48÷2(9+3) = ????

[winders]

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

[Bill Verburg]

Originally Posted by winders

What is the answer to this:

1/2pi = ?

.5pi

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

[Bill Verburg]

Originally Posted by winders

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

Unfortunately they are perfect and perfectly consistent, they are not guidelines to be followed on a whim.

[Bill Verburg]

Originally Posted by Bill Verburg

.5pi

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

for consistency sake
write 1/2pi in rational form



.5pi is the same no?

[winders]

Originally Posted by Bill Verburg

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.

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

[RWebb]

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

[Geary]

Originally Posted by DARISC

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

Johnny and his wannabe teacher don't know basic algebra.
48÷2(9+3) =
48÷2(12) = 2(12) without a "x" sign means that this multiplication is the next step in the equation. Every time. No exception. You can't just drop the parenthesis at will and replace it with "x". Basic algebra.

[sammyg2]

Originally Posted by RWebb

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

Here's some more people who couldn't behave at a convention. (shoulda went kent state on all of em)

[Bill Verburg]

Originally Posted by winders

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

please cite the reference

I agree that it should and could be written more clearly, nevertheless w/o implementing any new rules or exceptions you get consistent results by following the basic order of operation rules

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.

If you try to evaluate the expressions 6 / 2 (1 + 2) and 48 / 2 (9 + 3) using computer systems like the Google search engine, the answer engine Wolfram Alpha (which even changed the rule earlier in 2013 so that implicit and explicit multiplication have the same order ), the Microsoft spreadsheet excel, the answer would all be the same: 9 for 6 / 2 (1 + 2) and 288 for 48 / 2 (9 + 3)

[RWebb]

War Criminal = Math Criminal

[winders]

Originally Posted by Bill Verburg

please cite the reference

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

[DARISC]

Originally Posted by Geary

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

Of course you can't, arbitrarily. But below you can, you don't really NEED to, but, conventionally speaking, you really should...and you then need to stick in a multiplication symbol, of course.

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

Surely i jest?

No, 48÷2(12) = 48÷2x12

48÷2x12 = 24x12 = 288

Once (9+3) was executed to give (12), the only function the parentheses serve is to indicate that that sum is to be multiplied by 2, i.e., 2(12).

Since parentheses are used to contain operations to be performed before another operation is performed on those results, once 9 is added to 3, there are no more operations to be performed and the parentheses are therefore not needed any more.

So they are dropped and x is inserted in their place.

Would you write 2(3)=6 or 2x3=6?

See? I bet that clears it up for you, right? Like you say: basic algebra!

[winders]

Originally Posted by Bill Verburg

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.

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

[DARISC]

Originally Posted by winders

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

I couldn't find the document either so I shot them an email earlier today. I cited this thread, stating that I wanted to help settle an argument. They said they'd get back to me.

Well, they just emailed me stating that they'd read the thread and that Bill Verburg had enlightened them, resulting in their pulling down the document.

I cannot seem to find that email or I would post it.

[sammyg2]

[sammyg2]

[Bill Verburg]

Originally Posted by winders

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

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





now do the rest any way you want

[Bill Verburg]

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

[DARISC]

Originally Posted by Bill Verburg

That's because it's not there



now do the rest any way you want

"That's because it's not there" LOL!

= 288!

[winders]

Originally Posted by Bill Verburg

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





now do the rest any way you want

Bill,

The document was there. There are too many references to it to infer that it never was there.

Your last formula makes is fine if you don't use the convention that says multiplication indicated by juxtaposition is carried out before division. This convention is not uncommon or we would not be having this debate.

I am not arguing that the answer is "2". I am arguing that equation is ambiguous and should not be written the way it is. I am arguing that it is easy to see how many people come up with "2" as the answer.

Your position is far too black and white considering the division this equation inspires in the mathematical community.

Scott