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

12062018, 11:49 PM
Post: #1




Order of operations  what is 6÷2(1+2) ?
Physicsastronomy.com
Usually we would work from the inside out in RPN. I keyed this as written on my PRIME app with the implied multiplication and it gives the answer the website above says is incorrect. So... ? 

12072018, 12:03 AM
Post: #2




RE: Order of operations  what is 6÷2(1+2) ?
The answer is 1
More interestedly is the fact that you can’t put just 1 in this message  it moans that it must be 5 Chars minimum Denny 

12072018, 12:42 AM
(This post was last modified: 12072018 12:44 AM by cdmackay.)
Post: #3




RE: Order of operations  what is 6÷2(1+2) ?
(12072018 12:03 AM)Leviset Wrote: The answer is 1 The point was, I think: why isn't the answer 9, which the normal rules of operator precedence seem to imply? The video claims that taking everything after the ➗ as the denominator has been obsolete for 100 years, and that current practice should evaluate the division before the implied multiplication (left to right). But the calculator result would seem at odds with that. Unfortunately, my video stopped playing halfway though, so I may have missed something vital Cambridge, UK 41CL/DM41X 12/15C/16C DM15/16 71B 17B/BII/bII+ 28S 42S/DM42 32SII 48GX 50g 35s 30b/WP34S Prime G2 & Casios, Rockwell 18R :) 

12072018, 12:44 AM
Post: #4




RE: Order of operations  what is 6÷2(1+2) ?
My HP20s gives me an answer of 9.
Hp50g in algebraic mode also give 9 Prime gives 1 Jim 

12072018, 12:46 AM
(This post was last modified: 12072018 12:53 AM by cdmackay.)
Post: #5




RE: Order of operations  what is 6÷2(1+2) ?
This is presumably because the Prime doesn't enter the division symbol as is, but uses it to immediately present a fractional input, thus enforcing the (wrong?): everything else is the denominator.
Cambridge, UK 41CL/DM41X 12/15C/16C DM15/16 71B 17B/BII/bII+ 28S 42S/DM42 32SII 48GX 50g 35s 30b/WP34S Prime G2 & Casios, Rockwell 18R :) 

12072018, 02:06 AM
(This post was last modified: 12072018 02:54 AM by Steve Simpkin.)
Post: #6




RE: Order of operations  what is 6÷2(1+2) ?
Some other examples of different calculator interpretations of the rules of operator precedence.
My HP48GX returns an answer of 9 when I enter '6/2*(1+2)' EVAL or 1 if I use the Equation Writer and use implied multiplication of 6/2(1+2) which is converted to 6/(2*(1+2))'. My Casio fx115ES Plus returns an answer of 1 if I enter 6/2(1+2) or 9 if I enter 6/2*(1+2). WolframAlpha returns 9 to 6/2*(1+2) or 6/2(1+2). Google returns 9 to 6/2*(1+2) or 6/2(1+2). My Prime app returns 1 if I enter 6/2*(1+2) or 6/2(1+2). I can't seem to use an implied multiply on the Prime without it being converted to a *. Another discussion on this topic: https://www.quora.com/Whatwillbethev...3%B721+2 

12072018, 02:13 AM
Post: #7




RE: Order of operations  what is 6÷2(1+2) ?
Additional discussions of this topic at this forum:
http://www.hpmuseum.org/forum/thread8982.html http://www.hpmuseum.org/cgisys/cgiwrap/...ead=246984 

12072018, 02:57 AM
Post: #8




RE: Order of operations  what is 6÷2(1+2) ?
CASIO fx991LA X:
6÷2×(1+2) = —> 9 6÷2(1+2) = —> 1 and afterwards the expression is automatically rewritten as 6÷(2(1+2)) 

12072018, 03:40 AM
Post: #9




RE: Order of operations  what is 6÷2(1+2) ?
nspire and voyage200 both return 9 and convert to 6/2.(1+2) no matter if it is entered with an explicit multiplication or not. My old eyes have a hard time seeing the dot on the nspire screen.


12072018, 08:19 AM
Post: #10




RE: Order of operations  what is 6÷2(1+2) ?
"egg or chicken came first" "problem" once again.


12072018, 09:44 AM
(This post was last modified: 12072018 09:45 AM by Maximilian Hohmann.)
Post: #11




RE: Order of operations  what is 6÷2(1+2) ?
Hello!
We've discussed this before, but without some "strage unwritten agreement" the answer is 9. This is how they teach mathematics at schools and universities in my part/most parts of the world and how, as is obvoius from the postings above, most smart calculators are programmed too. Maybe it is time to trash those ambiguos unwritten agreements and start doing things in a standardised way instead of digging them up year after year? Regards Max 

12072018, 10:07 AM
Post: #12




RE: Order of operations  what is 6÷2(1+2) ?
I think most programming languages do it right.
I tried it in python and perl, and both threw an error. Mathematical expressions in programming and on calculators should be unambiguous. JSBach 

12072018, 10:22 AM
Post: #13




RE: Order of operations  what is 6÷2(1+2) ?
What this boils down to is whether or not implicit multiplication takes precedence over "normal" multiplication and division. While it was many years ago, I have no recollection of this being taught in maths classes in either of two different countries (the approach to teaching in France is quite different to that in the UK), so I would say that the expression is equivalent to (6÷2)(1+2) = 9.


12072018, 10:53 AM
Post: #14




RE: Order of operations  what is 6÷2(1+2) ?
(12072018 10:22 AM)grsbanks Wrote: What this boils down to is whether or not implicit multiplication takes precedence over "normal" multiplication and division. While it was many years ago, I have no recollection of this being taught in maths classes in either of two different countries (the approach to teaching in France is quite different to that in the UK), so I would say that the expression is equivalent to (6÷2)(1+2) = 9. For me, it's not the 'implicit multiplication' but the fact that writing ÷ by hand is so uncommon. What's much more common is writing \( \frac{6}{2(1+2)} \) or \( \frac{6}{2} (1+2) \) where the scope of the division is given by the length of the line and unambiguous. Either way, children are taught BODMAS / PEMDAS [1] and it's just a case of applying the rules, taking care not to assume you know what the question is. [1] Or the equivalent in other languages 

12072018, 10:53 AM
Post: #15




RE: Order of operations  what is 6÷2(1+2) ?  
12072018, 11:01 AM
Post: #16




RE: Order of operations  what is 6÷2(1+2) ?
(12072018 10:53 AM)BruceH Wrote: Either way, children are taught BODMAS / PEMDAS [1] and it's just a case of applying the rules, taking care not to assume you know what the question is. Exactly. Absent the traditional, unambiguous notation, BODMAS/PEMDAS is what has to be applied, hence the answer being \( \frac {6}{2}(1+2) = 9\) 

12072018, 12:08 PM
Post: #17




RE: Order of operations  what is 6÷2(1+2) ?
Never trust a calculator


12072018, 01:41 PM
Post: #18




RE: Order of operations  what is 6÷2(1+2) ?
If any calculator has the nerve to say that 6÷2(1+2)=1, but then turn around and say that 2^2=4, then it can just go straight in the bin.


12072018, 03:58 PM
Post: #19




RE: Order of operations  what is 6÷2(1+2) ?
The result is undefined (both results are correct till somebody clarifies such types of expressions) due to ambiguity and depends purely on implementation of calc manufacturers. The order of operations is written in each user guide, at least I hope.
Engineers from Casio decided to solve this ambiguity by adding another pair of brackett, I agree with this solution. Personally I prefer the result is "1" since I evaluate the 2(1+2) first. 

12072018, 05:12 PM
Post: #20




RE: Order of operations  what is 6÷2(1+2) ?
(12072018 12:03 AM)Leviset Wrote: The answer is 1 That's only the case if the implied multiplication is done before the division. If you're doing it by hand using the PMDAS rules, you would do this: Parentheses first: (1+2) = 3 multiplication and division are left to right: 6/2 = 3 3 * 3 = 9 so the answer would be 9. The implied multiplication doesn't take precedence over the division which comes first, reading left to right. Tom L Cui bono? 

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