# Difference between revisions of "Variable"

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− | + | A '''variable''' is a symbol used to represent either a quantity which is unknown (for example, the solutions of a [[quadratic equation]]) or a quantity which may change (that is, which may vary). | |

− | + | Variables are very useful in solving many problems [[algebra]]icly. For instance, [[word problem]]s can often be solved using variables to represent desired but unknown [[expression]]s. | |

− | Any symbol may be used as a variable, but the most common variables are x, y, z, n, a, b, c, p, and | + | Any symbol may be used as a variable, but the most common variables are <math>x, y, z, m, n, a, b, c, p, q</math>, and many [[Greek alphabet|Greek letters]]. |

− | + | By [[mathematical convention|convention]], certain variables are often used for certain types of quantities. <math>z, w, \omega</math> and <math>\zeta</math> are often used as [[complex number|complex]] variables. <math>m</math> and <math>n</math> are often used as variables representing [[integer]]s. <math>p</math> and <math>q</math> are often used as variables representing [[prime number]]s. And <math>a</math>, <math>b</math> and <math>c</math> are often used as variables representing [[geometry|geometric]] quantities such as [[length]]. | |

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− | <math> | + | == Problems == |

+ | ===Preintroductory=== | ||

+ | *What number, when added to <math>7</math>, gives a sum of <math>10</math>? ([[Variable/Problems|Source]]) | ||

+ | ===Introductory=== | ||

+ | ===Intermediate=== | ||

+ | ===Olympiad=== | ||

+ | |||

+ | [[Category:Algebra]] | ||

+ | [[Category:Definition]] |

## Latest revision as of 21:35, 15 November 2007

A **variable** is a symbol used to represent either a quantity which is unknown (for example, the solutions of a quadratic equation) or a quantity which may change (that is, which may vary).

Variables are very useful in solving many problems algebraicly. For instance, word problems can often be solved using variables to represent desired but unknown expressions.

Any symbol may be used as a variable, but the most common variables are , and many Greek letters.

By convention, certain variables are often used for certain types of quantities. and are often used as complex variables. and are often used as variables representing integers. and are often used as variables representing prime numbers. And , and are often used as variables representing geometric quantities such as length.

## Problems

### Preintroductory

- What number, when added to , gives a sum of ? (Source)