Order of operations  what is 6÷2(1+2) ?

12212020, 11:54 PM
Post: #61




RE: Order of operations  what is 6÷2(1+2) ?
(12212020 08:39 PM)EugeneNine Wrote: I was always taught that you do the () first (without mention of implied * or not)But that's only if you multiply (or distribute) the 2 by what's in the parentheses before you do the division. Tom L Cui bono? 

12222020, 12:56 PM
Post: #62




RE: Order of operations  what is 6÷2(1+2) ?
Let's make a deal here: if people get to claim that 6/2(1+2)=1 then I get to say that 2^2=4.


12222020, 03:41 PM
Post: #63




RE: Order of operations  what is 6÷2(1+2) ?
(12222020 12:56 PM)Dave Britten Wrote: Let's make a deal here: if people get to claim that 6/2(1+2)=1 then I get to say that 2^2=4. Of course it does! That's something we can all agree on. Negation does take priority over powers in all versions of the hierarchies I've seen. (2)^2 = 4 Tom L Cui bono? 

12222020, 08:03 PM
(This post was last modified: 12222020 08:05 PM by robve.)
Post: #64




RE: Order of operations  what is 6÷2(1+2) ?
(12222020 03:41 PM)toml_12953 Wrote:(12222020 12:56 PM)Dave Britten Wrote: Let's make a deal here: if people get to claim that 6/2(1+2)=1 then I get to say that 2^2=4. Not so for Python: >>> 2**2 4 Yes for Prolog: ? X is 2^2. X = 4. Yes for Unix bc: bc 1.06 Copyright 19911994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. 2^2 4 Not so for Basic (all Sharp PC and Visual Basic): 2^2 4 Yes for Fortran. Not so for Casio fx115ES+. The jury is still out on this one... "I count on old friends"  HP 71B,PrimeTi VOY200,Nspire CXII CASCasio fxCG50...Sharp PCG850,E500,2500,1500,14xx,13xx,12xx... 

12222020, 10:33 PM
Post: #65




RE: Order of operations  what is 6÷2(1+2) ?
When I went to college, I was fortunate enough to have a professor who was part of the massive layoff from NASA at the end of the Apollo program.
His advice .... hammered into us constantly .... was to NEVER write an equation, a line of code, or make a drawing that required any "assumption" on the part of the reader. (At NASA, it was observed many times that if you gave someone multiple ways to interpret your equation/design, and one of those ways could cause a massive failure .... that would invariably be the one they chose to use.) He would frequently write the word "assume" on the chalkboard, and do the standard "Why we never assume." comedic routine. He also mentioned .... apparently in direct conflict with many current math teachers .... that it doesn't actually cost money (or effort) for each parenthesis you use. I found his advice invaluable when writing code for realtime data acquisition and control systems, as it seemed/seems every programming language handled equations differently, and indeed the parenthesis became my best friend. ENTER > = 

12222020, 10:42 PM
Post: #66




RE: Order of operations  what is 6÷2(1+2) ?
Article about Order of arithmetic operations; in particular, the 48/2(9+3) question.
https://math.berkeley.edu/~gbergman/misc...d_ops.html 

12222020, 10:50 PM
Post: #67




RE: Order of operations  what is 6÷2(1+2) ?
(12222020 08:03 PM)robve Wrote: Yes for Prolog: Prolog should return 4 for this, according to its precedence table. (pow higher than unary minus) Problem is it parsed first number as 2, removed the unary minus. Forcing it to parse first number as 2, we get the right answer. BProlog Version 8.1, All rights reserved, (C) Afany Software 19942014.  ? X is 2**2 X = 4 yes  ? Two = 2, X is Two**Two Two = 2 X = 4 yes You should not get 2 different answers by replacing Two for 2. This bug had been fixed in Picat Picat> X is 2**2 X = 4 yes Picat> Two = 2, X is Two**Two Two = 2 X = 4 yes 

12222020, 11:33 PM
Post: #68




RE: Order of operations  what is 6÷2(1+2) ?
(12222020 10:33 PM)trojdor Wrote: When I went to college, I was fortunate enough to have a professor who was part of the massive layoff from NASA at the end of the Apollo program. Hardware: Hp48S  Hp50g (5x black + 1 blue)  HP39gII  Hp27s  Casio fxCG50 

12232020, 12:38 AM
Post: #69




RE: Order of operations  what is 6÷2(1+2) ?
(12222020 08:03 PM)robve Wrote: Not so for Basic (all Sharp PC and Visual Basic): ... and the alwaysforgottenbymostMoHPCmembers HP71B BASIC as well. Matter of fact, if I ever saw a BASIC evaluating 2^2 as 4 I'd get rid of it. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

12232020, 01:46 AM
Post: #70




RE: Order of operations  what is 6÷2(1+2) ?
(12232020 12:38 AM)Valentin Albillo Wrote:(12222020 08:03 PM)robve Wrote: Not so for Basic (all Sharp PC and Visual Basic): The ANSI/ISO committees agree with you. The international Standard for Full BASIC calls for 2^2 to be 4. Tom L Cui bono? 

12232020, 03:14 AM
(This post was last modified: 12232020 03:26 AM by robve.)
Post: #71




RE: Order of operations  what is 6÷2(1+2) ?
(12222020 10:50 PM)Albert Chan Wrote:(12222020 08:03 PM)robve Wrote: Yes for Prolog: I agree. Parsers should not consider the  to be part of the number to avoid this flaw. So it is ridiculously funny to see the following (note the spacing between  and 2): ? X is 2^2. X = 4. ? X is  2^2. X = 4. On the other hand, SWIProlog has a reasonably powerful implementation of multiprecision arithmetic with bigint and rationals (bigint/bigint) https://www.swiprolog.org/pldoc/man?section=arith something I contributed to to this project many years ago and now fully integrated. "I count on old friends"  HP 71B,PrimeTi VOY200,Nspire CXII CASCasio fxCG50...Sharp PCG850,E500,2500,1500,14xx,13xx,12xx... 

12232020, 07:06 AM
Post: #72




RE: Order of operations  what is 6÷2(1+2) ?
Hello!
The answer is 1, but why? We must keep in mind that the sequence of operations is "x" and "÷" and after "" and "+". First solve "( )" after, "[ ]" and after "{ }" For the given expression: Lets assume this expressiona as X =6÷2x(1+2) Soving "( )" X = 6÷2x(1+2) X =6÷2x(3) X = 6÷6 X =1 In RPN: 6 2 1 2 + x ÷ Solution, X = 1 Carlos  Brazil Time Zone: GMT 3 http://area48.com 

12232020, 09:03 AM
Post: #73




RE: Order of operations  what is 6÷2(1+2) ?
I am finding this whole discussion rather humorous as it all boils down to which convention you are using, like spelling color or colour.
The Prime completely eliminates this issue in Textbook entry by always using a horizontal fraction bar. Problem solved! Everyone is happy! Every multiline calculator should do this. Some have indicated that we use juxtaposition when writing by hand. I encourage my students to avoid using / for division unless there is only one value after it, like 2/3 or 1/x. If a student writes "1/2x", I might interpret it as 1/(2x). But "1/2 x" with a space might be interpreted as (1/2)x. But when you write with pencil and paper, spaces can vary in size. At what point do you switch meanings? 1/2x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x Therefore, I avoid using / except for the unambiguous cases. Even the symbol can be problematic. I had one former engineer tell me that he would say that a + b ÷ c + d = a + (b ÷ c) + d but a + b / c + d = (a + b) / (c + d) because he took the / to be a text replacement of the horizontal fraction bar. 

12232020, 09:19 AM
Post: #74




RE: Order of operations  what is 6÷2(1+2) ?
(12222020 03:41 PM)toml_12953 Wrote:(12222020 12:56 PM)Dave Britten Wrote: Let's make a deal here: if people get to claim that 6/2(1+2)=1 then I get to say that 2^2=4.Of course it does! That's something we can all agree on. Negation does take priority over powers in all versions of the hierarchies I've seen. (2)^2 = 4 At first I thought you were being facetious, but now I'm not sure. If 2^2 = (2)^2 = 4 then would \(e^{x^2}\) be \(e^{(x)^2}\) ? If so, then you'd have to write the bellcurve equation written as \(e^{(x^2)}\) which I've never seen done. 

12232020, 10:41 AM
Post: #75




RE: Order of operations  what is 6÷2(1+2) ?
(12232020 09:19 AM)Wes Loewer Wrote:(12222020 03:41 PM)toml_12953 Wrote: Of course it does! That's something we can all agree on. Negation does take priority over powers in all versions of the hierarchies I've seen. (2)^2 = 4 I really was on the fence but since I'm a BASIC programmer, I use the Standard BASIC convention of 2^2 = (2^2) = 4. Tom L Cui bono? 

12232020, 03:25 PM
(This post was last modified: 12232020 03:26 PM by Thomas Radtke.)
Post: #76




RE: Order of operations  what is 6÷2(1+2) ?
2^2=x
> x+2^2=0 > x=(2^2)=4 IAW: x^2 is comfortable way to write 0x^2 

12242020, 08:31 AM
Post: #77




RE: Order of operations  what is 6÷2(1+2) ?
(12232020 03:25 PM)Thomas Radtke Wrote: 2^2=x This is only true if 2^2 is interpreted as (2^2). If it is interpreted as (2)^2 then your second line should be: x  (2^2) = 0 And this is just as ambiguous as the first line There are only 10 types of people in this world. Those who understand binary and those who don't. 

12302020, 05:41 PM
Post: #78




RE: Order of operations  what is 6÷2(1+2) ?
(12232020 03:14 AM)robve Wrote: Parsers should not consider the  to be part of the number to avoid this flaw. You are right. I peeked at Lua 5.4 source code, llex.c, llex() read_numeral() only allowed to convert nonnegative numbers. Code: case '': { /* '' or '' (comment) */ 

01042021, 04:16 AM
Post: #79




RE: Order of operations  what is 6÷2(1+2) ?
2^2 on the 41CV evaluates to 4


01042021, 04:26 AM
Post: #80




RE: Order of operations  what is 6÷2(1+2) ?
(01042021 04:16 AM)WrongWay Wrote: 2^2 on the 41CV evaluates to 4 No, that's not correct. You have interpreted the algebraic equation shown there to be (2) ^ 2 and you entered it as 2 CHS ENTER 2 Y^X which is not what is written, and that's what this entire discussion is about. If an equation is written in an ambiguous manner, the results are meaningless. The above equation could also mean  (2^2) which would be 4; most systems that state the orders of precedence put exponentiation at a higher priority than unary negation, so the way I wrote at the start of this sentence would be the correct way to process it. If the equation is ambiguous and precedence rules are not provided, a 'correct' answer is not possible, and it probably means someone is trying to lure you in to a conversation like this one. Bob Prosperi 

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