WHAT IS ALGEBRA ? -
EXAMPLES WITH A PATTERN -
ARITHMETIC WITH LITERALS

Before proceeding further,
see the Algebra page
What is Algebra
if you have not already done so.

You might have already studied numbers, operations on numbers and properties of numbers. you might have applied the knowledge to various problems.

The branch of mathematics in which you studied numbers is ARITHMETIC.

Let us see an example from Arithmetic.

Example 1 of What is Algebra :

Suppose on your birthday, you want to give 2 chocolates per student.

How many chocolates are needed

i) if there are 10 students?
ii) if there are 20 students?
iii) if there are 30 students?
iv) if there are 40 students?

You are ready to answer the question as

i) chocolates needed = 2x10 = 20.
ii) chocolates needed = 2x20 = 40.
iii) chocolates needed = 2x30 = 60.
iv) chocolates needed = 2x40 = 80.

Did you observe any pattern?

I am sure you understand, if I write

chocolates needed = 2xNumber of students.

or more simply, chocolates needed = 2xN
where 'N' stands for Number of students.

suppose, you want to give 3 chocolates per student instead of 2,
How many chocolates are needed?

I am sure you can answer it as
chocolates needed = 3xN.

If you want to distribute 4 chocolates per student,
chocolates needed = 4xN.

So, chocolates needed = CxN
where C stands for chocolates per student
& N stands for Number of students.

CxN is the generalised answer for the chocolates needed.

This is what Algebra deals with.

So you can say,

Algebra also deals with numbers, but in a general way.
Here Letters are used to represent Numbers.

We observe that use of letter symbols for numbers enables us to generalise oft repeated numerical statements.

Let us see one more example.

Example 2 of What is Algebra :

Your mother has made some sweets. She wants to keep 5 sweets for you, after distributing some sweets to guests and family members.

How many sweets your mother should make

i) if she distributes 12 sweets to guests and family members.
ii) if she distributes 15 sweets to guests and family members.
iii) if she distributes 19 sweets to guests and family members.
iv) if she distributes 25 sweets to guests and family members.

You answer is,
i) The number of sweets mother should make = 12+5 = 17.
ii) The number of sweets mother should make = 15+5 = 20.
iii) The number of sweets mother should make = 19+5 = 24.
iv) The number of sweets mother should make = 25+5 = 30.

Are you ready to answer in a general way as,
The number of sweets mother should make is: n+5
where 'n' stands for the number of sweets to guests and family members.

Suppose your mother wants to keep 10 sweets for you instead of 5,
then the answer is n+10.
or if your mother wants to keep 25 sweets for you
then the answer is n+25.

can you say the number of sweets mother should make is: n+m
where 'n' stands for the number of sweets to guests and family members
and 'm' stands for the number of sweets for you.

Congratulations. You have caught the spirit of algebra.

Now, you are in a position to define Algebra.

Before defining, let us know the name given to the letter symbols
( 'C' and 'N' in Example 1 and 'n' and 'm' in Example 2 )
standing for numbers.

They are called literal numbers or simply literals.

Thus the question "What is Algebra ?" can be answered as

ALGEBRA is generalized arithmetic in which numbers are represented by letters called literal numbers or simply literals.

By using literals, we can talk about any number and not just a particular number. This allows us to write rules and formulas in a general way.

For further discussion on What is Algebra and links
to Basic Algebra and other Algebra Topics, Go to

ALGEBRA 1 HELP