RATIONAL NUMBERS

Counting numbers are called natural numbers.

It is denoted by N.N=(1,2,3,4………………)

NATURAL NUMBERS

Natural numbers together with 0 are called whole numbers. It is denoted by W.

W=(0,1,2,3,4……………..)

WHOLE NUMBERS

The numbers less than 0 are called negative numbers.

-1,-2,-3,-4……….

NEGATIVE NUMBERS

Number line

The collection of whole numbers and negative numbers are called integers. It is denoted by I or Z.

I or Z=(………. -3,-2,-1,0,1,2,3,4……….)

INTEGERS

The numbers which can be written in the form

of p/q , where q≠0 and p,q are integers are called rational numbers. It is denoted by Q .

for example:- -1/2 ,-5/7, 2/3,0/1 etc.

Rational numbers

Closure property

Properties of Rational Numbers

Whole numbers

INTEGERS

RATIONAL NUMBERSAddition

So rational numbers are closed under addition.

If a and b are any two rational numbers,

then a+b is also a rational number.

conlusion

Subtraction

conclusion So rational numbers are closed under

subtraction. If a and b are any two rational numbers, then a-b is also a rational number.

Multiplication

coclusionSo rational numbers are closed under multiplication.If a and b are any two rational numbers, then axb is also a rational number.

Division

7÷0=not defined So for any rational number a, a÷0 is not defined . So rational numbers are not closed under

division. If a and b are any two rational numbers, then a÷b is not a rational number.

Division by o

Complete the following table

Representation of rational numbers on number line

Rational numbers on number line

Home work