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Elementary algebra consists largely of a review of the rules of arithmetic applied to variable expressions, including the rewriting of such expressions into simplest form, along with the application of those techniques to the solving of equations. As an academic subject, it is typically studied in secondary school (7th to 9th grade in the United States).

The above usage of the term distinguishes it from intermediate algebra, which deals mainly with functions and graphs. The university-level course typically called college algebra includes material from both levels.

None of the above terms refer to the area of mathematics usually called abstract algebra (or sometimes modern algebra), in which abstract structures such as groups and fields are studied.