Thanks to the Sacramento Kings, this math problem that went viral a while ago went viral again. It is:
My initial reaction is that the answer is 1. Other people—especially younger people, who were apparently taught the mnemonic algorithm “PEDMAS” instead of being taught math—think the answer is 9. The actual answer is, it is a waste of time.
The fight, currently going on in God knows how many terrible chatrooms at once, is about the order of operations. Do you multiply (1+2) by 2, because they are next to one another, or do you divide 6 by (1+2), because you are working through all the multiplication or division operations from left to right?
My instinct is to read “2(1+2)” in exactly the same way I’d read “2y”: it’s 2 times the thing you solve for, directly. The ÷ symbol would be a separate operation that comes later (either unrelatedly or in testimony to its formal distance, I couldn’t even type it in Google Documents using the standard Macintosh keystroke of the option key and the slash).
Six years ago, when this problem was going around, Slate wrote a piece unpacking the conflicting assumptions and conventions around it, and their histories. If you got 9, Tara Haelle wrote, by working left to right, you were following the rule as standardized tests would apply it:
If you were taking the ACT, SAT, or GRE (which would probably use parentheses to eliminate confusion), this method would yield the correct answer.
But that sentence itself contains a parenthetical that changes its answer. If that problem were on a standardized test, that problem would not be on the standardized test, because the standardized test would not have written it that way. There is an unclarified ambiguity created by using the ÷ symbol and a symbol-free act of multiplication in the same problem.
What is an arithmetic problem meant to do? If you were solving this in everyday life, because you needed to know the answer, what you would do is identify what actual relationship among actual quantities you were trying to work out. Are you distributing six ice cream bars among two families, each family consisting of one child and two parents? Or are you figuring out how many ice cream bars you end up with if one child and two parents each get half of a box of six?
I emailed Hmm Daily contributor Jordan Ellenberg, a math professor at the University of Wisconsin and the author of the bestselling book How Not to Be Wrong, to ask what the real-life approach would be.
“In real life,” he wrote, “you would resolve the ambiguity by asking whoever wrote that ‘could you write that in a non-ambiguous fashion?'”