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Messy Math

What is the answer to this problem?

48 / 2(9 + 3) = ?

It depends. Usually, math has one right answer, but in this case, the order of operations can get a little quirky.

There are two ways to solve this. First, like so:
48 / 2 × (9 + 3) = ?
48 / 2 × (12) = ?
24 × 12 = 288

But another, arguably valid way is:
48 / 2 × (9 + 3) = ?
48 / 2 × (12) = ?
48 / 24 = 2

Thanks to KnowYourMeme for providing a great overview on this one. Math StackExchange has more discussion.


Posted in Brain Teasers

 

14 Comments on "Messy Math"


Benubird says
January 24, 2015 @ 15:08

This is not a real puzzle. The standard order of operations is: Brackets, Indices, Division, Multiplication, Addition, Subtraction. Therefore the 48/2 (division) happens BEFORE the multiplication, and the only possible answer is 288.

Learn more: https://en.wikipedia.org/wiki/Order_of_operations


Dan says
January 24, 2015 @ 20:45

Wikipedia (the page you linked to) contradicts what you wrote. “Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to “Please Excuse My Dear Aunt Sally”, with the first letter of each word creating the acronym PEMDAS. Canada uses BEDMAS, standing for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Most common in the UK and Australia[8] are BODMAS and BIDMAS.”

And “different calculators follow different orders of operations.”

The distributive property of multiplication further complicates the issue. You may think you have the one true answer, but others claim they do too, and you disagree with them. That’s the whole point. :)


Allison (mathematician) says
April 1, 2015 @ 22:34

Ahem. First off no offense but you are wrong!!!! The correct answer is 2. There is such thing as other of operations so don’t go around and confuse people. It’s PEMDAS: (meaning) paranthesis, which means anything in paranthesis you do first. Exponents are next, then multiplication and division whichever one comes first in the problem from left to right then addition and subtraction the first one from left to right. You see math always has one correct answer. You should do a better job of researching before you post something. Thanks for the confusion.


Allison (mathematician) says
April 1, 2015 @ 22:37

Wait I’m sorry. The correct answer is 144.

48 / 2 x (9+3)
48 / 2 x (12)
12 x 12
144!!!!!!


Allison (mathematician) says
April 1, 2015 @ 22:38

Oops. In really tired and out of it.

48 / 2 = 24
24 x 12
= 288

Sorry


Dan says
April 2, 2015 @ 15:23

Hah! That was funny.


Aravind says
July 15, 2015 @ 12:12

Actually it is supposed to be 2.

Look:

Brackets first: which leave us with

48/(2×12)

Then division is done:

48/24=2.

Why it is not 2? Can somebody pleease explain?


Mark says
August 14, 2015 @ 21:47

It’s not 2. It’s 288.
1) original problem: 48 / 2(9 + 3)
2) Simplify what’s in parentheses first and get this: 48/2(12)
Brackets were not added underneath the division symbol so after you perform the operation in the parentheses you are left with 48/2(12). You have division and multiplication so you have to do whichever comes first from left to right. In this case you must divide first.

48/2(12)
24*12
288


Craig says
January 7, 2016 @ 16:35

I always thought it was PEMDAS but for Multiplication and Division (and Addition and Subtraction) it is was done in the order from left to right as you come upon them.

That would be:
48 / 2(9 + 3) = ?
48 / 2(12) (Parenthesis)
This is same as
48 / 2 * 12
You would do the division because it is first from left to right
24 * 12 = 288

If I am right that is the one and only correct answer.


Dan says
January 8, 2016 @ 11:09

@Craig The PEMDAS convention is specific to the US.


Bonnie says
February 13, 2016 @ 15:44

The debate for this can go on and on and on, but the real problem isn’t the interpretation. The problem really is that whoever first came up with this riddle is being deliberately unclear. Both interpretations are valid if there is no context.


Jared says
February 13, 2016 @ 21:46

Look guys, the original problem is written as 48 / 2(9+3). Note that the 2 and the (9+3) are TOUCHING, noting that they are being multiplied by each other. If the problem were written as “(48/2)(9+3)”, then the answer would be 288, because (9+3) would be multiplied by the entire fraction, and not the denominator. But (9+3) is in the denominator, and therefore the answer is 2.


vignesh says
June 29, 2016 @ 12:59

Correct Jared. What tried to explain, u did it clearly!!!☺☺☺


Joe says
July 22, 2016 @ 13:54

Thank you Jared. People need to go back to math class.


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