Properties of Whole numbers with examples

Properties of Whole Numbers

Addition Properties of Whole Numbers:

1. Closure Property:  The sum of two whole numbers is always a whole numbers.

Example: Let two whole numbers 5 and 7 then 

                          5 + 7 = 12 is a whole number.

2. Commutative Property: Let a and b are two whole numbers,

                                               a + b = b + a 

Example: Let two whole numbers are 5 and 6 then 

                 5 + 6 = 11 

                 6 + 5 = 11  

then        5 + 6 = 6 + 5 

Hence commutative property is verified
3. Associative Property:  Let a, b and c are three whole numbers,
                                            a + ( b + c) = (a + b ) + c
Example: Let three whole numbers are 3, 5 and 6 then
                  3 + ( 5 + 6 ) = 3 + 11 = 14
                  (3 + 5 ) + 6  =  8 + 6  = 14
 then          3 + ( 5 + 6 ) =  (3 + 5 ) + 6 
Hence Associative property is verified
4. Existence of Additive Identity:  For any whole number a ,  we have          a + 0 = 0 +a = a 
0 is called the additive identity.
Example: 4 is any whole number, 
                 4 + 0 = 0 + 4 = 4

 Multiplication Properties of Whole numbers:

1. Closure Property:  The product of two whole numbers is always a whole numbers.

Example: Let two whole numbers 3 and 5 then 

                           3 x 5 = 15 is a whole number.

2. Commutative Property: Let a and b are two whole numbers,

                                               a x b = b x a 

Example: Let two whole numbers are 3 and 7 then 

                 3 x 7 = 21 

                 7 x 3 = 21  

then        3 x 7 = 7 x 3 

Hence commutative property is verified
3. Associative Property:  Let a, b and c are three whole numbers,
                                            a x ( b x c) = (a x b ) x c
Example: Let three whole numbers are 3, 5 and 6 then
                  3 x ( 5 x 6 ) = 3 x 30 = 90
                  (3 x 5 ) x 6  = 15 x 6  = 90
 then          3 x ( 5 x 6 ) = (3 x 5 ) x 6 
Hence Associative property is verified
4. Existence of Multiplicative Identity: For any whole numbers a, we have          a x 1 = 1 x a = a 
0 is called the additive identity.
Example: 5 is any whole number, 
                 5 x 1 = 1 x 5 = 5
5. Distributive Property of Multiplication over Addition: Let a, b and c are three whole numbers,

                 a x ( b + c ) = a x b + a x c

Example: Let 2, 3 and 4 are three whole numbers,

                2 x ( 3 + 4 ) = 2 x 7 = 14

               2 x 3 + 2 x 4 = 6 + 8 = 14 

Hence Distributive property is verified.