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 DIVISION When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and viceversa. Division of a negative integer by another negative integer gives a positive integer as quotient. For any integer a, we have
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