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Ellipse: Definition, Properties, Applications, Equation, Formulas
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Ellipse: Definition, Properties, Applications, Equation, Formulas
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April 8, 2025In algebra, we come across two types of symbols, namely, constants and variables. A symbol with a fixed numerical value in all situations is called a constant. For example,
Do you know there are different types of variables as well? And are you aware that the constant and variable combined form an algebraic expression connected by signs of fundamental operations, i.e.,
A variable is a quantity that may change within the context of a mathematical problem. When a variable is used in a function, we know that it is not just one constant number, but that can represent many numbers. Letters like
Check the figure given below for a better understanding.
Sample this, the taxi fare in Bangalore is calculated as
Thus, what we understood about the variable from the above-given situation can be generalized as ‘a variable is a symbol or an alphabet representing an unspecified term, or which works as a placeholder for an algebraic expression that may vary or change with the situation.
Have a look at the image given below for a better understanding
We have learned about the variables and their usage in algebraic expressions. The term variable is used in statistics also. In statistics, a variable at times is called a data item. It represents the number or, let’s say, characteristics that can be counted or measured. For example, age, income, capital expenditure, gender, and class grades are examples of variables in statistics.
We come across equations with variables such as
Assume you went out to eat pizza at your favourite restaurant. They sell double cheese Margherita for
Now, each double cheese Margherita costs
Did you notice, you just used the variable to help you solve the problem and helped yourself to figure out the number of double cheese Margherita you can buy with the amount you have.
Now let’s solve and find out the number of double cheese Margherita you can have.
And, thus, you can have
We are now thorough with the definition of variables. Variables can be mainly classified into
To understand, let us start with the image given below,
As we can see on the left side of the given image, the amount of water is a type of independent variable. Now, have a look at the other half of the image; we can see that the growth of the plants is dependent on the amount of water given to the plants to nurture. And, since the growth of plants is dependent on the water provided, so, the growth of plants is a type of dependent variable.
1. Dependent variable: A dependent variable is a type of variable that depends on the value of some other number. It can also be characterised as a variable whose output solely depends on the estimation of another variable. In short, the dependent variable is the output of a function. And, thus, the outcome of the dependent variable changes every time if there is a change in the value of an independent variable.
For instance, in the equation
2. Independent variable: According to the algebraic expressions, the independent variable (as they have their own value), does not depend on any other values. It is also known as the input of a function.
For instance, the equation
Apart from dependent and independent variables, there are three more types of variables.
As mentioned above, variables are used in various other fields apart from Maths. Some of the fields where variables are significantly used are as follows:
Q.1. Solve the equation
Ans: The given equation is
Q.2. Find the value of the variable
Ans : Given equation:
Now, substituting
Therefore, the value of
Q.3. When
Ans: When
Hence, the value of the
Q.4. The area,
Ans: Given,
Therefore, the area of the rectangle is
Q.5. Given the formula
Ans: When
Note: The formula
In this article, we learned about the need for variables in real life, and in addition to that, we understood the definition of a variable with the help of examples. In algebra, we come across two types of symbols, namely, constants and variables. A symbol with a fixed numerical value in all situations is called a constant. The constant and variable combined form an algebraic expression connected by signs of fundamental operations, i.e.,
Q.1. What is the definition of a variable?
Ans: A variable is a quantity that may change with the context of a mathematical problem. When a variable is used in a function, it is not just one constant number, but it can represent many numbers.
Q.2. What are the types of variables?
Ans: The types of variables are as follows:
1. Dependent variable
2. Independent variable
3. Random Variable
4. Continuous Variable
5. Categorical Variable
Q.3. What is variable and example?
Ans: A variable is a symbol or an alphabet representing an unspecified term or which works as a placeholder for an algebraic expression that may vary or change with the situation. In the equation,
Q.4. Define dependent variable.
Ans: Dependent variable is defined as a type of variable that depends on the value of some other number.
Q.5. What is an independent variable?
Ans: The independent variable is defined as a type of variable that does not depend on any other values.
Now that you are provided with all the necessary information about variables in Mathematics and we hope this article is helpful to you. If you have any queries on this page, post your comments in the comment box below and we will get back to you as soon as possible.
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