5) Properties of multiplication of integers with one example each.
Answers
Answer:
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)