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Reposting since I am unable to validate the previous account,I asked the same question

https://math.stackexchange.com/questions/674426/right-to-left-order

Can someone please clarify unable to understand this basic math :(

I am sorry if this too basic math to ask

How can i represent this statement without order of precedence/ with order of precedence in a right to left flow

3+5/2*7-6

What I think : when we use right to left with no order the statement would come as

(7-6) = 1 (2*1) = 2 (5/2) = 2.5 3+2.5 = 5.5 when we use right to left with order the statement would come as

2*7 = 14 5/14 = 0.35 3+0.35 =3.35 3.35-6 = -3.35 Am I right about the above statements? How will right to left affect the order of operations?

Please clarify

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  • $\begingroup$ The second one looks like the correct use of "PEMDAS", as it's usually done. Not many people would really do it the first way, but it is fun (or maybe instructive, in certain contexts..) Actually the 5/2*7 woulod really go (5/2)*7=17.5, since in PEMDAS the multiplications and divisions are done left to right. $\endgroup$ – coffeemath Feb 12 '14 at 23:34
  • $\begingroup$ Please do not repost. Please flag the question for moderator attention to get the accounts linked. $\endgroup$ – Ross Millikan Feb 12 '14 at 23:55
  • $\begingroup$ @RossMillikan: Please read this. $\endgroup$ – Willie Wong Feb 13 '14 at 11:29
  • $\begingroup$ Since there were no other activity on the other account then asking the duplicate question, I've merged the two questions and removed the other account. $\endgroup$ – Willie Wong Feb 13 '14 at 11:33
  • $\begingroup$ In regards to tagging, since you are new here (welcome!), let me give a useful hint: please use the tag-wiki excerpts to help guide your selection of appropriate tags. These excerpts are shown automatically when tag names are shown as auto-complete suggestions. $\endgroup$ – Willie Wong Feb 13 '14 at 11:37
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What you call it is right to left, but don't you really mean left to right? The operations may be right justified in the calculator, but no expression is ever evaluated right to left. Where did you hear about this? Maybe you can explain this to me, but I'm afraid I don't think I know what you're talking about. mathematical expressions are evaluated in the order in which they are written, not reverse order. Am I missing something?

The correct way to evaluate $3+5/2\cdot7-6$ (with multiplicative precedence) is $$\begin{align}3+(\tfrac{5}{2}\cdot7)-6&=3+(2.5\cdot7)-6\\&=3+17.5-6\\&=14.5\end{align}$$ Simple left-to-right order would be $$\begin{align}(3+5)/2\cdot7-6&=8/2\cdot7-6\\&=4\cdot7-6\\&=28-6\\&=22\end{align}$$ Right-to-left order is complete nonsense.

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I am not aware of uses of right to left-some calculators do left to right with no order: $\\3+5=8\\8/2=4\\4*7=28\\28-6=22$ Aside from that, it is standard to consider the order of operations

The only issue I see with your approach-you have said what you want to do and done it accurately-is $5/14\neq 0.35$ It doesn't round to $0.35$, it is $0.3\overline{571428}$

Under the usual approach $5/2*7$ is ambiguous and we see things on the site that intend $(5/2)*7$ and others that intend $5/(2*7)$

The best approach is to make sure your expression is unambiguous and to use parentheses to make sure it is.

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  • $\begingroup$ never played with RPN-based calculators much, eh? Though admittedly users usually key things in step by step. $\endgroup$ – Willie Wong Feb 13 '14 at 11:41
  • $\begingroup$ @WillieWong: Actually I have, but long ago. Here the operators are written infix, not postfix $\endgroup$ – Ross Millikan Feb 13 '14 at 13:59

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