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I am postulating that one reason they may teach physics students an unambiguous interpretation is to get them thinking about how to write expressions clearly. In this context, when you see the slash as a "divide by" symbol, what appears to the left of the slash is the numerator, and what appears to the right of the slash is the denominator. When I typed the formula into Mathway, it interpreted and displayed the formula as such:
the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash, and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lif#z and the Feynman Lectures on Physics. Wolfram Alpha changed in early 2013 to treat implied multiplication the same as explicit multiplication (formerly, implied multiplication without parentheses was assumed to bind stronger than explicit multiplication).
In this context, the "O" in BOMDAS means "Order" and is referring to exponents or powers, not the order in which terms appear, and there seems to be some confusion about that which I'll come to shortly.
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. It stands for Brackets, Exponents, Division, Multiplication, Addition, Subtraction...Since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BOMDAS.
However this idea of left to right is actually extraneous, but at least now I understand why so many people have this extraneous idea, because that's what they were taught:
An example is the convention known as the Rules for the Order of Operations, introduced into the school curriculum in the fifth or sixth grade:
(1) Evaluate all expressions with exponents.
(2) Multiply and divide in order from left to right.
(3) Add and subtract in order from left to right.
In short, these rules dictate that, to carry out the computations of an arithmetic expression, evaluate the exponents first, then multiplications and divisions, then additions and subtractions, and always from left to right
(B) exponents first, then multiplications and divisions, then additions and
Except for the stipulation about performing the operations “from left to right”, (B) is seen to be exactly the same as the Rules for the Order of Operations. It is important to note that this stipulation about “from left to right” is entirely extraneous, because the associative laws of addition and multiplication ensure that it makes no difference whatsoever in what order the additions or multiplications are carried out.
Not enough time apparently, because I was wondering if the illuminati had something to do with it but I didn't have time to look into that.
reply to post by Arbitrageur
Ahh the old TI 85 vs TI 86 conspiracy. Btw, you really have way too much time on your hands.
reply to post by bigfatfurrytexan
That's interesting, that the calculator was apparently wrong.
One other thing I ran across is that Microsoft Excel does some "wrong" things too, in opposition to certain conventions which are accepted. For example, Excel doesn't handle nested exponents in the generally accepted ways, and the answers in Excel can be considerably off as a result. So, you have to be real careful when using Excel.
It's accepted by some, but not universally, but why it's not more accepted I don't know. I I think it would be a good thing if it was. But since the 9+3 is in parentheses, that gets added to 12 before anything else.
reply to post by Arbitrageur
The general accepted rules of mathematics Multiplication, Division, addition and subtraction is that it occurs in that order. Therefore /2 operand takes place before 9+3.
reply to post by roadgravel
yeh they are, but that doesn't override 48/2 ....its not 48/(9+3) first.