PROPERTIES OF ADDITION AND SUBTRACTION OF INTEGERS
1. Closure under addition: The sum of two integers is an integer. For any two integers a and b, a + b is also an integer.
2. Closure under subtraction: The difference between two integers is an integer. For any two integers a and b, a – b is also an integer.
3. Commutative property: Addition is commutative for integers i.e. a + b = b + a. However, subtraction is not commutative.
4. Associative property: Addition and subtraction both are associative for integers i.e. ( a + b ) + c = a + ( b + c ),
5. Additive identity: Zero is the additive identity for integers. Adding zero to any number gives the number itself.
MULTIPLICATON OF INTEGERS
1. Multiplication of a positive and a negative integer: Multiply the integers as whole numbers and the put a minus sign before the product i.e. a x -b = - (a x b)
2. Multiplication of two negative integers: Multiply the negative integers as whole numbers and put a positive sign before the product i.e. (-a) x (-b) = a x b
3. Product of three or more negative integers: Product of even number of negative integers is positive and the product of odd number of negative integers is negative.
PROPERTIES OF MULTIPLICATION OF INTEGERS
1. Closure under multiplication: The product of two integers is an integer.
2. Commutative property: Multiplication is commutative for integers i.e. a x b = b x a
3. Multiplication by zero: Any integer multiplied by zero gives zero.
4. Multiplicative identity: 1 is the multiplicative identity for integers. Any integer multiplied by 1 gives the integer itself.
5. Associative property: Multiplication is associative for integers i.e. (a x b) x c = a x (b x c)
6. Distributive property: Multiplication over addition is distributive for integers i.e. a x (b + c) = a x b + a x c
When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.
Division of a negative integer by another negative integer gives a positive integer
For any integer a, we have