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.
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.
Exactly correct.
48/2(9+3)=
48/2(12)=
48/(24)= 2
See a Packer fan and a Seahawk Fan agree.