Knowra Order of operations Order of operations Order of operations is the set of conventions for deciding which operations to evaluate first in a mathematical expression. It determines how an expression is grouped when parentheses do not specify the grouping.
Operator precedence : Rules that assign different binding strengths to operators in an expression. Precedence ranks operations such as multiplication and addition when parentheses are absent.
PEMDAS : A mnemonic for the conventional hierarchy of parentheses, exponents, multiplication, division, addition, and subtraction. Its letter order can misleadingly suggest multiplication always precedes division, and addition always precedes subtraction.
Arithmetic operation : A mathematical procedure such as addition, subtraction, multiplication, or division. These operations are the basic actions whose order the conventions specify.
Shunting-yard algorithm : An algorithm that converts infix expressions into postfix notation or an expression tree using precedence rules. It implements operator precedence and associativity when processing arithmetic expressions.
Associativity : A rule specifying how operators of equal precedence group in an expression. Associativity decides how a chain of equal-precedence operations is grouped.
Polish notation : A notation that places operators before their operands, avoiding parentheses for many expressions. Operator position makes precedence conventions unnecessary for parsing its expressions.
Mathematical expression : A combination of numbers, variables, and operations that represents a mathematical value. Order-of-operations rules apply to expressions whose written form leaves grouping implicit.
Recursive descent parser : A parser built from mutually recursive procedures that recognize parts of a grammar. Its grammar levels commonly encode operator precedence directly.
Parentheses : Paired punctuation marks used to group parts of a mathematical expression. Parentheses explicitly set grouping and can override default precedence.
Reverse Polish notation : A notation that places operators after their operands and commonly uses a stack for evaluation. Its operand order makes evaluation explicit without conventional precedence rules.
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