Quote:
Originally Posted by winders
That's the thing, Bill, these conventions are not based on the math. They are to help make equations easier to read and interpret. Basically, some group of mathematicians decided on the convention PEMDAS based on their idiosyncratic needs and convenience.
There are competing conventions in mathematics as well. One example:
Natural number - AoPSWiki
The whole idea behind conventions like PEMDAS is too make it so we can all interpret equations as the person that wrote the equation intended. The math community thinks equations like these are ambiguous:
48÷2(9+3) = ?
6÷2(1+2)= ?
Even this is considered ambiguous:
1/2x = ?
These equations should be written differently to avoid ambiguity.
Scott |
They should but things are are written by people, wacky, crazy, stoned people, so you fall back on the basics, you don't do what English majors do by makeing up all sorts of new rules w/ exceptions.
the basics
left to right
every operand has 1 for a coefficient, 1 for an exponent and 1 for a denominator unless explicitly written differently
simplify anything inside parenthesis(there is no need for clearing the parenthesis as so many erroneously insist)
exponents
multiply or divide( left to right), division is the equivalent of multiplication by the inverse
add or subtract (left to right)
follow these rules and you get consistent results no matter what method you use