Answer
Algebraic expressions are mathematical phrases composed of numbers, constants, variable names and operators that combine them.
(for details, please see the step-by-step section)
Work Step by Step
As a phrase is to common language, an algebraic expression is to a mathematical statement.
Algebraic expressions are composed of numbers, constants, variable names and operators that combine them.
Their purpose is a "shorthand" of common language phrases that involve quantities and their inter-relationships.
Examples:
$3x+1$ ... " one more than triple the number x"
$\displaystyle \frac{1}{2}(x+y)$ ... " half the sum of numbers x and y"
Algebraic expressions are mathematical phrases by which mathematical statements are built.
Example:
For any real numbers a and b, a+b=b+a.
(This law states that the sum of any two numbers is the same regardless of which one we take to be the first number in the addition. The symbollic expression said this in "shorthand". )
