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
MY God, my friend...
Ok, here is a suggestion; go to your nearest high school and talk to the Math teacher or the Computer Science teacher and ask them to explain the answer (288) to you..
I am/was a good soldier.. and I will admit when I am/was wrong... but, in this case, I (and pretty much all the others here in this thread) am not.
Take care FRiend :)
Bikk
I drug out the heavy guns to get an answer and called the Chinese kid next door
Finally, someone on the "2" has found something to cite in favor of their position. Good job.
Unfortunately, this seems to be a minority and/or obsoleted opinion.
So, bottom line is:
2'ers are either misunderstanding a division operator for a fraction, implying a grouping of all to the right of "/" which is not actually stated.
Or applying a minority view about "implied" multiplication taking precedent over regular multiplication and division.
The fact that TI changed from this "implied" rule to standard parsing and that all other computer implementations adhere to standard order of operation rules makes 288 the proper answer today.
Since my math learning predates the computer age, I was taught that “÷” and “/” were exact equivalents. This apparently is not the case any longer. My ninth grade algebra teacher would have evaluated the expression and got 2 for the answer. Today, the correct answer appears to be 288. As I said before, even the online calculators I used provided different results when the the different operators were used.
yup, i survived another winter... hope all is well on your end too
the order of operations is left to right.
since division and multiplication are on the same level of priority, you first divide 48 by 2, getting 24--then you multiply by 12.
288 is the correct answer.
You are exactly correct and that was the point I had been trying to make all along:
48 divided by 2 times (9+3) is not the problem; it is 48 divided by 2(9+3). And as you see, the answer can only be two.
I would consider them to be the same, but apparently some calculators allow people to enter fractions using “/” as the divider.
No programming language I have ever used does this. “/” is simply the division operator.
Not according to the rules.
x = 48 / 2 x (9+3)
Parentheses (evaluate what's inside them)
Exponents
Multiplication and/or division from left to right
Addition and/or subtraction from left to right
And the EXAMPLE: 9 ÷ 3 × 3= 3×3= 9
Multiplication and division are performed at the same time...working from left to right....after the parentheses and any exponents. Thus:
x = 48 / 2 X (12)
x = 24 x 12
x = 288
The rules...and I ask you to simply go anywhere you wish to look them up...are when you get done with parenthesis and exponents you begin working on all the multiplication and division in the problem....and you work from left to right.
Your error is you are doinging all the multiplication FIRST...then starting over from left to right with the division. And that is the error of many. That is not what the rules say:
That is how I solved it also.
“Once again you rewrote the formula with a backslash to satisfy your computation method. Throw that calculator away”
The original question was because of 2 calculators which had the expression written with a backslash. The expression in question properly has a backslash.
Notice that nowhere in the following quotation does it mention greater precedence should be given to implied mult.
From http://jeff560.tripod.com/mathsym.html:
The convention that multiplication precedes addition and subtraction was in use in the earliest books employing symbolic algebra in the 16th century. The convention that exponentiation precedes multiplication was used in the earliest books in which exponents appeared.
In 1892 in Mental Arithmetic, M. A. Bailey advises avoiding expressions containing both ÷ and ×.
In 1898 in Text-Book of Algebra by G. E. Fisher and I. J. Schwatt, a÷b×b is interpreted as (a÷b)×b.
In 1907 in High School Algebra, Elementary Course by Slaught and Lennes, it is recommended that multiplications in any order be performed first, then divisions as they occur from left to right.
In 1910 in First Course of Algebra by Hawkes, Luby, and Touton, the authors write that ÷ and × should be taken in the order in which they occur.
In 1912, First Year Algebra by Webster Wells and Walter W. Hart has: “Indicated operations are to be performed in the following order: first, all multiplications and divisions in their order from left to right; then all additions and subtractions from left to right.”
In 1913, Second Course in Algebra by Webster Wells and Walter W. Hart has: “Order of operations. In a sequence of the fundamental operations on numbers, it is agreed that operations under radical signs or within symbols of grouping shall be performed before all others; that, otherwise, all multiplications and divisions shall be performed first, proceeding from left to right, and afterwards all additions and subtractions, proceeding again from left to right.”
In 1917, “The Report of the Committee on the Teaching of Arithmetic in Public Schools,” Mathematical Gazette 8, p. 238, recommended the use of brackets to avoid ambiguity in such cases.
In A History of Mathematical Notations (1928-1929) Florian Cajori writes (vol. 1, page 274), “If an arithmetical or algebraical term contains ÷ and ×, there is at present no agreement as to which sign shall be used first.”
Modern textbooks seem to agree that all multiplications and divisions should be performed in order from left to right. However, in Florida Algebra I published by Prentice Hall (2011), a problem asks the student to evaluate 3st2 ÷ st + 6 for given values of the variables, and the answer provided comes from dividing by st. A representative for the publisher has acknowledged that the expression is ambiguous and promises to use (st) in the next revision.
That's why I find it to always be best to explicitly include parentheses to reflect the equation as I want it solved, even if it's "overkill". I don't want to be reliant on an implementation of precedence that may vary from device to device (or even compiler to compiler, for a computer). In any event, I'd rather not think that I know how the machine will interpret it, I'd rather know it will evaluate exactly the way I want it to.
“Once again you rewrote the formula with a backslash”
It’s actually a forward slash.
Agreed.
Almost 500 posts, and the thread hasn’t devolved into an all out flame war.
Congratulations to all!
Yes, it is interesting that some mathematicians seem to have this juxtaposition rule. Keep in mind that they are referring to algebraic expressions, like 2/4x, and not simple math problems like we have here.
But engineers program the software and the consensus there is that there is no juxtaposition rule.
We should all be able to agree that this question is poorly defined and that parentheses are our friends.
500.
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