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Why RPN?

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Sorunome:
I learned that multiplication+devision are same level, same with addition+subtraction. And if those are combind you just go from left to right, so the TI is actually correct IMO

Eeems:
##6/2(1+2) =\ 6/2(3) =\ 6/6 =\ 1##MathJax.Hub.Queue(["Typeset", MathJax.Hub, document.getElementById("bbclatex6638ba157854c")]);console.log("Queued!");
##\frac{6}{2(1+2)} =\ \frac{6}{2(3)} =\ \frac{6}{6} =\ 1##MathJax.Hub.Queue(["Typeset", MathJax.Hub, document.getElementById("bbclatex6638ba1578559")]);console.log("Queued!");

This is due to how their division works. It's a fraction, not the ÷ symbol. So its 6 over 2(1+2) not six divided by 2(1+2). The way that TI-OS does it there is wrong according to that.

##6÷2(1+2) =\ 6÷2(3) =\ 3(3) =\ 9##MathJax.Hub.Queue(["Typeset", MathJax.Hub, document.getElementById("bbclatex6638ba1578561")]);console.log("Queued!");

If we aren't treating it as a fraction then it is correc according to standard order of operations.

supergems:
The problem is the interpretation of the arithmetic expression, for PEMDAS the correct order is 6/2(1+2) = 6/2*3 = 6/6 = 1.

Ivoah:

--- Quote from: supergems on February 03, 2016, 05:06:34 pm ---The problem is the interpretation of the arithmetic expression, for PEMDAS the correct order is 6/2(1+2) = 6/2*3 = 6/6 = 1.

--- End quote ---

As Sorunome said above, multiplication and division are on the same level and are evaluated left to right, same with addition and subtraction: https://www.mathsisfun.com/operation-order-pemdas.html

supergems:
No, the interpretation is ambiguous for calculators!

https://en.wikipedia.org/wiki/Order_of_operations

--- Quote ---Exceptions[edit]
There exist differing conventions concerning the unary operator − (usually read "minus"). In written or printed mathematics, the expression −3^2 is interpreted to mean 0 − (3^2) = −9,[1][5] but in some applications and programming languages, notably Microsoft Office Excel (and other spreadsheet applications) and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus (negation or +/-) has higher precedence than exponentiation, so in those languages −32 will be interpreted as (−3)^2 = 9.[6] This does not apply to the binary minus operator −; for example while the formulas =-2^2 and =0+-2^2 return 4 in Microsoft Excel, the formula =0-2^2 returns −4. In cases where there is the possibility that the notation might be misinterpreted, a binary minus operation can be enforced by explicitly specifying a leading 0 (as in 0-2^2 instead of just -2^2), or parentheses can be used to clarify the intended meaning.

Similarly, there can be ambiguity in the use of the slash ('/') symbol in expressions such as 1/2x.[7] If one rewrites this expression as 1 ÷ 2 × x and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes:

1 : 2 * x = 1 * (1/2) * x = (1/2)*x.

With this interpretation 1/2x is equal to (1/2)x.[1][8] However, in some of the academic literature, implied multiplication is interpreted as having higher precedence than division, so that 1/2x equals 1/(2x), not (1/2)x. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[9] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[nb 1] Wolfram Alpha changed in early 2013 to treat implied multiplication the same as explicit multiplication. Formerly, implied multiplication without parentheses was assumed to bind more strongly than explicit multiplication. 2x/2x, 2·x/2·x, and 2(x)/2(x) now all yield x2.[10] Newer Texas Instruments calculators (TI-83 or later) also yield x2 in all three cases.[11]
--- End quote ---

[10] http://www.wolframalpha.com/input/?i=2x%2F2x,+2*x%2F2*x,+2(x)%2F2(x)+
[11] https://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=103110

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