Properties of multiplication
    (i)    Closure Property : If a and b are whole numbers, then their product a x b = c will always be a whole number. That is whole numbers are closed under multiplication.
        For ex.     7 x 3  = 21x 6 x 8 = 48 x 3 x 0 = 0  

    (ii)    Commutative Property :  In general a x b = b x a  for all whole numbers a and b.
        Consider the following example
            2 x 3 = 3 x 2 = 6
            8 x 9 = 9 x 8 = 72

    (iii)    Associative Property : If a,b and c are whole numbers, then (a x b) x c = a x (b x c)
        That is, whole numbers have the associative property of multiplication.
        For ex.    (3 x 4) x 2 = 3 x  (4 x 2)
            12 x 2 = 3  x 8
            24 = 24

    (iv)    Multiplicative Identity : 1 x a = a x 1 = a. Hence, 1 is called the multiplicative identity for whole numbers.
        For ex.              10 x 1 = 1  x 10  = 10
                     3  x 1  = 1 x 3  = 3
                  672  x 1 = 1  x 672 = 672
                       0 x 1 = 1 x 0 = 0

Properties of division

(i)    Closure Property : If a and b are whole number , then the quotient a ÷ b need not always be a whole number. So, division in whole numbers is not closed.

Commutative Property : If a and b are whole numbers, then a ÷ b is not equal to b ÷  a. So, the commutative property does not hold true for whole numbers.

Related Topic Name

1. Introduction to The Whole Numbers