Nature Numbers
All the counting numbers like 1, 2, 3, . . . . and so on.
Whole Numbers
Natural numbers along with O are whole numbers.
Every narural number is a whole number.
Integers
All the positive numbers, O and negative numbers make up integers.
Eg: . . . . . . . 4, 3, 2, 1, 0, 1, 2, 3, 4, . . . . . are all integers.
O is neither positive nor negative.
The intergers can be represented on the number line as
Numbers that lie to the right side of 'O' area called positive integers.
Numbers that lie to the left side of 'O' are called negative integers.
Absolute Value
The distance of the integers from O irrespective of its sign is the absolute value of that integers.
Addition of Integers
Subtraction of Integers
To subtract one integer from the other, convert the integer to be subtracted to its negative and then add them.
Multiplication of Integers
S.N  Property  Statement  Examples 
1  Closure  If a and b are integers then a \(\times\) b is also an integer.  5 \(\times\) (2) = 10 
2  Commutative  If a \(\times\) b area two integers then a \(\times\) b = b \(\times\) a 
2 \(\times\) (3) = (3) \(\times\) 2 
Associative  If a,b and c are three integers then a \(\times\) (b \(\times\) c) = (a \(\times\) b) \(\times\) c 
2 \(\times\) (3 \(\times\) 4) = (2 \(\times\) (3)) \(\times\) 4 or, 2 \(\times\) (12) = (6) \(\times\) 4 or, 24 = 24 

4  Multiplication by zero 
For any integer 'a' 
(4) \(\times\) 0 = 0 or, 0 \(\times\) (4) = 0 
5  Multiplicative identity  For any integer 'a' a \(\times\) 1 = 1 \(\times\) a = a 
2 \(\times\) 1 = 2 5 \(\times\) 1 = 5 
6  Distributive property  For any integer a,b and c a \(\times\) (b + c) = a \(\times\) b + a \(\times\) c and a \(\times\) (b  c) = a \(\times\) b  a \(\times\) c 
3 \(\times\) (2 + 5) = 3 \(\times\) 2 + (3) \(\times\) 5 
Division of Integer
Properties at Glance
Closure  Commutative  Associative  
Addition  a + b is an integer  a + b = b + a  a + (b + c) = (a + c 
Subtraction  a  b is a integer  a  b \(\neq\) b  a  a  (b  c) \(\neq\) (a  b)  c 
Multiplication  a \(\times\) b is an integer  a \(\times\) b = b \(\times\) a  a \(\times\) (b \(\times\) c) = (a \(\times\) b) \(\times\) c 
Division  a \(\div\) b may or may not be an integer  a \(\div\) \(\neq\) b \(\div\) a  a \(\div\) (b \(\div\) c) \(\neq\) (a \(\div\) b) \(\div\) c 