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Constants and Variables are two very important terms in the subject of Mathematics. They are well-known in the fields of Algebra, Trigonometry and practically in all branches of Mathematics. A variable is a value that changes or has the possibility to change. A constant is a value that does not vary over time. The primary difference between constants and variables is that constants are fixed values, whereas variables are often used to represent uncertain or changeable values in order to reflect scientific situations. For instance, in x + y = 7, x and y are variables and 7 is a constant.
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Key Terms: Constants, Variables, Algebra, Trigonometry, Integers, Irrational Numbers, Alegrbraic Formula, Equations, Fractions, Decimals, Rational Numbers
What are Constants?
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A constant is defined as a term that has a fixed numerical value. Constant value never changes. Constants are typically expressed as numbers, such as 12 or -4, 8/3, and so on. Numbers and integers are used in order to represent constants. Some essential constants on the other hand can have names and symbols that are recognised throughout Mathematics and Science. For example: 3, 5,9, 8,7/2, 5/2 are constant values.
Now, consider the algebraic formula 5a + 2b = 11, here, the number 11 is a constant. However, 5a and 2b are not constants since variables a and b can alter their values.
Read More: Addition and Subtraction of Integers
What are Variables?
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A variable is not a fixed-term and refers to a value that can be altered over time. Anything other than a constant number can be used to represent a variable. The letters x, y, z etc, are mostly used to represent variables. A variable is represented by a letter such as x, y, z, u, v, and more. The Greek letters like θ are used to represent variable angles, for which the worth of a variable fluctuates from time to time.
Variables are crucial to solve a lot of problems in Mathematics.
For example, in the algebraic equation 5a + 2b = 11, a and b are variables that vary depending on the equation.
Variables
Read More: Linear Equation in Two Variables
Difference Between Constants and Variables
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Constants and Variables are two terms that are very essential in the field of Mathematics and related concepts. Here are the key differences between Constants and Variables:
| Constants | Variables |
|---|---|
| A constant’s value is fixed and it doesn’t change over time. | A variable’s value is not fixed, it changes according to the equation. |
| Constants are usually denoted using numbers that can be negative as well as positive integers. Apart from that, irrational numbers like pi are also constants. | Variables are commonly represented using alphabets be it in English or Greek, etc. |
| Constants are used in computer languages. | Variables are also used in computer applications. |
| Constants have already known face value. | Variable values are mostly unknown. |
| Constants' values are fixed, one can’t customize the value of a constant by themselves. | The value of a variable can be customized. One can choose it from any language, using uppercase or lowercase letters, or even use words for variables. |
| For instance, in the equation 5b + 10 = 33, 10 and 33 are both constants. | For instance, in the equation, 5b - 13y = 21, b and y are variables. |
Constants and Variables
Things to Remember
- Constants are typically represented by numbers. These can be both positive and negative integers and even irrational numbers like 1 and π etc.
- Variables are defined as a value that can be altered over time. They can also have no value if we conclude that the equation has no solution in some instances.
- Whole numbers, fractions, decimal numbers, rational or irrational numbers are all examples of constants.
- The height and weight of a person are variables because they do not always remain constant.
- Variable angles are represented by Greek letters such as θ as the value of variable changes with time.
Sample Questions
Ques. Find the variables and constants in given equations:
a.2x = 8
b.x – y = -8. (4 Marks)
Ans. (a) 2x = 8
Here, x is variable and 8 is the constant value.
If we simplify further that equation,
2x = 8
x = 8/2
x = 4
Here 4 is constant and x is variable.
(b) x – y = -8;
Here, -8 is the constant value & x and y are the variables.
Ques. Find the value of x in given equations:
(a) 2x+4 = 14
(b) 8x = 64. (4 Marks)
Ans. (a) Given that 2x +4 = 14
2x = 14-4
2x = 10
x = 10/2
x = 5.
(b) Given: 8x = 64
x = 64/8
x = 8.
Ques. Find the value of x for equation 3x + 9 =36. (3 Marks)
Ans. Given: 3x +9 = 36
3x = 36- 9
3x = 27
x = 27/3
x = 9.
Therefore, the value of x is 9.
Ques. Find the value of x for the equations:
(a) x +2 = -10
(b) x +3 = -12 (4 Marks)
Ans. (a) Given: x +2 = -10
x= -10 -2
x = -12.
Therefore, the value of x is -12.
(b) Given: x +3 = -12
x = -12 -3
x = -15
Therefore, the value of x is -15.
Ques. Find the value of x for the equation 4x +8 = -36. (3 Marks)
Ans. Given;
4x +8 = -36
4x = -36 -8
4x = -44
X = -44/4
x = -11.
Therefore, the value of x is -11.
Ques. Find the value of x for the equations:
(a) x +2 = 16
(b) 2x +6 = -180 (4 Marks)
Ans. (a) Given: x +2 = 16
x= 16-2
x = 14.
Therefore, the value of x is 14.
(b) Given: 2x +6 = -180
2x = -180- 6
2x = -186
x = -186/2
x = -93.
Therefore, the value of x is -93.
Ques. Find the value of x for the equation 4x +18 = -72. (3 Marks)
Ans. Given;
4x +20 = -72
4x = -72 -20
4x = -92
x = -92/4
x = -23.
Therefore the value of x is -23.
Ques. What is the value of x in the given equation x+2= 10? (2 Marks)
Ans. Given: x+2= 10
x= 10-2
x = 8.
Ques. Find the value of x for the equations:
(a) x +8 = 40
(b) 5x +5 = 195 (4 Marks)
Ans. (a) x +8 = 40
x= 40-8
x = 32.
Therefore, the value of x is 32.
(b) Given: 5x +5 = 195
5x = 195- 5
5x = 190
x = 190/5
x = 38.
Therefore, the value of x is 38.
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