Vagabond

I lost my dad to cancer about two week before last Christmas. And my birthday is a few days after Christmas as well. I'll be damned if I ever feel like celebrating Christmas or my birthday ever again

I see what you're getting at but the issue isn't really the assumed multiplication symbol and it's priority. It's the fact that when there is implicit multiplication present in an algebraic expression, and really best practice for any math above algebra, you should never use the '÷' symbol. You need to represent the division as a numerator and denominator which gets rid of any ambiguity since the problem will explicitly show whether (2+2) is modifying the numerator or denominator. Honestly after 7th grade I can't say I ever saw a '÷' being used and I guess this is why.

That said, I'll die on a hill that this is 16.

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.

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.

8÷2(2+2) comes out to 16, not 1.

Saw it posted on Instagram or Facebook or somewhere and all of the top comments were saying 1. Any comment saying 16 had tons of comments ironically telling that person to go back to first grade and calling them stupid.