Arithmetic Operators and Order of Operations

A program does not read an arithmetic expression the way you read a sentence, left to right. It ranks the operators first and does the highest-ranked ones first, wherever they sit. Parentheses win every time. After that, multiplication and division outrank addition and subtraction. When operators tie in rank, like a division next to a multiplication, the program works left to right between just those two.

Mechanically, evaluation collapses the expression step by step until one number is left. Take 7 + 3 x 4 - 10 / 5. The program scans for the highest-ranked operations: 3 x 4 becomes 12, and 10 / 5 becomes 2. The expression is now 7 + 12 - 2. Only addition and subtraction remain, so it finishes left to right: 7 + 12 is 19, then 19 - 2 is 17. Parentheses override all of this by forcing a sub-expression to resolve first, as in (14 - 2) / 4 + 3 x 2: the parentheses give 12, so the expression becomes 12 / 4 + 3 x 2, then 3 + 6, then 9.

This topic matters because every variable assignment and every condition in a branch or loop relies on an expression being evaluated the same way every time. If order of operations were ambiguous, the same line of code could produce different values on different runs, which would break the predictability that algorithms depend on. Later, when expressions mix arithmetic with comparisons like greater-than or boolean operators like AND, the same idea of ranked evaluation extends to decide what resolves first.