It seems this innocent little equation has sparked a lengthy discussion among physicists, mathematicians, engineers, and now even a lowly chemist has become involved.

Not everyone agrees with this last statement, Leon M. Lederman and Dick Terese wrote in 2006 in their book, "The God particle: if the universe is the answer, what is the question?","Above physics sits chemistry, which requires the discipline of physics; ... defer only to the mathematicians, and the mathematicians defer only to God ..."

I sent the equation (48÷2(9+3)=? to my FB friend Emily LeBlanc. Emily is a Math teacher. Here is that letter

Dear Emily,

I have a question for you. My younger daughter posted the following equation on her Facebook page 48÷2(9+3)=? This has resulted in over 70 posts so far. It seems people are split between two answers. They are 288 and 2. You can see the controversy by clicking my Facebook page than click friends than Kiona . Well I took algebra about a hundred years ago so I don't know the correct answer. I did some playing around with the formula using Excel. The results are below. My question to you is what is the correct answer? I remembered you saying on our Austrian ski trip that you were teaching 9th and 11th graders algebra and loved your job. So professor Emily what is the correct answer?

Thanks, Ron

Excel Results:

If I enter the formula as fx=48÷2(9+3) I get an error message i.e. "The formula you typed contains an error: To get assistance in entering a function, click OK, than click function of the insert menu. If you are not trying to enter a formula, avoid using an equal sign (=) or minus sign (-) or precede it with a single quotation mark ()."

If I change the formula to fx=48/2(9+3) I get another error message stating the formula is again entered incorrectly and if I click OK Excel will fix it, when I do so Excel recommends this as the formula fx=48/2*(9+3). If I accept this than Excel says the result is 288.

If I enter it as fx= 48/(2*(9+3)) as Kiona suggests the result is 2. So which is correct? I took algebra almost a hundred years ago and did not know which answer is correct. I recall you telling me you are teaching ninth and eleventh graders algebra. If I haven't put you to sleep yet what is the correct answer to 48÷2(9+3)=?

Thanks again,

Ron

Professor Emily's response follows:

Re: A Simple Algebra Question

Dear Ron,

It's great to hear from you! I find your question amusing because I am constantly reminding my students "Please Excuse My Dear Aunt Sally" which is a device to help remember the Order of Operations. When working with an expression you start with your Parenthesis (or grouping symbols) and evaluate the expression(s) inside first, then evaluate Exponents, then Multiplication and Division (in the order they appear when reading from Left to right), and finally evaluate Addition and Subtraction (again in order from Left to Right).

So, to answer your question please follow my work:

48÷2(9+3)= evaluate the inside of the parenthesis first
48÷2(12)= Division appears first, so evaluate 48 divided by 2
24(12)= the only operation that remains is the multiplication
288

and your final answer is 288.

Hi Emily,

Thanks. I think my college calculus professor would agree with you. A physics forum site i.e. http://www.physicsforums.com/showthread.php?t=488334 is split between 288 and 2 but what do physicists know anyway? Well maybe one did, "Everything should be made as simple as possible, but not simpler." - Albert Einstein and a philosopher also said, "Simplify, simplify," - Henry David Thoreau.

Skiing is over for this season at Whiteface but fishing, kayaking, canoeing, and hiking and this giant playground called the Adirondacks leave plenty to do out doors. I hope you and Jay enjoy every season. It sure looks that way from your FB page.

It's great to hear from you,

Ron

I will remind those reading this of the following hierarchy,
"Pecking order of the sciences:
Biologists answer only to Chemists.
Chemists answer only to Physicists.
Physicists answer only to Mathematicians.
Mathematicians answer only to God.
-or-
The biologist wants to be a chemist. The chemist wants to be a physicist. The physicist wants to be God. God wants to be a mathematician."

A little algebraic poem from:. http://wilk4.com/humor/humore30.htm
((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0
A Dozen, a Gross and a Score,
Plus three times the square root of four,
Divided by seven, plus five times eleven,
Equals nine squared
And not a bit more.
i.e.
((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0

Google solution for left side of the equation: ((12 + 144 + 20 + (3 * (4^(1 / 2)))) / 7) + (5 * 11) = 81

Google solution for the right side of the equation: 9^2+0=81

Step by step solution following PEMDAS (Order of Operation where):
P Parentheses first
E Exponents (i.e. Powers and Square roots, etc.)
MD Multiplication and Division (left to right)
AS Addition and Subtraction (left to right)
Division and Multiplication rank equally (and go left-to-right).
Addition and Subtraction rank equally (and go left-to-right).
Solving the left side of the equation:
((12 + 144 + 20 + (3 * (4^(1 / 2)))) / 7) + (5 * 11) = ?
Step 1. 4^(1 / 2)=2 Evaluate the inside of the parenthesis first this results in
((12+144+20+(3*2))/7)+(5*11)=?
Step 2. Evaluate the inner parenthesis here first (3*2)=6 resulting in ((12+144+20+6)/7)+(5*11)=?
Step 3. Evaluate the inner most parenthesis of(12+144+20+6)) and we get (182/7)+(5*11)=?
Step 4. Evaluate the inner most parenthesis left to right 26+(5*11)=?
Step 5. Evaluate the parenthesis next we get 26+55
Step 6. Do the addition and we get 81 i.i. the right side of the equation = 81
Step 7. Lets look at the right side i.e. = 9^2 + 0
Evaluate the exponent first 9^2=81
Step 8. than add 81+0=81
The right side of the equation = 81 therefore
Solutiion 81=81

Our little poem is correct.

Recap:

1. ((12+144+20+(3*2))/7)+(5*11)=9^2+0 reducing ()
2. ((12+144+20+6)/7)+(5*11)=9^2+0 reducing ()
3. (182/7)+(5*11)=9^2+0 reducing ()
4. 26+(5*11)=9^2+0 reducing ()
5. 26+55=9^2+0 reducing ()
6. 81=9^2+0 solving left side of the equation
7. 81=81+0 reducing using exponent
8. 81=81 reducing and solving using subtraction

A little mathematical joke, "There are 10 kinds of people, those that understand binary, and those that don't."

Now don't blame me for this, it's all the fault of my nerdy younger daughter. I am learning from our countries politicians how to ,"pass the buck."

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