What Is the Answer to That Stupid Math Problem on Facebook?

This math equation has been passed around on Facebook precisely because people argue about it. Having not taken a math class in 40 years or so, I only got halfway through it before I became stuck. Sure, if it were a mortgage amortization or a sale on beans, I would be able to figure out what I want to know, but the way problems are presented in math class are beyond my long-term memory. The problem is in the way it is written. Tara Haelle at Slate explains:

Some of you are already insisting in your head that 6 ÷ 2(1+2) has only one right answer, but hear me out. The problem isn’t the mathematical operations. It’s knowing what operations the author of the problem wants you to do, and in what order. Simple, right? We use an “order of operations” rule we memorized in childhood: “Please excuse my dear Aunt Sally,” or PEMDAS, which stands for Parentheses Exponents Multiplication Division Addition Subtraction.* This handy acronym should settle any debate—except it doesn’t, because it’s not a rule at all. It’s a convention, a customary way of doing things we’ve developed only recently, and like other customs, it has evolved over time. (And even math teachers argue over order of operations.)

“In earlier times, the conventions didn’t seem as rigid and people were supposed to just figure it out if they were mathematically competent,” says Judy Grabiner, a historian of mathematics at Pitzer College in Claremont, Calif. Mathematicians generally began their written work with a list of the conventions they were using, but the rise of mass math education and the textbook industry, as well as the subsequent development of computer programming languages, required something more codified. That codification occurred somewhere around the turn of the last century. The first reference to PEMDAS is hard to pin down. Even a short list of what different early algebra texts taught reveals how inconsistently the order of operations was applied.

That cleared up nothing at all for me, because where I was stuck was in a much siller place. I had to read the entire article before I figured out what to do. See if you can come up with an answer before you read the rest. More