• Another common issue is thinking “parentheses go first”

    There’s no “think” - it’s an absolute rule.

    then beginning by solving the operation beside them

    a(b) isn’t an operation - it’s a Product. a(b)=(axb) per The Distributive Law.

    (mostly multiplication)

    NOT Multiplication, a Product/Term.

    The point being that what’s inside the parentheses goes first, not what’s beside them

    Nope, it’s the WHOLE Bracketed Term. a/bxc=ac/b, but a/b( c )=a/(bxc). Inside is only a “rule” in Elementary School, when there isn’t ANYTHING next to them (students aren’t taught this until High School, in Algebra), and it’s not even really a rule then, it’s just that there isn’t anything ELSE involved in the Brackets step than what is inside (since they’re never given anything on the outside).