Theory:

Let's recall what we have learned about integers and its properties.
  
Integers:
Integers are the set of positive and negative numbers and zero. It is nothing but a whole number with negative numbers.
num.png
  
The properties of integers:
  
The following are the properties associated while performing operations with integers:
  • Closure
  • Associative
  • Distributive
  • Commutative
  • Identity.
The table below will make you understand all the properties of integers regarding the mathematical operations:
 
 Property
Addition
Subtraction
Multiplication
Division
Associative
Yes
No
Yes
No
Closure
Yes
Yes
Yes
No
Commutative
Yes
No
Yes
No
Identity
Yes
Yes
Yes
Yes
Inverse
Yes
Yes
No
No
 
Now we will see application-oriented problems in this chapter using all the properties of integers.