Editing Elementary algebra (section)

===Variables===
[[File:Pi-equals-circumference-over-diametre.svg|thumb|right|Example of variables showing the relationship between a circle's diameter and its circumference. For any [[circle]], its [[circumference]] {{mvar|c}}, divided by its [[diameter]] {{mvar|d}}, is equal to the constant [[pi]], <math>\pi</math> (approximately 3.14).]]
{{Main|Variable (mathematics)}}
Elementary algebra builds on and extends arithmetic<ref>Thomas Sonnabend, ''Mathematics for Teachers: An Interactive Approach for Grades K-8'', Publisher: Cengage Learning, 2009, {{ISBN|0495561665}}, 9780495561668, 759 pages, [https://books.google.com/books?id=gBa2GzyXCF8C&q=extends+arithmetic&pg=PR17 page xvii]</ref> by introducing letters called variables to represent general (non-specified) numbers.  This is useful for several reasons.

#'''Variables may represent numbers whose values are not yet known'''. For example, if the temperature of the current day, C, is 20 degrees higher than the temperature of the previous day, P,  then the problem can be described algebraically as <math>C = P + 20</math>.<ref>Lewis Hirsch, Arthur Goodman, ''Understanding Elementary Algebra With Geometry: A Course for College Students'', Publisher: Cengage Learning, 2005, {{ISBN|0534999727}}, 9780534999728, 654 pages, [https://books.google.com/books?id=jsT7kqZubvIC&dq=%22elementary+algebra%22+variables+unknown&pg=PA48 page 48]</ref>
#'''Variables allow one to describe ''general'' problems,<ref name=leff>Lawrence S. Leff, ''College Algebra: Barron's Ez-101 Study Keys'', Publisher: Barron's Educational Series, 2005, {{ISBN|0764129147}}, 9780764129148, 230 pages, [https://books.google.com/books?id=XesryURrNKAC&dq=algebra+variables+generalize&pg=PA2 page 2]</ref> without specifying the values of the quantities that are involved.''' For example, it can be stated specifically that 5 minutes is equivalent to <math>60 \times 5 = 300</math> seconds. A more general (algebraic) description may state that the number of seconds, <math>s = 60 \times m</math>, where m is the number of minutes.
#'''Variables allow one to describe mathematical relationships between quantities that may vary.'''<ref>Ron Larson, Kimberly Nolting, ''Elementary Algebra'', Publisher: Cengage Learning, 2009, {{ISBN|0547102275}}, 9780547102276, 622 pages, [https://books.google.com/books?id=U6v78M5nYKAC&q=relationships&pg=PA210 page 210]</ref> For example, the relationship between the circumference, ''c'', and diameter, ''d'', of a circle is described by <math>\pi = c /d</math>.
#'''Variables allow one to describe some mathematical properties.''' For example, a basic property of addition is [[commutativity]] which states that the order of numbers being added together does not matter. Commutativity is stated algebraically as <math>(a + b) = (b + a)</math>.<ref>Charles P. McKeague, ''Elementary Algebra'', Publisher: Cengage Learning, 2011, {{ISBN|0840064217}}, 9780840064219, 571 pages, [https://books.google.com/books?id=etTbP0rItQ4C&dq=%22elementary+algebra%22+commutative&pg=PA49 page 49]</ref>