PROPERTIES OF ADDITION AND SUBTRACTION OF INTEGERS

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MULTIPLICATON OF INTEGERS

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PROPERTIES OF MULTIPLICATION OF INTEGERS

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DIVISION

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

as quotient.

For any integer

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 b3.

__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

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__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 a3.

__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 cDIVISION

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

as quotient.

For any integer

*a*, we have*a*÷ 0 is not defined*a*÷ 1 =*a*