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

12132020, 07:40 AM
(This post was last modified: 12132020 07:43 AM by Kostas Kritsilas.)
Post: #41




RE: Order of operations  what is 6÷2(1+2) ?
(12122020 07:59 PM)rprosperi Wrote:(12122020 02:11 PM)Massimo Gnerucci Wrote: Bob, have a look at the video I linked above. it wasn't called PEJMDAS, but that is the method I was taught mathematics. I am in Canada, though, so I was never exposed to the teachers that taught PEMDAS. My math teachers described it as simplify all the terms to the extent possible, then apply the rules of precedence. So, everything inside the brackets first, then any terms that apply to the bracketed terms, then the rest from right to left foolwing the rules of precedence. I went to school from the late 1960s onward though, so the teachers I learned basic math from all taught what is now called the PEJMDAS method. I find it interesting in the video, that the higher level sources for precedence that are quoted are all calling for PEJMDAS. The only people who are putting PEMDAS forward are US school teachers. Seems to me, they need to go back to school themselves. This may be the source of the confusion, as to anybody outside the US, the answer is obvious, as it is to the higher level sources cited in the video. 

12132020, 09:01 AM
(This post was last modified: 12132020 09:02 AM by toml_12953.)
Post: #42




RE: Order of operations  what is 6÷2(1+2) ?
(12122020 01:55 PM)ijabbott Wrote:(12122020 04:58 AM)toml_12953 Wrote: Yes, to most programmers I know it means (x/2)*y. Syntax error is exactly why programmers put the missing multiplication sign in there. x/2y becomes x/2*y If the author wanted x/(2*y) (s)he should have used parentheses or a textbook notation Code: x Tom L Cui bono? 

12132020, 12:39 PM
Post: #43




RE: Order of operations  what is 6÷2(1+2) ?
I think x/2y is ambiguous.
NOT ambiguous is \(\frac x{2y}\) because the full denominator, \(2y\), is clearly separated from the numerator by the division bar. This forum allows the use of mathjax. Use it to make expressions unambiguous. If you just use ASCII then use parentheses to remove any ambiguity. There are only 10 types of people in this world. Those who understand binary and those who don't. 

12132020, 04:06 PM
(This post was last modified: 12132020 04:07 PM by Hlib.)
Post: #44




RE: Order of operations  what is 6÷2(1+2) ?
`rprosperi` Wrote:`Hlib` Wrote:The calculator manual always specifies the priority of operations, so we can use private rules to get rid of ambiguous interpretation. In one of the short guides to TI85,86 we can read the following rules: Quote:Priority of operationsThe instructions for the calculator do not claim to be absolute truth, but we have to take into account the rules in the instructions. The calculator can`t read our thoughts and guess what we mean. 

12132020, 05:58 PM
(This post was last modified: 04152024 07:16 PM by Steve Simpkin.)
Post: #45




RE: Order of operations  what is 6÷2(1+2) ?
I find it interesting that TI changed their approach to the priority of implied multiplication over time. (A reference from the above video.)
"Does implied multiplication and explicit multiplication have the same precedence on TI graphing calculators? Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI80, TI81, TI82, and TI85 evaluate 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper. This order of precedence was changed for the TI83 family, TI84 Plus family, TI89 family, TI92 Plus, Voyage™ 200 and the TINspire™ Handheld in TI84 Plus Mode. Implied and explicit multiplication is given the same priority. Please see the graphing calculator guidebooks for additional information." https://education.ti.com/en/customersup...sage/11773 Edit: Fixed the above link from TI. 

12132020, 07:09 PM
Post: #46




RE: Order of operations  what is 6÷2(1+2) ?
(12132020 05:58 PM)Steve Simpkin Wrote: This order of precedence was changed for the TI83 family, TI84 Plus family, TI89 family, TI92 Plus, Voyage™ 200 and the TINspire™ Handheld in TI84 Plus Mode. Implied and explicit multiplication is given the same priority. Probably because North American teachers just love PEMDAS... Q.E.D. Greetings, Massimo +×÷ ↔ left is right and right is wrong 

12132020, 08:50 PM
Post: #47




RE: Order of operations  what is 6÷2(1+2) ?
(12132020 07:09 PM)Massimo Gnerucci Wrote: Probably because North American teachers just love PEMDAS... That's all they were taught in Education classes so why shouldn't they love it? I just asked a dozen of my friends (mix of math teachers, computer programmers and mere mortals) and none of them ever heard of the J. Some think it's a good idea, though. As for me, I say just pick one and be consistent, unlike some of the calculator manufacturers. Tom L Cui bono? 

12132020, 09:04 PM
Post: #48




RE: Order of operations  what is 6÷2(1+2) ?
Looking at all of the comments on these videos and blog posts are quite entertaining. Watching teachers, professors and scientists call each other names is amusing. They usually evolve into something like, "Well, professor Johnson. The only conclusion I can reach is that you are a doodoohead." Seems like a punch line on a Far Side comic. Very funny.


12152020, 12:21 AM
(This post was last modified: 12152020 12:26 AM by CMarangon.)
Post: #49




RE: Order of operations  what is 6÷2(1+2) ?
Hello!
1 solve ( ) 2  solve the [] 3  solve { } 6÷2x(1+2) 6÷2x(3) 6÷2x(3) 9 In a set of values 2+3*4 4 5 +9 1st  multiplication and division 2nd  sum and subtraction Try this, http://www.risolviespressioni.it Carlos  Brazil Time Zone: GMT 3 http://area48.com 

12152020, 12:38 AM
(This post was last modified: 12152020 12:39 AM by toml_12953.)
Post: #50




RE: Order of operations  what is 6÷2(1+2) ?
(12152020 12:21 AM)CMarangon Wrote: Hello! The above site gets 6 for the answer! They treat implied multiplication like addition! Tom L Cui bono? 

12152020, 12:53 AM
(This post was last modified: 12152020 01:01 AM by Gerson W. Barbosa.)
Post: #51




RE: Order of operations  what is 6÷2(1+2) ?
(12152020 12:21 AM)CMarangon Wrote: Try this, Peccato ma non funziona, almeno su Safari: Too bad, that doesn’t work, at least on Safari: Risolvi Espressioni 6÷2(1+2) Risoluzione 6:2+(1+2)= =3+3= =6 — Tom was faster! 

12162020, 02:32 AM
Post: #52




RE: Order of operations  what is 6÷2(1+2) ?
slight aside: some UK schools currently teach it as "BODMAS". Opinions differ on what the O stands for. B==P, of course.
Of course, there's no mention of implied multiplication And UK schools all use Casio, so that must be right! Cambridge, UK 41CL/DM41X 12/15C/16C DM15/16 17B/II/II+ 28S 42S/DM42 32SII 48GX 50g 35s WP34S PrimeG2 WP43S/pilot Casio, Rockwell 18R 

12162020, 08:58 AM
Post: #53




RE: Order of operations  what is 6÷2(1+2) ?
When I was in school, we were taught this (but it is universally recognised as outdated now):
"Meneer Van Dale Wacht Op Antwoord". Machtsverheffen (power) Vermenigvuldigen (multiply) Delen (divide) Worteltrekken (taking the root) Optellen (add) Aftrekken (subtract) Brackets were not seen as an operation, with that ordering scheme, but were understood to be evaluated first. Dutch students were taught this until at least into the 1990's, I think? (definitely in the early seventies). 11C, 12C, 17Bii, DM42 

12162020, 03:59 PM
Post: #54




RE: Order of operations  what is 6÷2(1+2) ?
Just for fun
Code:
Remember kids, "In a democracy, you get the government you deserve." 

12202020, 02:47 AM
Post: #55




RE: Order of operations  what is 6÷2(1+2) ?
IMHO, both 1 and 9 are correct because the formulation is ambiguous to begin with.
The only calculator that I know that disambiguates this sort of input is my Casio fxCG50, among my collection. This exact problem is described in the User Guide version 3.40 in section 26 on page 52 fxCG50 user guide The expression 6÷2(1+2) is changed to a form with parenthesis showing the explicit evaluation order of the implied multiplication: 6÷(2(1+2)) I like this feature of the Casio. Apparently, no one reads calculator manuals any more ?  Rob "I count on old friends"  HP 71B,PrimeTi VOY200,Nspire CXII CASCasio fxCG50...Sharp PCG850,E500,2500,1500,14xx,13xx,12xx... 

12202020, 08:46 AM
Post: #56




RE: Order of operations  what is 6÷2(1+2) ?
According to me the implicit multiplication (multiplication with omitted multiplication sign) haas higher priority than explicit multiplication becasue I am treating such expression as variables as it shown in many physics and chemistry books or in post 29 written by Massimo
If I see something like this "6÷2(1+2)", then I see "a/bc" which is shortened "a/(b*c)" Fortunately there is no system like pemdas, bodas or something similar in Czechia. At least the higher priority for implicit multilipcation works well with no exceptions (I know it is empirical evidence and not the mathematical one) 

12202020, 08:58 AM
Post: #57




RE: Order of operations  what is 6÷2(1+2) ?
mathematics is a universal language that everyone can understand everywhere. if an expression causes a tread of 57 posts: it is wrong.
Hardware: Hp48S  Hp50g (5x black + 1 blue)  HP39gII  Hp27s  Casio fxCG50 

12202020, 09:20 PM
Post: #58




RE: Order of operations  what is 6÷2(1+2) ?
I've been following the discussion here with some interest, so I probably ought to declare that I'm firmly in the '1' camp but this is probably only because I group the 2 with the associated brackets,
so I 'see' the expression as; 6  2(2+1) rather than as; 6  (2+1) 2 which may (or may not) be what the author intended. Before anyone says the answer is obvious, I'd suggest this is only true if you know what convention the author was using when they wrote the expression as a single line. If this information is missing then it would seem that only thing that is obvious is that expression itself is ambiguous. Possibly deliberately so. :) Mike T. HP21, HP25, HP32E, HP33C, HP34C, HP10C, HP11C, HP12C, HP32S, HP22S 

12202020, 11:24 PM
Post: #59




RE: Order of operations  what is 6÷2(1+2) ?
Hi, Gene:
Gene Wrote:Order of operations  what is 6÷2(1+2) ? The SHARP PC1211, which is the very first pocket computer (released back in 1980, i.e.: 40 years ago as of 2020), declared these evaluation priorities: which clearly stablishes that implied multiplication (i.e., the "2(1+2)" part) is a highpriority operation, four levels higher than division, so when evaluating the expression it gives 1 as the result, which is fine by me. 6÷2(1+2) = 6÷2(3) = 6÷6 = 1 Best regards. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

12212020, 08:39 PM
Post: #60




RE: Order of operations  what is 6÷2(1+2) ?
I was always taught that you do the () first (without mention of implied * or not)
So 6÷2(1+2) should simplify to 6÷2(3) 6÷6 1 or distribute: 6÷(2+4) 6÷6 1 notice if you tried without doing the () first the distributive property wouldn't work properly 6÷2*3 3*3 9 or 6÷2+4 3+4 7 So you have to do the () first for the distributive property to work. 

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