Day: July 31, 2012

PEMDAS

Someone asked on Facebook: “5 + 5 + 5 – 5 + 5 + 5 – 5 + 5 × 0 = ?” Is it: (a) 40  (b) 0  (c) 20  (d) 15?

Take a moment to work it out. It’s not a trick question; it’s just arithmetic. Have you got it?

You will, of course, have seen that the problem could equivalently have been written as “5 + 5 + (5 – 5) + 5 + (5 – 5) + (5 × 0)”, which in turn is “5 + 5 + 0 + 5 + 0 + 0”, which is… 15.

As I write this, the Facebook poll shows these responses:

  • 2,225,250 answered 0 
  • 981,309 people correctly answered 15.
  • 518,062 answered 20
  • 86,759 answered 40

This is sad in so many ways. First and most obvious is that the majority of respondents answered incorrectly. It appears they ignored operator precedence (or “order of operations” rules), did the addition and subtraction first, and then multiplied the final result by zero.

But I’m willing to attribute this in part to the context. This isn’t a scientific survey (in any way), and the question’s title invites poor thinking. After the mathematical expression, the question adds “(I Bet More People Will Answer It Wrong :P) Give A Try !!”

This identifies the question as a trick, so instead of simply computing the answer mathematically many people will just scan for the trick. Spotting the “× 0” at the end, they’ll leap to the conclusion other people would not spot that, and then jump straight to the 0 answer without ever evaluating the rest of the expression. So some of those 2,225,250 wrong answers are not from people who have forgotten about operator precedence, but from people who just didn’t put a lot of thought into a Facebook poll.

I’m more interested in the other two wrong answers. More than half a million people answered “20” which I imagine means they missed the “× 0” entirely and did just the addition and subtraction. Worse, many arrived at 40 which I can only conclude is the result of counting the fives and ignoring the operators (and the 0) entirely — i.e., treating everything as addition.

Let’s just all keep this in mind the next time your local school district asks for more money.