Page 157 - Maths Class 06

Introduction to Algebra

Introduction

So far we have been using whole numbers, natural numbers viz., 1, 2, 3, 4,…, etc. and operations on
numbers such as ‘addition’, subtraction, ‘multiplication’ and ‘division’.
We have used these numbers in finding out the solution of various problems in our life. This branch of
mathematics in which we deal with numbers is called arithmetic.

Also, we have studied another branch of mathematics called geometry in which we have studied about
various figures such as ‘triangle’, ‘square’, ‘circle’ and their various properties. Now we will study another
such branch called algebra.

What is Algebra?

Algebra is a branch of mathematics which uses literals in various arithmetical calculations.
In other words we can say that in algebra, the numbers are represented by the letters.

Difference Between Arithmetic and Algebra

The basic difference between the two is that in arithmetic an operation on numbers can be performed but
in algebra it can only be indicated.
Suppose we have two numbers say 2 and 3. In arithmetic we can perform various operations on these
numbers such as addition and multiplication.

For example, one can say that 2 3+ = 5 and 2 3´ = 6, etc.
But if we replace these numbers by letters x and y, we cannot simply say that, x + y = z or x ´ y = S.
We can only indicate that x added to y is x + y and x
NOTE
multiplied to y is xy, etc.
Any rule or principle used in algebra
Thus in algebra when we say that x + y = z; means that the
applies equally well to arithmetic.
sum of any two numbers x and y is equal to the number
represented by z.
Concept of Generalization
In arithmetic we use the concept of generalization, i e. . we look for a set pattern in the problem given and
then find the solution of unknown terms.

For example, study the number series given below:
3, 6, 9, 12, 15, 18, 21, 24,…

Can the next term be found out? Yes, it will be 27. Now suppose one is asked to find the 150th term. It
looks very difficult and time consuming but if we generalize the series then it becomes very easy to
predict any term whatsoever. If you look at the series, you will find out that, in the series, each term is a
multiple of 3. So the formula 3n can be given for it where ‘n’ is any number.

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