The natural numbers
1, 2, 3, ...
are used for counting, and for labeling the terms of an infinite sequence. They obey the following laws.
Associative law of addition:
(a + b) + c = a + (b + c).
Commutative law of addition:
a + b = b + a.
Cancellation law of addition:
If a + c = b + c, then a = b.

Distributive law with multiplication on the left:
a.(b + c) = a.b + a.c.
Distributive law with multiplication on the right:
(a + b).c = a.c + b.c.

Associative law of multiplication:
(a.b).c = a.(b.c).
Commutative law of multiplication:
a.b = b.a.
Cancellation law of multiplication:
If a.c = b.c, then a = b.
So we can see examples of natural numbers to explain these .