When you say she starred in Smurfs, are you saying she actually starred in Smurfs or in Avatar, which is essentially a Smurfs movie?

There seems to be disagreement on this, and not just by me (see my sources).

That was just an error. I intended it to say 4 x 8 + 9 - 2 x 7 + 9 ÷ 3 + 5

So why not just have it be like SDPAEM? (subtract, divide, parentheses, add, exponent, multiply)? It doesn't make sense that the order is entirely arbitrary.

It seems to me that some arbitrary decisions were made, like to have addition before subtraction, or whether to have division before multiplication, but it seems clear the choice (for example) to have multiplication and division before addition and subtraction is not merely arbitrary and rather, is based on multiplication and division having a greater order of magnitude in their effect compared to addition and subtraction. Same with exponents being before multiplication and division.

This comment provides a similar explanation to what I'm saying:

https://www.quora.com/Is-there-a-logical-explanation-for-the-mathematical-order-of-operations/answer/Stephen-McBride-13?ch=10&oid=300169584&share=4e8656ca&srid=YAyd&target_type=answer

See also here: https://www.reddit.com/r/mathematics/comments/k2nfui/comment/gdvfjla/?utm_source=share&utm_medium=web2x&context=3

This comment provides a similar explanation to what I'm saying:

https://www.quora.com/Is-there-a-logical-explanation-for-the-mathematical-order-of-operations/answer/Stephen-McBride-13?ch=10&oid=300169584&share=4e8656ca&srid=YAyd&target_type=answer

See also here: https://www.reddit.com/r/mathematics/comments/k2nfui/comment/gdvfjla/?utm_source=share&utm_medium=web2x&context=3

I know what you're saying but I don't think so.

The numbers that are added or subtracted within a given formula are not subtracted from the number adjacent to them. They are just added or subtracted from the overall series of numbers.

Conversely, the multiplication and division symbols strictly indicate that the multiplication or division must occur between the numbers on either side of the multiplication or division symbol -- so you can't just move those numbers around that are on either side of those symbols.

This being the case, it's necessary to first do the multiplication and division calculations so those operators work first between the two numbers on either side and not along with some other number that is added or subtracted.

This is why we can't have nice things.

I bet there's a more precise explanation than just "we agreed to it." Without looking it up, it seems it's something having to do with this:

Consider this formula:

• 4 x 8 + 9 - 2 x 7 + 9 ÷ 3

We know that the multiplication sign between 4 and 8 only acts between those two numbers. And the multiplication sign between the 2 and 7 only acts on those two numbers and the division sign only acts on the 9 and 3. BUT, the +4 and -2 and +5 could literally be anywhere else in the formula and nothing would change. Basically, the exact location of the multiplication and division symbols between two numbers matter, whereas the exact location of the numbers added and subtracted doesn't matter.

I don't think this is just because we decided to do it this way as a convention. It's because the multiplication and division signs are unique in that they specifically imply that a calculation should happen between the two numbers on either side of the operation.

Maybe a way to think about it is that multiplication and division essentially transforms the adjacent numbers. Examples:
- 3 x 8 (three, eight times is 24; or eight, three times is 24).
- 45/3 (45 split into 3 is 15).

Numbers that are added or subtracted are more just independent from the rest of the numbers as they can appear anywhere (they don't necessarily need to be added to the adjacent number).