6 ÷ 2(1+2)
I would solve it like this:
The calculator on my iPhone solves it like this:
PEMDAS: Parentheses, Exponent, Multiplication, Division, Addition, Subtraction.
So:
Am I right, or is my phone right?
What makes you think that the iPhone calculator knows anything about the order of operations?
I would assume people much smarter than I am wrote the program.
If I recall high school math classes correctly (it’s been about 40 years so no guarantee 
), you’re correct and your iPhone is exhibiting artificial unintelligence.
The calculator is correct.
You are solving 6 divided by (2 x (1+2)). The equation does not say that the 6 is divided by the (1+2).
Multiplication is division. Addition is subtraction. PEMDAS is really PEMA.
I just plugged the equation into my (Safari) search bar, and it also says 9.
The equation says it is divided by the product of 2 x 3.
The purpose of parentheses is to indicate: « do this first ».
Once you do that step the parentheses are done and then it’s a division followed by a multiplication.
No need to add parentheses to (6 / 2), because multiplication and division are done in the order of the equation.
So, 6 / 2 * 3 = 9
We can all agreed that the (1+2) is just 3. This is not controversial.
Now write it like this
6 ÷ 2 x 3
Why do you think you would do the 2 x 3 first?
Because M comes before D in PEMDAS.
Which is why it isn’t taught like that anymore.
No it doesn’t. There is no rule that due to the convention of leaving out the implied “x” it means that the “x” is prioritised.
And as I said, multiplication is not really before division in the OOO, it’s equivalent to it. Thus the operations are performed literally in the order they appear. Like the calculator says.
Well, I wasn’t notified!
How many times can we do this?
Both are fine. It’s just a convention, not a law of mathematics. I prefer your answer, but your reasoning is incorrect.
It was in Memo 323.45 of 1989 Annex B at Chapter 6 section 5 paragraph 7(xii)(a) at the third dot point. On page 1248.
If you aren’t going to keep up with the Memos, you really can’t blame us.
Is it in a filing cabinet that has a sign that says ‘Beware of the leopards’?
What does your phone say it uses for the order of operations? If your phone does it the way it says it does then it’s right.
This is why Polish Notation (or better yet, Reverse Polish Notation) is superior to PEMDAS; no ambiguity because the “order of operations” is defined by the order in which operations are applied.
Stranger
I can’t speak to iPhones but my Android gets PEMDAS. Notably, it does not resolve each button push before going on to the next bit (well, actually it does but it re-evaluates the answer as the equation is typed in so, 1+2 and you see 3…when you add x 3 it resolves to 7). The whole equation is evaluated to produce an answer. (NOTE: This is the built in Android calculator and it is set at its most basic function and not scientific mode or whatever else it has).
