Why do folks get different answers for 48/2(9+3)? [duplicate]

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I did 48/2(9+3) as I thought I had been taught and got the incorrect answer of 2. There's got to be a reason why so many are not only getting the wrong answer but consistently getting the same wrong answer. This came up once before when another equation became an internet meme. Math rules didn't change so something else was different for those who get the right answer and those who get 2 for an answer. I suspect it has something to do with when we were taught math and how the problem is presented. I'm 65 and was never taught MDAS. Was it considered unnecessary when I was taught because this problem would have been presented in an alternative fashion to make the mistake unlikely? It would be interesting to do a study of the ages of those who get 2 and those who get 288. I sought an answer to this question back when the last "math problem meme" hit the Net and could not only not get an answer but no one could even understand my question. Hope I have better luck this time.

marked as duplicate by J. M. is a poor mathematician, Zev Chonoles, Daniel W. Farlow, kingW3, marwalixMay 1 '15 at 19:41

• Because 48/2(9+3) is awfully written. You either want 48/[2(9+3)] or (48/2)(9+3). Parenthesis are there to be used! – Pedro Tamaroff Dec 9 '13 at 0:14
• @Pedro: Could I get to vote for that as an answer, please? – Henning Makholm Dec 9 '13 at 0:26

Because 48/2(9+3) is awfully written. You either want 48/[2(9+3)] or (48/2)(9+3). Parenthesis are there to be used!

Some people don't pay a lot of attention to parentheses. The $(9+3)$ is not in the denominator. If we wanted it in the denominator, we have to have $48/(2(9+3))$. The extra set of parentheses puts it in the denominator.

It's the $2(9+3)$ part that makes things screwy. If you follow PEMDAS, you get this:

$$\frac{48}2(9+3)$$

Which is 288, as it's supposed to be. The problem is that a lot of people colloquially use $a(b+c)$ as if it was it's own self-contained expression, like it was actually written as $(a(b+c))$. If you're used to writing and reading it that way (super, super common in physics and other natural sciences), you automatically parse the expression as

$$\frac{48}{2(9+3)}$$

Which is the incorrect answer 2. I'd bet a lot of money that if you rewrote the problem as $48/2\cdot(9+3)$, people would be much less likely to treat the $2(9+3)$ as its own expression.