48÷2(9+3) = ?
Asked by
Charles (
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December 26th, 2011
48÷2(9+3) = ????
A) 2
B) 288
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24 Answers
Remember order of operations. (PEDMAS)
So we start by stuff between parenthesis, so 9+3 is 12
12×2 is 24
48 / 24 is 2
It is not 2. It is 288.
I wonder how many planes have crashed because engineers looking up at a powerpoint chart went forward with a design that they assumed it was 2 from inspection.
B.
9+3 = 12
Then 48/2 and 2*12 have the same priority, but 48/2 comes first so you do it first.
24*12 = 288
So the DMAS rule applies then?
The reason this is so problematic for some people is that our brain has learned to take shortcuts; because division is usually represented with / and multiplication with parenthesis, we see numbers that are close together (as opposed to separated by a + or – sign) and we think “do this first.” Due to the (unusual) use of the ÷ symbol, the division, which is supposed to happen before the multiplication, involves numbers being farther apart, and so our brains instinctively want to do the muliplication first.
Multiplication and division are of equal rank according to the PEMDAS rule that most of us know. When the problem has been simplified to where multiplication and division are the highest priority left, you perform the multiplication and division from left to right.
Therefore, once the problem has been narrowed down to 48/2(12), 48/2 comes first, making the problem 24(12), which results in the answer B. 288.
good example of the virtues of pen & paper.
Or, if you are wearing my glasses, 48 plus 24 = 72.
This was a great lesson! Thank you!
To be fair though, even if you write it as 48/2(9+3), I think there is a tendency in the sciences to give priority to what’s called “implicit” multiplication in @halabihazem‘s link.
Whether the same can be said about mathematicians, I don’t know.
Either way, as I said, it’s a great example of the limitations of standard word-processing. Nobody would ever write something like that on paper; the priority would be obvious from whether the (9+3) was part of the denominator, or to the right of the whole fraction.
You have to use a lot of brackets, if you want in-line expressions to be unambiguous.
This often results in something very difficult to read, however. Practically useless in a report. I don’t thank Microsoft very often, but the equation editor in the new versions of Word saves a lot of time for me.
Order of operations. :P
Anything in parentheses first. 9+3 = 12.
Multiplications and Division go together, so you just work from left to right.
48/2 = 24
24×12 = 288
:) Aren’t you proud of me? I learned 3rd grade math! :D
lol. See, now I would have picked A, giving multiplication higher precedence than division. I think could be wrong, that I learned that from computer programming. Probably why I don’t program anymore.
(And now you know why I use parenthesis liberally.)
(48/2)(9+3) = (48/2)*9 + (48/2)*3 = 24*9 + 24*3 = 24(10 – 1) + 24*3 = 24*10 – 24*1 + 24*3 = 240 + (24*3 – 24*1) = 240 +24*(3 – 1) = 240 +24*2 = 240 + 48 = 2?
42, it’s the answer to everything.
D) Improperly written formula.
While fully understanding the order of operations rules will get you the correct result, a proper formal language lacks ambiguity.
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