there be to solve the equation any other way? Which interpretation makes the most sense in this context? 9 or 1? Would a word problem make this easier to understand as well?

Also I very much appreciate any responses in this thread--All of us have access to the same Wikipedia and websites that have greater detail...however for my end users who are obstinate about unreliable sources I wanted to come to the most credible place.

That is a classic. The problem is that there is no universal agreement on how to parse expressions with a mix of multiplications and divisions, or with more than one division. Does 1/2a mean 1/(2b) or (1/2)a? It is a matter of convention. Mathematica treats it as (1/2)a, but you may find books where it is meant as 1/(2a), perhaps because this way you save typing parentheses. Usually the ambiguity can be decided from the context, as only one interpretation makes sense. I teach my students to avoid expressions such as a/b/c and always write parentheses to make sure they are not misunderstood. There is a Wikipedia article on the "Order of operations". The calculation 6 ÷ 2(1+2) = 6 ÷ 2 + 4 = 7 is a gross mistake in my view.