# How to Justify the way to solve “A / B * C”

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

$A/B*C$

It is clear that:

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

## One

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

• Parentheses
• Exponentiation
• Multiplication
• Division
• 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.

## Two

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?

• 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. – Crostul Apr 19 '16 at 17:23
• but 0 is or not part of N? heheh – onlycparra Apr 19 '16 at 18:10

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