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
- 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.
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?
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.