Elementary Algebra

Elementary algebra introduces the basic rules and operations of algebra, one of the main branches of mathematics. Whereas arithmetic deals with specific numbers and operators (e.g +,-,*,/) (e.g. 3 + 2 = 5), algebra introduces variables, which are letters that represent non-specified numbers (e.g. 3a + 2a = 5a). Algebra also defines the rules and conventions of how it is written (called algebraic notation). For example, the multiplication symbol, is sometimes replaced with a dot, or even omitted completely, because its context makes its use obvious (e.g. 3 × a may be written 3a).

Elementary algebra is typically taught to secondary school students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic as "algebra". As an introduction, elementary algebra can be found in books from the early 19th century.

Elementary algebra is useful in several ways, including (a) describing generalized problems (e.g. if Ann is 3 years older than Bob, this may be written algebraically as a = b + 3). (b) defining mathematical rules such as (a + b) = (b + a) stating that when adding two numbers, the order of numbers does not matter (see commutativity). (c) describing the relationship between numbers such as between temperatures on the Fahrenheit scale (F) and the Celsius scale (C), given by F = (9C ÷ 5) + 32.

The pushing of algebra from high school, where it has traditionally been taught, to elementary school has met with some controversy. Whereas students 30 years ago memorized multiplication tables in math class, students today, driven by the new Common Core Standards, are being introduced to variables as early as 6th grade. Educational theorists calculate that by age 11 children begin developing the ability to reason abstractly. However, this may not be true for all children and may account, at least in part, for the great difference in mathematical ability among students.

Still, there are ways to make algebra more concrete through the use of manipulatives and real-word problems. Equation-solving flowcharts allow students to work through abstract algebra problems in a more concrete way.

Read more about Elementary AlgebraAlgebraic Notation, Solving Algebraic Equations

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Elementary Algebra - Solving Algebraic Equations - Relation Between Solvability and Multiplicity
... When the multiplicity is only partial (meaning that for example, only the left hand sides of the equations are multiples, while the right hand sides are not or not by the same number) then the system is unsolvable ... For example, in the second equation yields that which is in contradiction with the first equation ...
Equation Solving - Methods of Solution - Elementary Algebra
... of a single real-valued unknown, say x, such as can be solved using the methods of elementary algebra ...
Common Logical Connectives - History of Notations
... from Boole's interpretation of logic as an elementary algebra ... is also used, in spite of the ambiguity coming from the fact that the + of ordinary elementary algebra is an exclusive or when interpreted logically in a two-element ring ... from Boole's interpretation of logic as an elementary algebra over the two-element Boolean algebra other notations include to be found in Peano ...
History Of Elementary Algebra
... Algebra is a branch of mathematics concerning the study of structure, relation, and quantity ... Elementary algebra is the branch that deals with solving for the operands of arithmetic equations ... Modern or abstract algebra has its origins as an abstraction of elementary algebra ...

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