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Infix notation is a method of writing mathematical expressions where operators are placed between their operands. This is the standard notation commonly used in everyday mathematics and programming languages. For example, in the expression 3 + 4, the plus sign (+) is the operator and 3 and 4 are the operands. The order of operations, often remembered by mnemonics like PEMDAS or BODMAS, dictates the sequence in which infix expressions are evaluated to ensure a consistent result. Parentheses are frequently used in infix notation to explicitly define the order of operations, overriding the default precedence rules if necessary. For instance, (3 + 4) * 5 clearly indicates that the addition should be performed before the multiplication.

Other notations exist for expressing operations, such as prefix notation (also known as Polish notation) and postfix notation (also known as Reverse Polish notation). In prefix notation, the operator precedes its operands, like + 3 4. In postfix notation, the operator follows its operands, like 3 4 +. Infix notation's familiarity makes it intuitive for humans, but it can be more complex for computers to parse and evaluate directly compared to prefix or postfix notations, which do not require explicit precedence rules or parentheses. Despite this, infix notation remains prevalent due to its widespread adoption and readability.