this post was submitted on 07 Dec 2023
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[–] [email protected] 14 points 11 months ago (3 children)

Not quite. It's true you resolve what's inside the parentheses first, giving you. 8÷2(4) or 8÷2x4.
Now this is what gets most people. Even though Multiplication technically comes before Division the Acronym PEMDAS, that's really just to make it sound correct phonetically. Really they have equal priority in the order of operations and the appropriate way to resolve the problem is to work from left to right solving each multiplication or division sign as you encounter them. Giving you 16. Same for addition and subtraction.

So basically the true order of operations is:

  1. Work left to right solving anything inside parentheses
  2. Work left to right solving any exponentials
  3. Work left to right solving any multiplication or division
  4. Work left to right solving any addition or subtraction

Source: Mechanical Engineering degree so an unfortunate amount of my life spent in math and physics classes.

[–] [email protected] 2 points 11 months ago* (last edited 11 months ago) (1 children)

Absolutely, its all seen as equal so it has to go left to right However as I said in the beginning the way I was taught atleast, is when you see 2(2+2) and not 2×(2+2) you assume that 2(2+2) actually means (2×(2+2 )) and so must do it together.

[–] [email protected] 4 points 11 months ago* (last edited 11 months ago) (1 children)

Ah sorry just realized what you were saying. I've never been taught that. Maybe it's just a difference in teaching styles, but it shouldn't be since it can actually change the outcome. The way I was always taught was if you see a number butted up against an expression in parentheses you assume there is a multiplication symbol there.

So you were taught that 2(2+2) == (2(2+2))
I was taught 2(2+2)==2*(2+2)

Interesting difference though because again, assuming invisible parentheses can really change up how a problem is done.

Edit: looks like theshatterstone54's comment assumed a multiplication symbol as well.

[–] [email protected] -1 points 7 months ago

if you see a number butted up against an expression in parentheses you assume there is a multiplication symbol there

No, it means it's a Term (product). If a=2 and b=3, then axb=2x3, but ab=6.

I was taught 2(2+2)==2*(2+2)

2(2+2)==(2*(2+2)). More precisely, The Distributive Law says that 2(2+2)=(2x2+2x2).

[–] taladar 1 points 11 months ago

Basically the normal arithmetic operators are all left-associative which means if you have more than one you solve them left to right.

[–] [email protected] -1 points 7 months ago

It’s true you resolve what’s inside the parentheses first, giving you. 8÷2(4) or 8÷2x4.

Not "inside parenthesis" (Primary School, when there's no coefficient), "solve parentheses" (High School, The Distributive Law). Also 8÷2(4)=8÷(2x4) - prematurely removing brackets is how a lot of people end up with the wrong answer (you can't remove brackets unless there is only 1 term left inside).