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I should say that I first got 288 because I remember being taught to do the parenthesis first then left to right. Since multiplication and division are related and occur simultaneously in the order of operations you must then move to the 'left to right' operation so that in this equation division goes first.
So you have 9+3 first = 12
Then you have 48/2 = 24 (Because it is left of Multiplication (2x12)) So you are not to multiply 2x12 which is 24 and then do 48/24. That's a NO NO!
Then you have 24x12 = 288
But since everyone is arguing over what counts as how to write an equation and how to do the order I posted the previous post.
How is a self-proclaimed "recreational mathmusician" a proper mathematician?
Quote:
Originally Posted by Alacran
I knew it.
I was right.
Can you provide some supporting info?
What we really need to do to put this to rest is determine whether the order of operation (or other mathematics rule) covers a scenario when both multiplication and division are used in the same expression.
What we really need to do to put this to rest is determine whether the order of operation (or other mathematics rule) covers a scenario when both multiplication and division are used in the same expression.
It was put to rest hundred of years ago. Apply the multiplication and division from left to right.
I can't show that 2+2 = 4 wasn't put to rest hundreds of years ago.
But that's not debatable. The multiplication and division order is and has been over atleast the past 120 years.
Quote:
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.
Those aren't considered proof. You would have to go back to early publishings by mathematicians. Those clearly take the "left to right" rule into consideration, but I haven't found support for it yet (although, I've hardly looked). The only thing that I've found is early texts with conflicting rules.
Anyways, my point was that a self-proclaim recreational mathmusician is not a proper mathematician and has very little impact on this debate.
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