Properties of natural numbers with examples

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Properties of Natural Numbers

Addition Properties of Natural Numbers:

1. Closure Property:  The sum of two natural numbers is always a natural numbers.
Example: Let two natural numbers 2 and 5 then 
                          2 + 5 = 7 is a natural number.
2. Commutative Property: Let a and b are two natural numbers,
                                               a + b = b + a 
Example: Let two natural numbers are 5 and 7 then 
                 5 + 7 = 12 
                 7 + 5 = 12  
then        5 + 7 = 7 + 5 
Hence commutative property is verified
3. Associative Property:  Let a, b and c are three natural numbers,
                                            a + ( b + c) = (a + b ) + c
Example: Let three natural 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 natural number a ,  we have          a + 0 = 0 +a = a 
0 is called the additive identity.
Example: 4 is any natural number, 
                 4 + 0 = 0 + 4 = 4

 Multiplication Properties of Natural numbers:


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

Example: Let two natural numbers 2 and 5 then 

                           2 x 5 = 10 is a natural number.

2. Commutative Property: Let a and b are two natural numbers,
                                               a x b = b x a 
Example: Let two natural numbers are 5 and 7 then 
                 5 x 7 = 35 
                 7 x 5 = 35  
then        5 x 7 = 7 x 5 
Hence commutative property is verified
3. Associative Property:  Let a, b and c are three natural numbers,
                                            a x ( b x c) = (a x b ) x c
Example: Let three natural 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 + ( 5 + 6 ) =  (3 + 5 ) + 6 
Hence Associative property is verified
4. Existence of Multiplicative Identity: For any natural number a, we have          a x 1 = 1 x a = a 
0 is called the additive identity.
Example: 4 is any natural number, 
                 4 x 1 = 1 x 4 = 4



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