# What is variable in math? Variables definition, concept and examples

## Variable Definition

An entity with no fixed value is called a variable.

In math, the variable is generally denoted by alphabet x , y , z etc.

Consider the below algebraic expression:

The expression is made of two entities 5x and 6.

Here;
5x is a variable and 6 is a constant value.

Why 5x is a variable?

Because as we change the value of x, the value of 1st part will also change.

Observe the below table:

Note that as we change the value of x, the value of 5x is also changing.

Hence, there is no fixed value for 5x, that’s why it is called variable.

Now consider the 2nd part of the expression; digit 6.

Number 6 is a constant value.
No matter what is the value of x, the value of digit 6 will remain the same.

### How to identify a variable?

In math, any number which is multiplied with alphabet is a variable.

For example;
6y is a variable
Since value of y is not fixed, then the entity value 6y is also not fixed.

Similarly entities like 5a, 3b, 9x, 88y are all examples of variables.

### Variables examples in Real life

(a) Height of human
The height of newly born baby changes with time, hence it’s a variable entity.

(b) Room Temperature
The temperature of a room fluctuates on daily basis, so its a variable.

(c) Speed of car
The car speed changes throughout the journey, hence its a non fixed value.

Examples of Non variables
Entities with a fixed value are non variables or constants.

(a) Number of ears in humans
Every human being has two ears.
This value is fixed, hence the entity is a constant.

(b) Distance between earth and sun

(c) Speed of light

## Solved problems on variables

(01) Identify the variables in below equation
10x + 6y -7 = 2x + 5

Solution
Simplifying the equation

10x – 2x + 6y = 5 + 7

8x + 6y = 12

Now the equation consists of three entities;
8x ⟹ Variable
6y ⟹ Variable
12 ⟹ Constant

The above two entities are variable since change in value of x and y will change their values.

(02) Identify the variable values
-6x + y -2 = -6

Solution
Simplifying the algebraic equation:

-6x + y = -6 + 2

-6x + y = -4

The equation consists of three entities.

-6x ⟹ Variable
y ⟹ Variable
-4 ⟹ Constant

(03) Check if the below expression is constant or variable.
(a) Number 0
(b) 0 . y

Solution
(a) Number 0 is a constant since it has a fixed value.

(b) The expression 0.y is also constant because multiplication of 0 with y results in 0 which is a constant.
⟹ 0 . y
⟹ 0
No matter what’s the value of y, the expression is simplified to 0, which is a constant.

(04) Identify the variables and constant in below expression.
\mathtt{\frac{10a}{7} \ +\ \frac{6b}{5} \ +100\ =\ 0}

Solution
The expression consists of three entities.

10a/7 ⟹ variable

6b/5 ⟹ variable

100 ⟹ constant

The above two entities are variable as the change in value of a & b will change the total value.

(05) Given below are some of the facts of general life. You have to identify the variables and constants among the given facts.
(a) Number of days in week
(b) Number of hours in a day
(c) Temperature of day
(d) Humidity in the air
(e) Number of months in a year

Solution
(a) Number of days in a week ⟹ Constant
There are 7 days in a week. The week days are fixed and doesn’t change with time.

(b) Number of hours in a day ⟹ Constant
There are fixed 24 hours in a day.

(c) Temperature of day ⟹ Variable
The temperature changes with time, someday we have warm weather and other .

(d) Humidity
The percentage of humidity in the atmosphere changes everyday.
Hence humidity is a variable.

(e) Number of months in year
There are fixed 12 months in a year.
Hence number of months is constant.