"The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. "

So it's not just a convention. There is rule for it. I never knew.

Fixed it for you

See the part I bolded in your quote. Technically, you changed the meaning of the equation there. The implied multiplication of the adjacent parentheses is considered a higher precedence than an otherwise notated mult/div operation and thus gets done first. Just like we tend to simply the entire numerator and denominator first when we see an equation notated in that style.

All of these are still just examples of poorly written equations. Parentheses are free, don't be miserly with them.

I've never heard that items OUTSIDE parentheses have priority over anything just because they are near parentheses.

here, here!!!

The fact that these types of threads go on and on for pages demonstrates that something that we hold as the epitome of objectiveness, mathematics, is as open to interpretation as anything.

Ultimately, math is a language. Like any language, there are multiple ways of saying the same thing, and depending on how precise you are, what you say can easily be misconstrued.

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.

"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."

I agree.


http://forums.pelicanparts.com/uploa...1302634172.jpg

Yeah, that sucks, apparantly Wolfram alpha has a different use of the () vs the []

I mearly used different brackets to show which closing bracket goes with which opening bracket. They were supposed to have equal weight in my examples

Note that I NEVER said anything about "my" way of doing anything, I am firmly in the 288 and 17 camps. However, I am pointing out that it's ambiguous, which is obvious by the volume of opinions, and ultimately is really the point of this whole thing, much more so than the number you come up.

The bracket priority thing is listed in the Order of Operations link someone else posted earlier on this page. It's just another example of why Google =/= research.

As far as whether any of this is human error, it's more of a philosophical discussion. If what you say is misinterpreted by the listener, is that your fault or his? Does the answer depend on how clear you were? What exactly is clear "enough"? Why do things we consider to be objective vary in meaning by listener, education, culture, region or language? If something as simple as putting in one more set of parentheses removes the ambiguity, isn't that a fault in the way the equation is written?

The answer is 2 now be off with you!

Well for a human, from a maths point of view, it shouldn't matter Without extra brackets it's 288

Same goes for binary :
01000010011001010010000001110011011101010111001001 1001
01001000000111010001101111001000000110010001110010 0110
10010110111001101011001000000111100101101111011101 0101
11001000100000010011110111011001100001011011000111 0100
01101001011011100110010100101110

For a computer, it makes perfect sense, there's no ambiguity at all for a computer
But i bet you have a hard time reading it without googling "binary2text".

There are 10 kinds of people in the world. Those that understand computers and those that don't.

That prooves my point, because that's not what it says

who started this damn thread anyway?

You'll decode your eye out. ;)

i thought there were 11 kinds? those that can count and those that can't

Ten pages in and a 60/40 split. Too funny.

Mine was easier: (3x9)+2 =???

( I say there IS a friggin' dollar gone missin' ) :p

*Who said "Math is an absolute"?

Can't we just divide 288 by 2 and everyone could be happy?

Perhaps we need to make a new equation describing this to discuss?:D

Distributive property = A(B+C) = AB+AC


Simplifying Using the Distributive Property Lesson -- Algebra.Help


2(9+3) is one term by defintion



Then order of ops

48/ 2(9+3) You must solve the () first

48/(18+6)

48/24 = 2