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