This problem, and ones like it, have become popular on Facebook. People enjoy arguing about "the right way" to do these problems. The discussions revolve around PEMDAS, or the mathematical order of operations.
While I would never want to deprive anyone of some good ol' math fun, these problems frustrate me. The answer to the question is: Use some parentheses please! No one writes strings of arithmetic like this. They use parentheses to make their meaning clear.
People find these problems fun, at least in part, because 6th grade math books teach problems like these. But this is an exercise in missing the point. What is the point, you ask? Let me tell you!
The point of PEMDAS (parentheses, exponents, multiplication, division, addition and subtraction. Or, Please Excuse My Dear Aunt Sally!) is to allow us to write algebraic expressions without parentheses! A simple quadratic like 3x^2 + 5x - 6 would require three sets of parentheses without order of operations.
My son's recent school work actually finished strong. The obligatory word problem at the bottom of the worksheet went like something like this:
Write an expression for buying x shirts for $10 each and y hats for $5 each.
So the answer, 10x + 5y is actually a great example of when and why we want to multiply before we add. Three cheers for context! Boo and hiss for random strings of arithmetic!
PS: The correctly written problem would read:
6 - (1*0) +(2/2) = 6 - 0 + 1 = 7