The set of numbers which consists of natural numbers, additive inverse of natural numbers and zero is known as integers. Thus, integers can either be positive or negative and they have a magnitude and a sign associated with them and are represented using Z or I.
For example: -53, 0, 1237, 31, -102, -401, -355, 86600 etc.
Integers can be located on the real number line as shown below.
The four basic mathematical operations i.e. Addition, subtraction, multiplication, division and the properties related to these operations can be applied to integers as well. In the upcoming discussion we will discuss the properties of multiplication of Integers.
Multiplication is basically repeated addition. Therefore multiplication of integers is the repeated addition as:
Where a and n are both integers.
The properties of multiplication of integers are:
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 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.
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
According to distributive property of multiplication of integers, if a, b and c are three integers then,
a× (b + c) = (a × b) + (a × c)
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