What are the principles or properties of number under addition and multiplication?

Answer 1

The properties are:

Commutativity: Both addition and multiplication are commutative. This means that the order of the operands does not matter: that is x # y = y # x where # represents either operation.

Associativity: Both are associative. That is, the order of the operation does not matter. Thus (x # y) # z = x # (y # z) so that either can be written as x # y # z without ambiguity.

Identity element: There are identity elements for both operations. This means that for each of the two operations there is a unique element, i such that for any element x,

x # i = x = i # x.

The additive identity is 0, the multiplicative identity is 1.

Inverse element: For each element x there is an element x' such that

x # x' = i = x' # x. In the case of addition, x' = -x where for multiplication, x' = 1/x.

Distributivity: Multiplication is ditributive over addition. This means that

a*(x + y) = a*x + a*y