[dayglored]

It's a classic "order of operations" problem. The order that I learned is:

1. Operations inside parentheses (fractional numerator and denominator are considered independently parenthesized)
2. Powers, exponentials, logarithms
3. Multiplication and division, proceeding left-to-right
4. Addition and subtraction, proceeding left-to-right

So to solve 8/2*(2+2) (I added the * to clarify the implied multiply)

1. Add 2+2, so the parenthesized value is 4
2. All remaining operations are multiplication and division, so proceed left to right. 8 divided by 2 is 4, times 4 is 16.

To get your answer of 1, we have to make an assumption: that everything to the right of the division is the denominator of a fraction in which 8 is the numerator, i.e.:

8 / ( 2 * (2 + 2) ) = 1

In this case the "consensus" is about the rules of order of operations. Under the set of rules I learned, the correct answer is 16.

Note that if the problem had been written using fractional notation it would have been obvious immediately which interpretation was intended.

And FWIW, the above is a good example of why I prefer calculators that use RPN (Reverse Polish Notation, XY+) to AN (Algebraic Notation, X+Y). RPN is unambiguous and does not require parentheses; it's also the way computers actually do arithmetic operations (get X, get Y, add them).

[dayglored]

I answered your question above BEFORE reading the PopMech link you sent, so I see now that I duplicated some of the information in that article. Sorry for being long-winded. :-)

[Still Thinking]

Agreed. That’s it’s even in question is an artifact of imprecise PC-era typesetting of expressions. If I saw that, I think I’d assume the (2*2) was intended to be a factor in the denominator, but strict PEMDAS says you’re right.

[Still Thinking]

Although, on further reflection, I have sometimes seen PEMDAS interpreted as P-E-M-D-A-S, as opposed to P-E-[MD]-[AS], which would give a result of 1.