Order of operations - what is 6÷2(1+2) ?

[Hlib]

`rprosperi` Wrote:

`Hlib` Wrote:The calculator manual always specifies the priority of operations, so we can use private rules to get rid of ambiguous interpretation.
Implied multiplication and division has a higher priority than normal multiplication and division. Operations with the same priority are performed sequentially from left to right. And that`s where all the arguments end.
6◢2(1+2)=(6÷2)×(1+2)=9 (CASIO)
6÷2(1+2)=6÷(2×(1+2))=1 (CASIO, TI-85,86)
6÷2×(1+2)=(6÷2)×(1+2)=9 (CASIO, TI-83,85,86,89, HP-50G)

I`ve seen people claim this priority, but have never seen this is in any mathematics book, nor ever found a mathematician or teacher that agrees. Do you recall where you learned this or have any reference?

In one of the short guides to TI-85,86 we can read the following rules:

Quote:Priority of operations
The meaning of a formula involving functions, powers, sums, dierences, products, and quotients depends on how the formula is interpreted to determine the order in which the operations are performed. Texas Instruments TI-86 calculators in most instances interpret formulas with the following rules, which are those generally used in manual calculations.
Rule 1 Operations are performed from left to right, except as described in Rules 2 through 5 below.
Rule 2 Expressions inside parentheses are evaluated as soon as they are reached.
Rule 3 Addition and subtraction have the lowest priority. If an addition or subtraction is followed by multiplication, division, a power, or a function, the addition or subtraction is postponed until another addition or subtraction or the end of the expression is reached.
Rule 4 Multiplication and division have medium priority. If a multiplication or division is followed by a power or a function, the multiplication or division is postponed until the power or function has been evaluated.
Rule 5 The taking of powers and evaluation of functions have the highest priority and are performed as soon as they are reached.
Rule 6 The taking of powers has priority over the evaluation of functions that appear before their variables, such as the trigonometric functions, logarithms, ex, p , and negation. Also, the parentheses in expressions such as sin(2) and e ^ (2) are ignored.
The TI-85 also uses the following two additional modications of Rules 1 through 5
Rule 7 Multiplication by juxtaposition has priority over division and multiplication represented by *.
Rule 8 Multiplication represented by juxtaposition, where the second term is a number or a variable, has priority over the evaluation of functions that appear before their arguments:
√4a=√(4*a) ; sin(5)(10)=sin(5*10)

The instructions for the calculator do not claim to be absolute truth, but we have to take into account the rules in the instructions. The calculator can`t read our thoughts and guess what we mean.