Constant in Maths

Constant simply is a fixed value or a value that does not change. A constant always has a known value such as pi(π) whose value is, π = 3.1415… Letter such as a, b, c used as the replacement for a constant.

In this article, we will discuss in detail about Constant in Mathematics.

What is a Constant in Math?

A constant in mathematics refers to a fixed value that remains unchanged throughout a particular context or problem. Constants don’t vary or take on different values and maintain their specific numerical value, providing stability and consistency within mathematical formulations.

Constant Term in Algebraic Expression

In algebraic expressions, a constant term does not contain any variables and represents a fixed value within the expression. For example, in algebraic expression 2x² + 3x – 11, -11 is constant. Constants provide stability and consistency within mathematical formulations serving as fundamental elements in various algebraic expressions, equations and functions.

How to Recognize a Constant in Algebraic Expression?

Identifying constants in algebraic expressions involves looking for terms that do not involve variables and maintain a consistent value regardless of any changes in the variables present in the expression. Constants can be represented using specific numerical values or variables, depending on the context of the problem or equation.

Constant Numbers

Constant numbers are numerical values that do not change and remain constant throughout mathematical operations or equations. Constants are used extensively in various fields such as physics, engineering, economics and computer science to represent fixed values and parameters in mathematical models and calculations.

Examples include integers, fractions, irrational numbers like π (pi), and transcendental numbers like e (Euler’s number).

Arbitrary Constants

Arbitrary constants are constants introduced into mathematical expressions or equations to represent unknown or unspecified values.

Example: They are typically denoted by letters such as “C” or “K” and are used in solving differential equations and other mathematical problems.

Operations on Constants

Mathematical operations, such as

• Addition
• Subtraction
• Multiplication
• Division

Can be performed on constants like any other numerical values, preserving their constant nature.

Difference Between Constant and Variable

Constants differ from variables in that they maintain a fixed value, whereas variables can vary and take on different values within a given context or equation. Below are the tabular differences between constants and variables:

Constant Vs Variable
Criteria	Constant	Variable
Definition	A value that remains unchanged over time or within a specified context	A symbol or value that can change typically represented by a letter or symbol
Representation	Often represented by specific symbols such as π (pi), e (Euler’s number), g (acceleration due to gravity)	Represented by letters or symbols which can vary in different contexts
Examples	π (pi) = 3.14159… e (Euler’s number) ≈ 2.71828 g (acceleration due to gravity) ≈ 9.81 m/s²	x, y, z (commonly used in algebra), a, b, c (coefficients in equations)
Role in Equations	Used as fixed values in equations or formulas	Represent quantities that can change and are manipulated in equations
Importance	Fundamental in mathematical calculations and constants in scientific laws	Important in expressing relationships and solving equations in various fields

Mathematical Constants

Mathematical constants are specific numerical values that arise frequently in mathematical calculations and theories such as π (pi). Below is the table of Mathematical Constants:

Constant	Name	Value
π (pi)	Archimedes’ Constant	Approximately 3.14159 . . .
e (Euler’s number)	Euler’s Constant	Approximately 2.71828 . . .
φ (phi)	Golden Ratio	Approximately 2.61803 . . .
γ (Euler-Mascheroni)	Euler-Mascheroni Constant	Approximately 0.57721 . . .
√2	Square root of 2	Approximately 1.414 . . .
√3	Square root of 3	Approximately 1.732 . . .

Constants Written as Variables

In some mathematical contexts, constants may be represented using variables, particularly when the exact value is unspecified or unknown. For instance, “k” may represent a constant rate in exponential growth equations.

Constants Written as Variables

Constant sometimes also is used to represent a variable (but a fixed) value when the exact value of that constant is not known in an expression or a word problem. In general term ‘C’ or ‘c’ is used to represent constant variable value.

Here, “c” is the variable, but its value will always be a “fixed number” when actually writing a polynomial or expression.

In quadratic equation, ax² + bx + c = 0 (c is a constant whose value is unknown)

What is Constant Function?

A constant function is a type of function in which the output value remains constant regardless of the input value. It is represented by a horizontal line on a graph.

Definition of Constant Function

Mathematically, a constant function can be represented as:

f(x) = c

Where c is a constant value. This means that no matter what value of x is chosen, the value of f(x) will always be c. For example, if f(x)=5, then for any input f(x) will always be 5.

Graph of Constant Function

This is represented in the image added below as,

Read More,

• Constant Function
• What is Arithmetic?
• Arithmetic Operations

Examples on Constant in Mathematics

Example 1: Identify the constant term in the given algebraic expression: 3x² + 2xy − 7.

Solution:

Given Expression,

3x² + 2xy − 7

Constant term in the expression is −7

Example 2: Compute the value of the given algebraic expression: 5a + 3 when a = 2.

Solution:

Given Expression,

5a + 3 when a = 2

Substituting a = 2 into the expression,

= 5(2) + 3

= 10 + 3 = 13

Example 3: Solve the equation 2x + 8 = 16 for the value of x.

Solution:

Given Expression,

2x + 8 = 16

Subtracting 8 from both sides,

2x + 8 – 8 = 16 -8

2x = 8

Dividing both sides by 2

2x/2 = 8/2

x = 4

Example 4: Evaluate the the given expression: 4×(3+2)−7.

Solution:

Given Expression,

4 × (3+2) − 7

= 4×5 – 7

= 20 – 7 = 13

Example 5: Find the value of the given algebraic expression for a if 3a – 6 = 15.

Solution:

Given Expression,

3a – 6 = 15

Adding 6 to both sides o

3a = 21

Dividing both sides by 3

a = 7

Practice Problems on Constant in Math

Problem 1: Determine the constant term in the given algebraic expression : 2x² + 5x −9.

Problem 2 : Solve the algebraic equation 3y – 7 = 5 for y.

Problem 3: Compute the value of 2b² – 3 when b = -4.

Problem 4: Simplify the algebraic expression 6 + 4x – 2x for x=3.

Problem 5 : Find the value of c in the given algebraic expression if 2c + 10 = 26.

FAQs on Constant in Math

What is a constant in mathematics?

A constant in mathematics refers to a fixed value that remains unchanged throughout a particular context or problem.

How do constants differ from variables?

Constants maintain a fixed value, while variables can vary and take on different values within a given context or equation.

What is a constant term in an algebraic expression?

A constant term in an algebraic expression is a term that consists solely of a constant. It does not contain any variables and represents a fixed value within the expression.

How can I recognize a constant in an algebraic expression?

Identify terms that do not involve variables and maintain a consistent value regardless of any changes in the variables present in the expression.

What are constant numbers?

Constant numbers are numerical values that do not change and remain constant throughout mathematical operations or equations.

What are arbitrary constants in mathematics?

Arbitrary constants in mathematics are constants introduced into mathematical expressions or equations to represent unknown or unspecified values. They are typically denoted by letters such as “C” or “K” and are used in solving differential equations and other mathematical problems.

Can mathematical operations be performed on constants?

Yes, mathematical operations such as addition, subtraction, multiplication, and division can be performed on constants like any other numerical values, preserving their constant nature.

What is a constant function?

A constant function is a type of function in which the output value remains constant regardless of the input value. It is represented by a horizontal line on a graph.

What are mathematical constants?

Mathematical constants are specific numerical values that arise frequently in mathematical calculations and theories such as π (pi), e (Euler’s number) and φ (phi).

How are constants represented in mathematical expressions?

Constants can be represented using specific numerical values or variables depending on the context of the problem or equation.