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Discussion in 'Bad Dog Cafe' started by Agave_Blue, Apr 9, 2011.
It is 2...no question
What he said .
My old algebra prof always said,
"If you don't know the answer, just say purple!"
I agree, my opinion it must be 2.
I think adding the extra brackets is a better way for the "without" logic calculator to process the calculation and also how excel would do it right (from memory).
I also agree if it were to be 288 it would require the x between the 2 and the ( ).
As an aside, I used to be hopeless at maths in school. Couldn't and still can't memorise multiplication tables etc but as I have gotten older I have constantly worked at it and am now (VERY surprisingly) better than many people I work with.
My old maths teacher said when I left school in 6th form (16 years old) "as far as maths goes....your doing the right thing". I hated her for that!
My favorite Four Deuces song
This is not mathematics, it's arithmetic.
BODMAS, and no calculator
If you use Excel =48/2*(9+3), it will do it wrong, but it is written 48/2(9+3), so the divisor is a bracket, an "Of" i.e.
it becomes =48/(2*(9+3)) for a spread sheet
If you take the problem AS IS and follow the instruction literally, you get 288.
Those instructions regarding Order of Operations are not "random" or "opinion" or anything of the kind. They are the same as every other site that clearly lays out the rules for Order of Operations.
Rule 1, Parentheses first: 48÷2(12)
Rule 2, Next perform all multiplications and divisions, working from left to right. : 48÷2 = 24; 24(12) = 288.
And yet, I am quite certain the answer is 2.
I asked my highly mathletic 16 year old. Just showed him the problem. In about 3 seconds, He said "2" without batting an eye. Then he said, well you could argue it to come out with 288...but that's technically wrong.
That's without having read the thread or any help from his not quite as math talented Old Man or a calculator.
...makes me proud, that boy.
Rules is rules.
Unless you're missing a rule.
I'm studying for my engineering finals and I answered 2. However, right after that I realized that it should be 288. Things aren't looking good for my exams!
48/2(9+3) = 288
48/(2(9+3)) = 2
Brackets are very important.
(9+3) = 12 is very obvious, but when you write the whole thing as 48/2(12) that is the same as 48/2*12 ...working from the left that becomes (48/2)*12 = 24*12 = 288
Who me? No, never.
The grouping of 2(9+3) is the main issue. We cannot treat that group as separate components that can be recombined with the 48÷ component.
The proximity of the 2 to the (9+3) means that the resulting number is desired prior to the 48÷ calculation.
For BEDMAS to be applied, we need a multiplication symbol between the 2 and the (9+3). As there is none, the 2(9+3) calculation is done first.
Also without the multiplication symbol the equation should be written thus:
If you want BEDMAS to apply, it must be written 48÷2x(9+3)= N
The original premise is written incorrectly. It makes for a nice trick question, but it is flawed. You can't apply a hard rule to something that is incorrect from the start.
But what if C-A-T really spelled "dog"?
There are formal rules for mathematics. That expression, 48÷2(9+3), is evaluated as:
48 x (1/2) x (9+3).
Division and multiplication are equal precedence and so are evaluated from left to right.
One way to understand it better is to look at division as a multiplication by the inverse.
So 48/2 is same as 48 X (1/2).
As a standard math problem, the answer is 288. Some things in math follow logically from
preceding laws and are therefore inherent laws of math. But the order of precedence is
not. It is an arbitrary rule, made so that there will be universal agreement about how an
expression should be evaluated. And it has been agreed that division and multiplication
have the same precedence and should be evaluated from left to right.
The C computer language also evaluates that as 288. Other languages may may be different.
Calculators can be different. You have to know how the calculator evaluates
an expression and make sure you enter the problem accordingly.
Calculators and computer languages do not necessarily follow formal math rules.
There is no "original premise", nothing is "incorrect from the start". Just a question: 48÷2(9+3) = ?. It has one answer.
And Order of Operations does apply, BEDMAS, BEMDAS, etc.
Could it have been written to show a particular intent? Yes. But that doesn't make it an invalid question.
Unless you're missing a rule.
R gave me 288:
I learned order of operations as Please Excuse My Dear Aunt Sally...that says you do what's in parentheses first, then multiplication, then division. So it's 9 + 3 = 12; 12 * 2 = 24; 48 / 24 = 2.
So Aunt Sally says it's 2!
Now: How many licks does it take to get to the Tootsie Roll center of a Tootsie Pop?