Variable in Maths
Last Updated :
26 May, 2024
In mathematics, variables are used for substitute values that allow us to solve problems and equations in various ways. Suppose, we must consider the space must be filled with numbers. Even though, they allow us to represent variable or unknown values.
For Example: Let’s consider If we have an equation like “x + 5 = 10,” the “x” is a variable that represents the number we want to find. So, now we answer the problem after determining what “x” is. Therefore, In this example, x is equal to 5.
In this article, we’ll look at the concept of variables in mathematics.
Variable Definition
A variable is an alphabet that represents an unknown quantity. A variable is a quantity that can be changed based on a mathematical issue. The general letters used in many algebraic expressions and equations are x, y, and z. In other words, a variable is a sign representing a number whose value is unknown.
Variable in Algebra
Variables are algebra’s essentials Even, their symbols are usual letters such as x, y, and z, that denote unknown numbers or values.
- Versatility: Variables can change values throughout a problem or equation. It allows us to investigate many scenarios and develop generic solutions.
- Relationships: Variables can be used to describe relationships between unknown quantities. For example: The given equation is 2a + b = 5. So, In this equation, we will see the link between a and b.
Examples of Variables
Example 1: Solve for x in the equation 3x + 5 = 17.
Solution:
3x + 5 = 17
⇒ 3x = 17 – 5
⇒ 3x = 12
⇒ x = 12/3
⇒ x = 4
Therefore, the value of “x” in the given equation is 4.
Example 2: Solve for “x” in the equation x2 − 4x + 3 = 0.
Solution:
x2 − 4x + 3 = 0
⇒ (x -3) (x – 1) = 0
Now, Let’s set each factor equal to 0.
(x -3) = 0 ⇒ x = 3
⇒ (x – 1) = 0 ⇒ x = 1.
Example 3: Solve x in the equation 2/x = 3.
Solution:
2/x = 3
⇒ 2 = 3/x
⇒ x = 2/3
Therefore, the value of x is 2/3.
Constant in Math
Constants are dependable and unchangeable integers in a mathematical expression or equation.
- Fixed values: In Constants, the number that has a consistent value throughout the equation does not differ or change within the context of the expression. Suppose, the equation is 2x + 4 = 10. Here, 4 is the fixed value.
- Coefficients: Constants can also be used as coefficients to multiply variables in expressions. Therefore, The equation 2y + 3 = 7 uses the number 2 as a coefficient, which multiplies the variable y. It specifies the rate at which the variable influences the expression.
Variable in Statistics
Variables are the fundamental components of statistical analysis that represent the characteristics we want to measure or observe within a population or sample. Assume you are studying the heights of kids in a classroom. “Height” is the variable. Each student’s exact height measurement would be a data point.
Some major points of Variable in statistics:
- Variables can represent the values measured or seen in data points. For example: in a height study, height would be the variable, with each person’s height serving as a data point.
- Variables can be used to define population parameters or sample statistics. For example: The variable denoting height represents both the population mean (µ) and the sample mean (x̄).
Types of Variables in Math
There are two variables in maths that are as follows;
- Dependent Variables
- Independent Variables
Dependent Variables
The dependent variables illustrate the effects of changing or introducing the independent variables. For Example: In a study examining the effects of various teaching methods on student performance, the dependent variable would be the students’ test scores, as they represent the outcome influenced by the teaching methods.
Independent Variables
The independent variables are those over which the researcher has direct control. This ‘control’ might include manipulating the current variables, such as changing the existing methods of the instruction. For Example: In a classroom experiment, the independent variable would be the teaching method used, with one group receiving standard instruction and the other receiving an unusual teaching approach.
Operations on Variables
Variables are manipulated in mathematical expressions or equations. These operations include addition, subtraction, multiplication, division, and exponentiation. Even though, They allow us to conduct calculations and solve problems in a variety of mathematical contexts. So, Some of the common operations are given below with the example;
- Arithmetic operations include +, -, *, and /. Even, They even allow you to combine variables and numerical quantities to produce new values. For Example: Let’s consider buying oranges at Rs.10 each (x) and bananas at Rs.20 each (y). Therefore, to calculate the total cost (T) of buying “2 oranges” and “12 bananas”. This can be expressed as the equation T = 2x + 12y.
- Exponentiation (x^y) increases a variable (x) to the power of another number (y). For Example: The area of a square can be stated as s^2, where s is the length of its side.
- Advanced Expressions can produced by combining fundamental operations. For example: (2x + 5y) / (z – 3) requires several arithmetic operations on variables.
Application of Variables
Some of the applications of variables are given below;
- Generalize formulas: One formula (e.g., area = l x w) works for all rectangles by using variables for length (l) and width (w).
- Solve problems: Find unknowns in equations (e.g., 2x + 5 = 11) by manipulating variables (x).
- Model real-world: Variables represent quantities in physics (e.g., F = ma) to understand how things work.
Read More,
Variable – FAQs
What is variable?
A variable in mathematics, is a symbol (such as x, y, or z) that can be represents as an unknown number and allows us to experiment with alternative values while solving problems.
What are dependent variables?
The dependent variables illustrate the effects of changing or introducing the independent variables. For Example: In a study examining the effects of various teaching methods on student performance, the dependent variable would be the student’s test scores, as they represent the outcome influenced by the teaching methods.
What is an independent variable?
An independent variables are those over which the researcher has direct control. This ‘control’ might include manipulating the current variables, such as changing the existing methods of the instruction.
What is a random variable?
A random variable in statistics is a mathematical concept that describes the outcome of a random experiment whose value is not guaranteed but is determined by chance.
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