When two positive integers are added, we get a positive integer.  
Eg: 8 + 2 = 10
When two negative integers are added, we get a negative integer.
Eg:  -6 + (-3) = -9
When a positive and a negative integer are added, the sign of the sum is always the sign of the bigger number of the two, without considering their signs.
Eg:  45 + -25 = 20 and –45 + 20 = -25
The additive inverse of any integer a is – a, and the additive inverse of (– a) is a.
Eg: Additive inverse of (-12) = - (-12) = 12
Subtraction is the opposite of addition, and, therefore, we add the additive inverse of the integer that is being subtracted, to the other integer. 
Eg:  23 – 43 = 23 + Additive inverse of 43 = 23 + (- 43) = - 20

The product of a positive and a negative integer is a negative integer.  The product of two negative integers is a positive integer. If the number of negative integers in a product is even, then the product is a positive integer. Similarly, if the number of negative integers in a product is odd, then the product is a negative integer. 

Division is the inverse operation of multiplication.  The division of a negative integer by a positive integer results in a negative integer.  The division of a positive integer by a negative integer results in a negative integer.  The division of a negative integer by a negative integer results in a positive integer.  For any integer p, p multiplied by zero is equal to zero multiplied by p, which is equal to zero.  For any integer p, p divided by zero is not defined, and zero divided by p is equal to zero, where p is not equal to zero.