Difference between revisions of "Variable"

 
(Problems: haeder)
 
(7 intermediate revisions by 5 users not shown)
Line 1: Line 1:
== Definition ==
+
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).
  
A '''variable''' does not have a set valueIts value can change, and a '''variable''' is used to represent unknowns in equations.
+
Variables are very useful in solving many problems [[algebra]]iclyFor 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, i, a, b, and c.
+
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]].
  
== Examples ==
+
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]].
  
What plus 7 is 10?
 
  
Write an equation that uses a '''variable''' to represent the part that is unknown.
 
  
<math>\displaystyle7+n=10</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 $x, y, z, m, n, a, b, c, p, q$, and many Greek letters.

By convention, certain variables are often used for certain types of quantities. $z, w, \omega$ and $\zeta$ are often used as complex variables. $m$ and $n$ are often used as variables representing integers. $p$ and $q$ are often used as variables representing prime numbers. And $a$, $b$ and $c$ are often used as variables representing geometric quantities such as length.


Problems

Preintroductory

  • What number, when added to $7$, gives a sum of $10$? (Source)

Introductory

Intermediate

Olympiad

Invalid username
Login to AoPS