Posted on 04/12/2011 1:32:09 PM PDT by grundle
Texas Instruments TI-85 says:
48÷2(9+3) = 2
But Texas Instruments TI-86 says:
48÷2(9+3) = 288
It’s not a fraction. The backslash is another way to write a division sign just as a * is used instead of x for multiplication
OK, good point. My point is that a division operator does not automatically make everything to the right of it a denominator.
People who read it that way are considering the sign to be making a fraction. That’s not what the symbol means. As I said in my post 308.
I've pretty-much done all my fun math with pencil and paper, saving the calculator for larger numbers. Just wrote things the way I did for 20 years. Never dove much into using the computer for these things, outside of a few interesting Excel spreadsheets and some old BASIC calculations. Precious little compared to the pencil and paper stuff though.
BTW, I take it that B=brackets, as opposed tParentheseses.
It's amazing how much fun we seem to have had with a simple math problem with NO variables!
Yes, that is the key takeaway. If people can confuse your meaning, use some parentheses.
“As you have said, the answer is 2. I’ve done more math in my life than I care to admit (I’m a civil engineer). Having said that, a few more parentheses would have made the equation alot less ambiguous.”
You’d better brush up a bit, then. Otherwise, perhaps you can explain how you arrive at an answer of 2?
If it looked like that, the answer would be 2. But if you want to write that in a single line (as a programming expression), you need to add parentheses to your denominator. Without them, the rules of order yield 288.
So, as written, the answer is 288.
“It really didn’t discuss this specific form; however, the precedence rules along with the associative and communitive rules just don’t provide a means to invent an imaginary parenthetical grouping......”
Which is why you cannot regroup the equation to (48/2)((9+3)
Nor can you arbitrarily add a * between the 2 and the (9+3) in order to justify incorrectly applying precedence rules....
The answer, as the equation is written, is 2.
Nothing to brush up on. I’m right. Anybody that comes up with 288 is wrong. Thanks for the advice, though.
Not in the digital age, my FRiend.
The answer IS 2 and you will never convince me otherwise.
Just a dumb old man here...
Lol, all division is an expression of a fraction, or vice versa, which is the same. Or rather that is to say that all fractions are expressed ratios of two numbers or equations, and all division is a quotient of that ratio. They are intertwined. The horizontal line in a fraction is just a useful tool to help visually clarify the equation, and even simple division is indeed an equation.
What is this operation called when there is no "*" or "x" to tell you it is multiplication?
Where are these precedence rules given that you are following? I have cited the standard, accepted rules. As many others have. There is no exception listed for "multiplication without an explicit symbol." Tell us where this rule is.
your examples all hinge on denominators that have higher precedence than the division. That is not equivalent to the case at hand.
LOL
Thank hubby for me, please. :D
http://en.wikibooks.org/wiki/Algebra/Order_of_Operations
These are the rules. Can you find this rule of yours:
“Do all the math on either side of the symbol AND THEN do the division.”
“Nothing to brush up on. I’m right. Anybody that comes up with 288 is wrong. Thanks for the advice, though.”
Tell us why you’re right. FYI, if you are right, that means that Excel, Google, bc, and programs written in C, C#, PHP, JavaScript, and my HP50g are wrong. If you’re right it should be easy to explain.
Before you can ask, I’ll tell you why 288 is right. The order of operations is
Parens
Mult and Div (equal to each other)
Add and Subt (equal to each other)
Operators with equal precedence are evaluated from left to right.
48÷2(9+3) =
48÷2(12) = [Because operations inside parens are evaluated first]
24(12) = 288 [Because mult and div have equal precedence & evaluated L to R]
Where is the error in my work?
In the digital age, the slash is an operator, with expressions on either side subject to the order of operations.
See my post at 368
Ah yes, but in this case the original post read 48÷2(9+3) and math books do use the backslash to denote division. This particular problem is not 48 as the numerator over 12 as the denominator...it’s 48 divided by 2.
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