What is 9-5+2 ?

9-5+2 = 6; //With Calculator

9-5+2 = 2; //Using BODMAS

If you evaluate from the right it give you "2" which follows the law: Brackets-Of-Division-Multiplication-Addition-Subtraction

Why don't calculators follow that rule?


9-5*2 = -1


closed as not a real question by Grigory M, Asaf Karagila, The Chaz 2.0, Did, Aryabhata Apr 6 '12 at 18:08

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Why are you telling us to "remember" something about "BODMAS" when you clearly don't know how to use it yourself? $\endgroup$ – The Chaz 2.0 Apr 6 '12 at 14:16
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    $\begingroup$ Not sure about the weight of downvotes... this is a fair and considered question fitting the stated brief "We welcome questions about: Understanding mathematical concepts" $\endgroup$ – Ronald Apr 6 '12 at 15:36
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    $\begingroup$ @Ronald: Not sure about the weight of upvotes... This is 1. certainly not about understanding mathematical concepts and 2. a multi duplicate. $\endgroup$ – Did Apr 6 '12 at 16:11
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    $\begingroup$ "Why don't calculators follow that rule" is not a mathematical question, but a user interface question. $\endgroup$ – Aryabhata Apr 6 '12 at 18:08
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    $\begingroup$ There's a meta thread on this question (please vote this comment up so that it becomes visible above "the fold") $\endgroup$ – t.b. Apr 6 '12 at 23:50

The rule as I learned it was: do brackets, then do both multiplication and division at the same time from left to right, then do both addition and subtraction at the same time from left to right. I did not learn a rule that would do all subtractions before all additions.

Note that most programming languages also evaluate addition and subtraction from left to right (this is called "left associative" evaluation).

In this case the "calculator" way matches 9 + (-5) + 2 which is how, in some sense, we ought to read expressions that involve subtraction. The motivation is that subtraction is not an associative operation, but addition is, and so if we just rewrite the subtractions as additions then we no longer have to worry about these things. If someone wants to write 9 - (5 + 2) then they will need to use parentheses. Unfortunately, we generally teach subtraction before negative numbers, which leads to this sort of confusion. The same situation exists with division and multiplicative inverses.

  • $\begingroup$ Why do you start making a moral argument here? Saying that you won't have to worry about these things just because one of the operations associates only works when a-b=a+(-b). How many binary operations work that way in the first place? Let Letting "+" and "-" stand for any binary opeartions. Suppose them both non-associative. What does x+y-z mean? Suppose them both associative, what does x+y-z mean? x+(y-z)=(x+y)-z for binary operation isn't something which holds very often, and how often can you introduce a unary operation "-" such that a-b=a+(-b)? $\endgroup$ – Doug Spoonwood Apr 9 '12 at 12:05
  • $\begingroup$ And how do you deal with the equivocation that has happened when you have a-b=a+(-b), since on the left - is binary, and on the right - is unary? Is "-" an operation of variable arity? But, "-" isn't this way, unless you have another convention which tells us what a-b-c means. And what if we want to consider a system with the same set, those two binary operations "-" and "+", and a third binary operation "x"? Or a fourth, a fifth, a sixth, a seventh, or an eighth? Saying that one has to use parentheses to say something like 9-(5+2), since -9+52, and 952+- both say it! $\endgroup$ – Doug Spoonwood Apr 9 '12 at 12:13

In BODMAS, division and multiplication are to be performed from left to right followed by addition and subtraction from left to right. The scientific calculator has done it correctly.


This illustrates an important misconception: BODMAS doesn't work in the way you think it does.

In training for mathematics education, we were told to avoid using BODMAS because it's confusing to most people... nonetheless teachers often use it at a low level of education because it's convenient. Other people may use PEMDAS, which may illustrate to you that the order of M and D is not strict (nor is the order of A and S).

A clear way to consider the situation is to split the expression into separate terms, by the location of $+$ and $-$:

$9$ is one term, $-5$ is another term, $+2$ is another term. We're effectively adding the terms. So we have $9 + (-5) + 2$. This avoids any notion of ambiguity.

A question that will generate more controversy is "What is the value of $1/2\pi$?" ;)

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    $\begingroup$ Ronald: 1. I downvoted the question. 2. " $1/2 \pi$" isn't a question... :) 3. This is spam, and possibly what you had in mind? $\endgroup$ – The Chaz 2.0 Apr 6 '12 at 15:44
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    $\begingroup$ @TheChaz Understood. It's your right to downvote the question. However, I believe it was asked in good faith and with an interest in understanding the mathematical concept: which is the clearly stated purpose of these pages. I think it's essential to provide a satisfactory answer to this poorly-understood question, at least once. $1/2\pi$ is an interesting and insightful edge case, I have updated it to a question for your benefit. $\endgroup$ – Ronald Apr 6 '12 at 18:03
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    $\begingroup$ In particular, the closure reason (ambiguous, vague, incomplete, etc) of this question does not apply here. The question is, contrary to the given reason, very specific. I think this is a poor closure decision. This is a valid question - a better solution would be to redirect to a duplicate that answers the question appropriately (if one exists). $\endgroup$ – Ronald Apr 6 '12 at 18:15
  • $\begingroup$ @Ronald: Well, if the question is "Why don't calculators follow that rule", then this is off-topic, and overly broad etc etc. Of course, don't go by the closure reasons, sometimes they are off, as it is a subjective matter. If the question is, how do you put the brackets in $9-5+2$, it either does not have a specific answer, is a dupe or is too localized. Any interpretation seems to be leading to closure. So IMO, closing is fine, and we should not worry about the exact close reason. Besides, OP probably got what they came here for. $\endgroup$ – Aryabhata Apr 6 '12 at 18:22
  • $\begingroup$ Maybe this, that or that? $\endgroup$ – Did Apr 6 '12 at 18:24

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