The concept of constants and variables are used extensively in algebra.

In this post we will understand the difference between constants & variables and then will solve some practice questions.

**Difference between constants and variables**

**Definition of constant and variable**

**Constant**

Any entity with fixed value is known as constant.

**Variable**

Entity with no fixed value is called variable.

**Examples of constant and variables**

**Constants**

All the integers, whole numbers, fractions or decimals are part of constants.

Numbers like 2, 99, -36, 6.98 , 4/5 etc. are constants as the value is fixed and doesn’t change with time.

**Variables**

In math, the variables are generally expressed by English alphabets.

In algebraic expressions, alphabets like x , y , b etc. are used to represent variables.

**Identification of constants and variables**

Follow the below rules to identify constants and variables in algebraic expressions:

(a) Isolated numbers in algebraic expression are constants

(b) Numbers with alphabets are variables.

For example, consider the expression:

7y + 10x – 13 = 0

Here;

7y & 10x are numbers with alphabets, hence they are variables.

Reasoning:

As the value of x and y changes, the value of entity 7y and 10x will also change. Since both the entity have no fixed value, they are termed as variable.

Number 13 is a isolated number whose value is constant.

Hence, number 13 is a constant.

**Entity 0.x is constant or variable.**

We studied the rule above that any number multiplied with alphabet is a variable. For example 8a, 10x etc. are all variables.

But the case of 0 . x is different.

We know that any number multiplied with 0 results in 0.

⟹ 0 . x

⟹ 0

Hence, no matter the value of x, the final value of entity 0 . x will always remain 0.

So, the value 0 . x is a constant.

**Entity 5 . 𝜋 is constant or variable?**

The value of 𝜋 is 3.14.

This value is constant and doesn’t change in any condition.

Multiplication of constant with constant results in constant.

5𝜋 = 5 x 3.14 = 15.7

** Examples in daily life**

**Constant**

The speed of light is fixed in universe.

Light can travel in different medium like air, water etc.; but the speed of light is fixed and doesn’t change.

**Variable**

Speed of sound changes with medium.

The speed of sound is different in air than in water, hence its speed is not fixed.

**Questions on Constants and Variables**

**(01) Find constant and variable in below expressions**

(a) 3x + y = 2x + 7

(b) 6x – y = 3

**Solution**

(a) 3x + y = 2x + 7

Simplify the expression

3x – 2x + y = 7

x + y = 7

The equation consists of three entities;

x ⟹ variable

y ⟹ variable

7 ⟹ constant

**(b) 6x – y = 3**

Solution

The equation consists of three entities;

6x ⟹ Variable

y ⟹ Variable

3 ⟹ Constant

(02) Given below are some of the sentence related to our daily life.**Identify the constants and variable** by providing relevant explanation.

(a) Number of sun in solar system

(b) Number of hairs in human head

(c) Number of eyes in a human

(d) Number of months in a year

(e) Population of the world

**Solution**

(a) Number of sun in solar system – **Constant**

There is only one sun in the solar system

(b) Number of hair in human head – **Variable**

The number of hair in head in average human changes with time, hence it is a variable entity.

(c) Number of eyes in human – **Constant**

There are two eyes in the human

(d) Number of months in a year – **Constant**

There are 12 months in a year which is fixed.

(e) Population of the world – **Variable**

The world’s population changes every second, hence it’s a variable.

**(03) Identify the constants and variables in below expression**.

\mathtt{\frac{5x}{7} \ +\ \frac{7y}{10} \ +\ 51\ =\ 0}

**Solution**

The equation consists of three entities;

5x/7 ⟹ variable

7y/10 ⟹ variable

51 ⟹ constant