Originally Posted by winders (Post 7496570)

What is the answer to this:

1/2pi = ?

Originally Posted by winders (Post 7496635)

The problem you (DARISC) and Peter are having is that you seem to think mathematical conventions are perfect and are in sync with one another. They are not. Mathematical conventions change over time too.

Scott

Originally Posted by Bill Verburg (Post 7496638)

.5pi

since pi is irrational any answer beyond that must be rounded or truncated

Originally Posted by Bill Verburg (Post 7496633)

another thing you don't understand

'There is a convention that says you do implicit multiplication before division'

is a rule only in your world, it is not a convention recognized anywhere else except in the minds of others that don't understand math.

Originally Posted by DARISC (Post 7496256)

Johnny walked up to the blackboard where his 8th grade algebra teacher had written the equation 48÷2(9+3) = n and wrote 288 after the = sign. Johnny then turned and began to walk back to his seat with a satisfied smile on his cherubic face (Johnny somewhat resembled a cherub).

Johnny's algebra teacher sprang to his feet (he always had a spring to his step) and hollered at the top of his lungs, "STOP RIGHT WHERE YOU ARE, YOU LITTLE PUNK ASS MATH WHIZ WANNABE AND MARCH BACK UP TO THAT BLACKBOARD AND SHOW YOUR WORK!!!

Little Johnny (he was small for his age) stopped dead in his tracks, spun on his heel, walked back to the blackboard and wrote:

48÷2(9+3) = 48÷2(12) = 48÷2x12 = 24x12 = n = 288

Surely you jest?

Little Johnny's algebra teacher glared at the little punk ass math wannabe standing at the blackboard, noting the sardonic smile on his face (Algebra 101 was right after lunch and little Johnny had eaten a big sardone sandwich), slumped back into his chair behind his desk and said, "Very good Johnny. That is correct, you may return to your seat now".

NOW do you understand? LOL

Originally Posted by RWebb (Post 7496860)

Here is an example of some people who did not obey conventions:

Originally Posted by winders (Post 7496756)

Again, the American Mathematical Society (AMS) says "...multiplication indicated by juxtaposition is carried out before division." Conventions are not laws. They are rules that make reading equations more universal. But conventions are not perfect nor are the always consistent with one another.

So, depending on whose convention(s) you are following, equations like "48÷2(9+3)" can have differing results. That's why this is an ambiguous equation and should be written with more clarity.

Scott

Originally Posted by Bill Verburg (Post 7496905)

please cite the reference

Originally Posted by Geary (Post 7496861)

You can't just drop the parenthesis at will and replace it with "x". Basic algebra.

Originally Posted by Bill Verburg (Post 7496905)

many entities make their own definition of how to handle these issues based on their idiosyncratic needs, which may or may not be based on the math, but rather on their convenience.

Originally Posted by winders (Post 7496953)

...The AMS changed their web site and I cannot fiond the document there.

Originally Posted by winders (Post 7496953)

Do on a google search using this search string:

American Mathematical Society (AMS) "multiplication indicated by juxtaposition is carried out before division."

The AMS changed their web site and I cannot fiond the document there.

Scott

Originally Posted by winders (Post 7496982)

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

Originally Posted by Bill Verburg (Post 7497001)

That's because it's not there

http://forums.pelicanparts.com/uploa...1371165444.gif

now do the rest any way you want

Originally Posted by Bill Verburg (Post 7497001)

That's because it's not there
I agree that there is a lot of controversy but don't see why

people often cite mnemonics like PEMDAS, P - simplify everything inside parenthesis as much as possible, E - exponents, MD - multiply or divide left to right, AS - add or subtract left to right

consistency using different tools/methods is essential

another way to do it is to use the rule that division is the same as multiplication by the inverse
48÷2(9+3) becomes



http://forums.pelicanparts.com/uploa...1371165444.gif

now do the rest any way you want