## what are the different properties of multiplication of integers define each of the property and give example for each. please define all th

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Answer:closure property,Associativity, commutative, existence of identity

1. closure property

the product of two integers is an integer.

for any a, b £ Z

then ab belongs to Z

2. Associativity

for any a, b, c £Z

(ab) c=a(bc) for all a, b, c belongs to Z

there fore multiplication of Z is associative

3. existence of identity

the element 1£Z satisfies the condition

a×1=a=1×a for all a belong to Z

there fore 1 £Z is the identity for the multiplication

4 commutativity

for any a, b£Z

ab =ba for all a, b £Z

multiplication of integers is commutative.

Answer:The properties of multiplication of integers are:

#Closure Property

According to this property, if two integers a and b are multiplied then their resultant a × b is also an integer. Therefore, integers are closed under multiplication.

a × b is an integer, for every integer a and b

#Commutative Property

The commutative property of multiplication of integers states that altering the order of operands or the integers does not affect the result of the multiplication.

a × b = b × a, for every integer a and b

#Multiplication by zero

On multiplying any integer by zero the result is always zero. In general, if a and b are two integers then,

a × 0 = 0 × a = 0

#Multiplicative Identity of Integers

On multiplying any integer by 1 the result obtained is the integer itself. In general, if a and b are two integers then,

a × 1 = 1 × a = a

Therefore 1 is the Multiplicative Identity of Integers.

#Associative Property

The result of the product of three or more integers is irrespective of the grouping of these integers. In general, if a, b and c are three integers then,

a × (b × c) = (a × b) × c

#Distributive Property

According to the distributive property of multiplication of integers, if a, b and c are three integers then,

a× (b + c) = (a × b) + (a × c)

HOPE THIS HELPS:)