Order of operations
A line such as 3 + 4 \times 5 could mean 35 or 23. What rule makes everyone read it the same way?
Where you are 5 inside
What this area is about
A written expression is only useful if every reader gets the same number from it. So there is an agreed order: grouping first, then powers, then multiplying and dividing from left to right, then adding and subtracting from left to right. The order is a convention, not a fact of nature, and grouping symbols let a writer override it.
How these fit together
The rule. Numerical expressions explains what an expression is and why the order is needed, settling 3 + 4 \times 5 = 23.
Overriding it. Grouping symbols mark a part to be worked first, as in (3 + 4) \times 5.
Translating. Writing expressions from words turns a phrase like “add 8 and 7, then multiply by 2” into (8 + 7) \times 2, and reads an expression back as words.
Extending it. Order of operations with powers settles powers before multiplying, so 2 + 3^2 = 11. Order of operations with negative numbers adds signs, and tells a minus that means subtract from one that means the opposite.
A path through it
Start with numerical expressions, then grouping symbols. Writing expressions from words and the order with powers both follow; negatives come last.
With the order settled, evaluating expressions and formulas and all of algebraic expressions rely on it.