**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.