It is also frustrating when different calculators have different orders of operations and dont tell you.

Yeah, but to be fair most of them do tell you the order of operations they use, they just bury it in a million lines of text about it. If they could all just check with some Maths teachers/textbooks first then it wouldn’t be necessary. Instead we’re left trying to work out which ones are right and which ones aren’t. Any calculator that gives you an option to switch on/off “implicit multiplication”, then just run as fast as you can the other way! :-)

Unfortunately some calculators, such as Google’s will ignore your brackets and put in their own anyway. You just gotta find a decent calculator in the first place.

8÷2(2+2)=8×(1/2)×(2+2)

No, that’s wrong. 2(2+2) is a single term, and thus entirely in the denominator. When you separated the coefficient you flipped the (2+2) into the numerator, hence the wrong answer. You must never add multiplication signs where there are none.

Brackets are ALWAYS first.