Variables and Constants in Algebra
LITERALS OR VARIABLES
The letters used to represent numbers or some other quantities in general are called literal numbers or simply literals. Literals can take any value. They are also called variables.
For example,
Rohan borrowed x = Rs. 50 from Suresh;
Mona got y = 16 candies.
Hence, x and y denote numbers and are called literal numbers.
In the formula for the area of a rectangle, the letters ‘l’ and ‘b’ are variables.
In a rectangle of length 16 cm and breadth 5 cm, l = 16 cm and b = 5 cm.
Area of the rectangle (A)
= l × b = 16 × 5 sq cm
= 80 sq cm.
Operations of literal numbers
Since literal numbers or variables are used to represent numbers, they follow all the rules for four fundamental operations of numbers.
- Addition: Let x and y be two literals, then the sum of literals x and y is written as x + y.
Example: The sum of two numbers is 60. In algebraic language we write it as x + y =60 - Subtraction: Let x and y be two literals, then the difference of these two literals is written as x – y or y – x.
Example: x is decreased by y. It is written as x – y. - Multiplication: In algebra, multiplication of two literals x and y is written as either with dot or multiplication sign, i.e., x.y or x × y.
Example: Let x = 6 and y = 5,
then x × y = 6 × 5 = 30 - Division: In algebra, x divided by y is written as x + y.
Example: If x = 3 and y = 5;
then x ÷ y = 3/5 - Power of a literal: If a literal x is multiplied five times by itself then it is written as x × x × x × x × x = x5
(read as x to the power 5)
Similarly,
y × y × y = y3 {y to the power 3)
a × a × a × a = a4 (a to the power 4)
Here, x, y, a are base and 5, 3, 4 are called exponent or power.
CONSTANT
A symbol having a fixed numerical value is called a constant. Its value does not change with the change in question or situation.
Example: The value of number 2 always remains 2, irrespective of the changing situations.