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

Question

what are the different properties of multiplication of integers define each of the property and give example for each. please define all the properties and please give me an example it is urgent​

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1 month 2021-09-17T09:55:07+00:00 2 Answers 0 views 0

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.

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:)