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3.1: Mathematical Expressions
Last updatedAug 15, 2020
3.0: Prelude to the Fundamentals of Algebra
3.2: Evaluating Algebraic Expressions
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David Arnold
Contributed by David Arnold
Retired Professor (Mathematics) at College of the Redwoods
Recall the definition of a variable presented in Section 1.6.
Definition: Variable
A variable is a symbol (usually a letter) that stands for a value that may vary.
Let’s add the definition of a mathematical expression.
Definition: Mathematical Expression
When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.
Thus,
2a, x + 5, and y2,
being formed by a combination of numbers, variables, and mathematical operators, are valid mathematical expressions. A mathematical expression must be well-formed. For example,
2 + ÷5x
is not a valid expression because there is no term following the plus sign (it is not valid to write +÷ with nothing between these operators). Similarly,
2 + 3(2
is not well-formed because parentheses are not balanced.