[svandamme]

Pete, what rule says that the brackets apply to what's outside of the bracket?
Can you show me something that backs up your way of doing it?


If i see 2 ( 5 +2 ) , the () only means i have to do the stuff , inside the ( ) first.
As soon as i've done that, I have a value left

2 (7)

At that moment, teh () becomes redundant.. so it becomes 2 x 7

The Parentisis ends once it's been executed and no operations are left within the brackets.

from the order of operations on wiki :

"Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of brackets will clarify the meaning and should be used if there is any chance of misinterpretation."

That explains the interpretation issue. IT does say that ideally more brackets ougth to be used. But technically in order for the equation to end with 2, it should be written explicitly , different, like so :

48/[2(9+3)]=48/(2x12)=48/24=2

Without these, the answer is 288

Same for 16 ÷ 2[8 – 3(4 – 2)] + 1

If you do not want 17 as an answer , More explicit parentisis must be provided

for instance
16 ÷{ 2[8 – 3(4 – 2)] }+ 1
16 ÷{ 2[8 – 3(2)] }+1
16 ÷[2(8 – 3 x 2)]+1
16 ÷[ 2(8 – 6)]+1
16 ÷[2(2)]+1
16 ÷(2x2)+1
16 ÷(4)+1
16 ÷4+1
4+1
5


So the equation , in any case, never was poorly written in a strict mathematical sense.
It was written in a way that leaves it prone for incorrect interpretation of the order of operations... The incorrect interpreation is human error, it's not mathematical.

Which is exactly why some calculators do it right, and some don't , human error during programming.