A variable is like a placeholder or a box that can hold different values. In math, it's often represented by a letter, like x or y. The value of a variable can change depending on the situation. For example, if you have the equation y = 2x + 3, the value of y depends on the value of x. So, if you change x, the value of y will change too i.e., if x = 2, then y = 2(2) + 3 = 7.
Some more examples of variables in real life are:
- If you buy 3 apples, each costing x dollars, how much do you pay?
- Where x is the changing price of apple due to season change.
- F = (9/5)C + 32
- In this formula, C is the temperature in Celsius, and F is the temperature in Fahrenheit.
- C=0, then F = (9/5)(0) + 32 = 32 degrees Fahrenheit.
Types of Variables
Variables can be classified into different types based on their characteristics including independent variables, dependent variables, discrete variables and continuous variables each serving distinct purposes in mathematical world.
Listed below are different types of variables:
- Independent Variables: These are variables that can be freely chosen or manipulated. They represent inputs or factors that influence the outcome of a mathematical relationship or function.
Eg: The time spent studying (in hours) before an exam. This variable can be freely chosen or manipulated by the student.
- Dependent Variables: Dependent variables are determined by the values of other variables in a mathematical equation or system. They represent the outputs or results of a mathematical relationship or function.
Eg: The score obtained on the exam. This variable is determined by the amount of time spent studying and represents the outcome of the study effort.
In algebra, one variable is defined in terms of other variable,
Besides dependent and independent variables, there are other classifications of variables in mathematics based on the nature or types of things that the variable can represent. Some of these types are:
- Discrete Variables: Discrete variables are those that can only take on specific, distinct values. They are often associated with counting or categorizing, such as the number of students in a class or the outcomes of a dice roll.
Eg: The number of books on a shelf. This variable can only take on specific, distinct values, such as 0, 1, 2, 3 and so on but cannot take fractional or continuous values.
- Continuous Variables: Continuous variables can take on any value within a certain range or interval. They are typically associated with measurements or quantities that can be infinitely divided such as time, distance or temperature.
Eg: The height of students in a class. This variable can take on any value within a certain range such as between 150 cm and 200 cm and can be infinitely divided into smaller units.
- Categorical Variables: Categorical variables represent qualitative characteristics or attributes that can be divided into distinct categories or groups. Examples include gender, nationality, or type of vehicle.
Eg: The type of car owned by individuals (e.g., sedan, SUV, truck). This variable represents qualitative characteristics or categories that cannot be ordered or measured on a numerical scale.
Note: We can add, subtract, multiply, or divide variables in the same way as numbers, but the result depends on the values assigned to the variables. For example, x + y will give a different result depending on the values of x and y, and x ÷ y is valid only if y ≠ 0.
Also read Random Variables in Probability.
Uses 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,
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.
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