grouping symbols

Grouping symbols are the punctuation marks of mathematics. Just as commas and brackets in a sentence tell you which words belong together, grouping symbols tell you which parts of an expression to treat as a single unit and evaluate first.

The common grouping symbols are parentheses ( ), square brackets [ ], and braces { }; a fraction bar and the bar of a radical sign also act as grouping devices. They override the usual order of operations: whatever sits inside a grouping symbol is computed before it interacts with the outside. So 2·(3 + 4) means 2·7 = 14, not 2·3 + 4 = 10.

When groups are nested inside one another, you resolve them from the innermost outward. Grouping symbols change the order of evaluation, and thereby the value — placing or removing them is not cosmetic. They are the writer's tool for saying exactly what should happen, and in what order.