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In mathematics, a variable is defined as a symbol that is used to represent one or more numbers. This concept is fundamental in algebra and other areas of mathematics because it allows for the expression of general relationships and the formulation of equations. By using variables, mathematicians can describe patterns, relationships, or functions without specifying exact values. For instance, in the equation \(y = mx + b\), \(x\) and \(y\) are variables that can take on different numeric values depending on the context, while \(m\) and \(b\) would typically represent constants that define the slope and y-intercept, respectively.

Other options present incorrect definitions. A fixed number does not change and therefore cannot be a variable. A constant in an equation refers to a defined value that remains unchanged, distinguishing it from a variable. A mathematical operation involves the processes of mathematics, such as addition or subtraction, rather than the concept of representing a value. Understanding these distinctions helps to clarify the role and definition of a variable within mathematical contexts.