2.  Counting numbers are called natural numbers.  It is denoted by N. N=(1,2,3,4………………)

3.  Natural numbers together with 0 are called whole numbers. It is denoted by W. W=(0,1,2,3,4……………..)

4.  The numbers less than 0 are called negative numbers. -1,-2,-3,-4……….

6.  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……….)

7.  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.

10.  Closure property

15.  So rational numbers are closed under addition.  If a and b are any two rational numbers, then a+b is also a rational number.

17.  So rational numbers are closed under subtraction.  If a and b are any two rational numbers, then a-b is also a rational number.

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

21.  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.