Operator — Definition, Formula & Examples
An operator is a symbol that tells you what mathematical action to perform on one or more numbers. The most common operators are addition (+), subtraction (−), multiplication (×), and division (÷).
An operator is a symbol or function that maps one or more input values (operands) to an output value according to a defined rule. In arithmetic and algebra, binary operators such as , , , and act on two operands, while unary operators such as negation () act on a single operand.
How It Works
An operator always needs at least one number (called an operand) to work on. In the expression , the operator is and the operands are and . The operator defines the rule: here, addition tells you to combine the two values to get . When multiple operators appear in one expression, order of operations (PEMDAS) determines which one you carry out first.
Worked Example
Problem: Identify each operator in the expression and evaluate it.
Identify operators: The expression contains three operators: × (multiplication), − (subtraction), and + (addition).
Parentheses first: The subtraction operator inside the parentheses acts first.
Multiplication next: The multiplication operator has higher precedence than addition.
Addition last: Finally, apply the addition operator.
Answer: The value of the expression is . The three operators (, , ) were applied in the order dictated by PEMDAS.
Why It Matters
Understanding operators is essential for reading and writing any mathematical expression, from basic arithmetic through algebra and beyond. In computer science and programming, operators like , , and logical AND/OR follow the same core idea: a symbol that defines an action on values.
Common Mistakes
Mistake: Confusing an operator with an operand.
Correction: The operator is the symbol that tells you what to do (, , etc.). The operands are the numbers it acts on. In , the operator is and the operands are and .