What is a Variable in Math, its Types and Uses?

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In a mathematical expression, a variable refers to an alphabet or term that symbolizes an unknown number, value, or quantity. It is a quantity whose value in most cases can be changed according to the mathematical operation performed. Variables are specifically used in arithmetic, algebra, and geometry. Apart from that, they are also significant for other academic purposes like research, science, statistics, and programming. A common expression of algebra is a linear equation x+9 = 6. Here, x is a variable, whereas 9 and 4 are consonants. If you are confused about what is a variable in math or want to know about its types and uses, read this blog. Here we have shared complete details on the subject.

What Is A Variable In Math?

In simple terms, you can express a variable as the alphabetic character that states a numerical value or a number. In mathematical equations, a variable performs the function of symbolizing an unknown quantity. These variables can be anything between a and z. However, usually, ‘a’, ’b’, ’c’, ‘x’, ’y’, and ‘z’ represents variables in an equation.

To make arithmetic calculations with variables, first, consider them as if they express numbers. It will help you to take care of the scope of variables in a single equation. A typical example of arithmetic calculations with variables is the quadratic formula. You can use it to explain every quadratic condition just by altering the estimated numerical coefficients of the provided condition with that of the given conditions of the variables corresponding to them.

Following is the most common example of a variable in an equation:

y = f(x).

Here, two variables, y, and x are present. They highlight the quality and the contention of the function. The expression “variable” begins with the way the argument shifts, then likewise the quality changes.

Typically, an equation has the following parts:

  • Variable
  • Constant
  • Coefficient
  • Operators
  • Term

Each equation must have a mandatory equal to sign “=” and include terms on both sides of the symbol.

For example, in equation, 4x+9 = 21,

  • X is the Variable
  • 3 is the coefficient of x
  • 9 and 21 are constants
  • ‘+’ is the operator

Also read: What is a Constant in Math? Definition, Examples, and Solved Problems

Examples of Variables

Following are the most common examples of variables:

  • X+2=8
  • Y+3=12
  • 5x-2=10
  • 4x/3=7

In the examples above, x and y are the variables.

Types of Variables in Math

what is a variable in math

You cannot get the complete answer to “What is a variable in math” unless you have an idea of its types. The variables can be broadly classified into two categories. For example,

Also read: Importance of Math in Our Daily Life

·  Dependent Variables

The dependent variable is featured as the variable whose value is based on the calculation of another variable in its condition. It means that the calculation of the word variable is dependent on the free variable of the math condition.

For example, consider the condition y = 4x + 3. Here, the calculation of the variable ‘y’ depends on the changes in the calculation of ‘x’. In this way, the variable ‘y’ is said to be a dependent variable.

·  Independent Variables

In an algebraic equation, an independent variable is a variable whose values do not dependent on the changes. Suppose x and y are two variables in an algebraic equation and every value of x is connected with any other value of y. In that case the values of ‘y’ are called a function of the value of x. Moreover, x is called an independent variable, and the ‘y’ value is termed a dependent variable.

Example: In the mathematic expression y = x2, x is an independent variable and y is a dependent variable.

Thus, you can summarize the variables mathematically as given below:

In mathematics, you can describe variables with the assistance of a function. In simple words, a function is a regulation for considering a number or set of numbers as input and generating an output which may also be a number or set of numbers. The most common feature used to indicate the input is x, and the result is y. Thus, the function can be noted in the form of y = f(x). Here, the character that symbolizes a random input is called an independent variable, like x. In contrast, a symbol that symbolizes a random output is called a dependent variable. Here, it is y.

Apart from these dependent and independent variables, there are other types of variables such as:

·  Random variables

It refers to the formation of a quantity or object that is reliant on random events. However, this term is quite misleading since it is not random or variable. It is a function that has possible outcomes within a sample space.

·  Categorical and continuous variables

It is called an infinite variable if it can presume an infinite number of real values within an infinite space

·  Intervening variables

It refers to the hypothetical internal condition that explains the connection between various observed variables like that of independent and dependent variables.

·   Moderator variables

This refers to a third variable that impact the relationship between an independent and dependent variable.

·   Control variables

An element that remains constant throughout an experiment is termed a control variable.

·   Extraneous variables

An investigating variable that can have an impact on the dependable variables are termed an extraneous variable.

·    Free variables

It is not a factor of a container expression but a symbol that highlights the places of an expression that can be substituted.

·    Bound variables

It refers to a variable whose value has been limited to a specific range.

Also read: Best Math Books To Augment Your Skills

Uses of Variables

Variables are used in 3 areas of mathematics:

·   Algebra

Variables are mostly found in algebraic equations. They symbolize unknown values. Apart from that they are used to create algebraic identities, expressions, and equations.

·   Geometry

In geometry as well, variables symbolize unknown values. It uses a variable to solve problems related to perimeter, area, and volume. Variables help to get precise measurements of the perimeter.

·   Arithmetic

In arithmetic, a variable represents unknown values. Additionally, it is often used to describe a distributive property and commutative property of the following:

  • Addition of two numbers, like a + b = b + a.
  • Multiplication of two numbers, like an x b = b x a.


The discussion above will resolve all queries related to what is a variable in math or what are its types and uses. You can use variables in various branches to solve a variety of mathematical problems.  However, if you need help to understand the context of a variable in a specific part of math or solve the problem, just share your concern with our assignment expert. They will provide detailed s

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