if you mean
Hi people, i just want to clear up a little arguement that has arisen between myself and my brother-in-law. The question is what is the answer of 10+10x0+10= ? I came up with the answer of 20 using bodmas,bidmas or pidmas...whatever you were brought up with.My brother-in-law says that coming from an engineering background they use applied maths order of equation to get the answer of 10.Can any Einsteins help me, are there two answers or are we both incorrect?
the statement 10 + 10 x 0 + 10 is ambiguous.
using "pedmas" or "bodmas" you would process 10x0 = 0 first, to obtain 10 + 0 + 10 = 20.
however, if you read (parse) this as:
10 + (= 10 so far)
10 x (= 100 so far)
0 + (= 0 so far)
10...you wind up with 10.
if you do it "RPN" (reverse polish notation) style, you get:
+ 10 = 10
x 0 = 0
+ 10 = 10
+ 10 = 20
the problem, in a nutshell, is that since we are "mixing operations", we can get to different results depending on what the SCOPE of each operation is meant to be.
take a simpler example:
a*b+c (here * stands for ordinary multiplication)
if we do the * first (as in pedmas) we wind up with (ab)+c
but if we intend the scope of * to be "everything to the right" we wind up with ab+ac
verbally, both may sound almost identical:
a times b plus c, with only a slight pause after "times" to indicate we mean a*(b+c), rather than (a*b) + c, although a conscientious speaker may well say: "a times quantity b plus c".
it is unwise to assume that the receiver of information is automatically using the same conventions to decode information that the transmitter uses to encode. conventions are just that: conventions. they are not universal laws, but "agreed-upon interpretations". the "agreement" part is essential, and has to occur BEFORE communication.
pedmas, in my humble opinion, is an abomination disguising itself as knowledge. it gives the wrong answer for:
10-3+2
as, interpreted literally, one should first add 3+2, and then subtract 5 from 10, whereas most mathematicians would interpret this as:
10 + (-3) + 2 = 9
parentheses matter, assuming "what you mean (intend)" is what "the other person hears (understands)" is a bad idea, in math or any other endeavor.