Variables

Variables :

Introduction :

In arithmetic,numbers represents the value of itself.There are different numbers, each represents its own value. But, in algebra, different letters represent different variables, and each variable can take any value. Here we will study the definition of variable and its significance.

Definition of variable :

The entity which can take on different values is called as variable. The commonly used letters such as x, y,a,n, t......, are variables.We can not predict the value of a varaible.

Below is an example for an expression containing variable x.

x + 25

Here we don't know the value of x.The value of the above expression is not known unless the value of x is decided. x can take any value. We can substitute the value of x and calculate the value of expression.

Two or more variables in an Expression :

An algebraic expression can have two or more variables.However all the variables should have different letters.

consider an expression

x +y +z + 10

Here we have used three variables x, y and z. The value of the above expression depends on the values of the variables x, y and z.

Important :

Two variables can take same or different values.Suppose x and y are the two variables, they might have the same value or they might be different.

Coefficient of variables :

The variable can hold any co-efficient ( numbers ) with it.For example, in the expression 3x+ 4y , 3 is the co-efficient of x and 4 is the co-efficient of y.

Examples :

1. Evaluate 4x + 5 when x = 3.

Solution : Given expression 4x + 5

Plug in the value of x in above expression, we get

= 4 (3) + 5

= 12 + 5

= 17.

2. Evaluate n (n - 4) when n = 6.

Solution : Given expression n ( n -4 ) ,

Plug in the value of n in above expression, we get

= 6 ( 6 - 4)

= 6 ( 2 )

= 12.

3. Evaluate x^₂ + 2x + 2 when x = 4.

Solution : Given expression X² + 2x + 2

Plug in the value of x in above expression, we get

= ( 4 )² + 2 (4) + 2

= 16 + 8 + 2

= 26.

Mathematical significance :

In mathematics, variables play a important role. We can use the variables in any mathematical formula. For example,the area of triangle is given by,

area = 1/2 × b × h

Here b and h are variables, also the area is different for different values of b and h.