How to do the properties of …

Closure Property

They can be closed under addition and multiplication, i.e., if x and y are two whole numbers then x. y or x+y is also a whole number.

Commutative Property of Addition and Multiplication

The sum and product of two whole numbers will be the same whatever the order they are added or multiplied in, i.e., if x and y are two whole numbers x+y=y+x and x.y=y.x

Additive identity

When a whole number is added to 0, its value remains unchanged, i.e., if x is a whole number then x+0=0+x=x

Multiplicative identity

When a whole number is multiplied by 1, its value remains unchanged, i.e., if x is a whole number then x.1 = x = 1.x

Associative Property 

When whole numbers are being added or multiplied as a set, they can be grouped in any order, and the result will be the same, i.e. if x, y and z are whole numbers then x+(y+z)=(x+y)+z and x.(y.z)=(x.y).z

Distributive Property

If x,y and z are three whole numbers, the distributive property of multiplication over addition is x. (y+z)=(x.y)+(x.z), similarly, the distributive property of multiplication over subtraction is x. (y-z)=(x.y)-(x.z)

Multiplication by zero

When a whole number is multiplied to 0, the result is always 0, i.e., x.0=0.x=0

Division by zero

Division of a whole number by o is not defined, i.e., if x is a whole number then x/0 is not defined.