elementary algebra

This article is about basic algebra in mathematics. For other uses of the term "algebra" see algebra (disambiguation). Elementary algebra is a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic. While in arithmetic only numbers and their arithmetical operations (such as +, −, ×, ÷) occur, in algebra one also uses symbols (such as x and y, or a and b) to denote numbers. These are called variables. This is useful because:It allows the generalization of arithmetical equations (and inequalities) to be stated as laws (such as for all a and b), and thus is the first step to the systematic study of the properties of the real number system.It allows reference to numbers which are not known. In the context of a problem, a variable may represent a certain value of which is uncertain, but may be solved through the formulation and manipulation of equations. It allows the exploration of mathematical relationships between quantities (such as "if you sell x tickets, then your profit will be dollars"). These three are the main strands of elementary algebra, which should be distinguished from abstract algebra, a more advanced topic generally taught to college students.
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