Question

How can we understand commutative property, closure property, associative property, distributive property

Answer 1

Closer property

If x and y are any two natural number then if you add them together you will get a a result in Natural number too..for example 2 and 5 are natural number , if we add them together we get result 2 + 3 = 5 , 5 is a natural number too...This is a one of the property of natural number so called Closer Property.

Associative Property :

1- a + ( b + c ) = ( a + b ) + c under Addition
2- a x ( b x c ) = (a x b ) x c. under Multiplication

For example :
Under Addition :
2 + ( 3 + 4 ) = 2 + 7 = 9
( 2 + 3 ) + 4 = 5 + 4 = 9
Thus LHS = RHS...

Under Multiplication :
2 × ( 3 × 4 ) = 2 × 12 = 24
( 2 × 3 ) × 4 = 6 × 4 = 24..
LHS = RHS..

Distributive Property

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

Example :

2 × ( 4 + 2 ) = 2 × 6 = 12
2 × 4 + 2 × 2 = 8 + 4 = 12
Thus LHS = RHS...

Commutative Property

Commutative Property under Addition
For any two natural number a and b
a + b = b + a
This property is known as Commutative property under Addition(See the opertaion between the number) For example : 2 +3 = 3 +2


Commutative Property under Multiplication:
a x b = b x a where a and b are any natural numbers...
For example : 2 × 3 = 3 × 2