this may be a silly (and duplicated or triplicated) question, but I don't know how justify one or other way to solve this:


It is clear that:

$(A/B)*C \neq A/(B*C)$


I have heard some people saying that the order of operations is:

  • Parentheses
  • Exponentiation
  • Multiplication
  • Division
  • Addition
  • Subtraction

In that case, $A/(B*C)$ is right, but I don't thing so...

Other people says tha Mult. and Div. are in the same level and you just do it in left-right order, in that case $(A/B)*C$ is the right one, but that "it depends of the order" doesn't convince me completely.


I have made an observation on this other situation

$D - E + F$

Here we don't think in solve it in two ways, it is clear because the $-$ sign is part of E, not an operation, so:

$D-E+F = D+(-E)+F$

That lead me to think that $/$ should be part of B too:

$A/B*C = A*(1/B)*C$

The fun part is that this observation match with the left-right aproach.

So my question is: What is the real justification to say solve it? I guess $A/(B*C)$ is wrong, but how to justify the opposite?

  • $\begingroup$ Such questions sound me like "is it true or not that $0 \in \Bbb{N}$?". I would say that: 1. It is all about conventions, 2. there is no correct answer, 3. why should we talk about this. $\endgroup$ – Crostul Apr 19 '16 at 17:23
  • $\begingroup$ but 0 is or not part of N? heheh $\endgroup$ – onlycparra Apr 19 '16 at 18:10

Order of operations for multiplication and division means doing these two operations left to right. So, absent parentheses (which have higher precedence) you do them left to right. So,

$$A / B \times C = \left[\frac{A}{B}\right] \times C = \frac{AC}{B}.$$

$P$lease $E$xcuse $M$y $D$ear $A$unt $S$ally: Parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

I haven't seen where multiplication has a higher precedence than division (or addition a higher precedence than subtraction). This may be "another camp" but it's likely misinformation.

  • 1
    $\begingroup$ Hey, I thougth that "Please Excuse My Dear Aunt Sally" was some slang :P, In spanish we use the meaningless "PAPOMUDAS = parentesis, potencias, multiplicaciones y divisiones, adiciones y sustracciones". After a second I got it. Thanks :) $\endgroup$ – onlycparra Apr 19 '16 at 17:29

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