Properties of natural numbers with examples
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
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
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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