When we calculate something using with some symbols to denote unknown or known numbers such method is known as Algebra.
Algebra is the sibling to geometry, analysis (calculus), number theory etc. this is a powerful tool for problem solving in science, engineering, economics, finance, architecture, ship-building and many other day-to-day.
In India many great Indian mathematicians, Aryabhatt (born 476AD), Brahmagupta (born 598AD), Mahavira (who lived around 850AD) and Bhaskara II (born 1114AD) and others, contributed a lot to the study of algebra. They gave names such as Beeja etc. So, in india this is called beejaganit.
The word‘algebra’ is derived from the title of the book, ’aljebar w'al almugabalah’, written about 825AD by an Arab mathematician, Mohammed Ibn Al Khowarizmi of Baghdad.
When you play with two match-sticks you can make many shapes, alphabets, numbers.
This patterns teach us that any two or more things you can make many things, So calculating that many thing to be assume in a alphabet and discover the result.
Number of matchsticks required = 2 x n.
Instead of writing 2 x n, we write 2n. Note that 2n is same as 2 x n.
Assuming that alphabet n is an example of a variable. So the variable has some value and that's value will be not fixed; it can take any value 1, 2, 3, 4, ... .etc.
For example-:
Number of matchsticks required = 2n
Making more shapes, numbers or anything comes with different patterns of idea.
So Making different and calculating that with the assumption.
Number of matchsticks required = 3n or 4a etc.
You can use any letter as a, b, m, l, p, x, y, z etc. to show a variable. But always remember, a variable is a number which does not have a fixed value.
There are some certain common rules in mathematics that we have already learnt are expressed using variables.
The perimeter of a square = Sum of the lengths of the sides of the square
= 4 times the length of a side of the square
= 4 x l = 4l.
Perimeter of a rectangle = length of AB + length of BC + length of CD + length of AD
= 2 x length of CD + 2 x length of BC = 2l + 2b
A number expression like (4 x 3) + 5 can be immediately evaluated as (4 x 3) + 5 = 12 + 5 = 17
But an expression like (4x + 5), which contains the variable x, cannot be evaluated. Only if x is given some value, an expression like (4x + 5) can be evaluated.
This expressions can be practically with some of story that we assuming and calculate there values.
Take Sarita's present age to be y years
What will be her age 5 years from now?
What was her age 3 years back?
Equation is a condition on a variable that satisfied only for a definite value of the variable. A statement that equality of two expressions means what is on the left side is equal to what is on the right side.
An equation has an equal sign (=) between its two sides.
x − 3 = 11
When the value of the variable in an equation which satisfies the equation is called a solution to the equation.
x− 3 = 11
x= 11 + 3
=14
So the value of x = 14.