Integers

1. Integers on a number line

2. Division of integers

2.1. (-ve) / (-ve) = +ve

2.2. (-ve) / (+ve) = -ve

2.3. (+ve) / (-ve) = -ve

3. Properties of division of integers

3.1. The properties do not hold for division of integers.

3.2. a/0 is not defined

3.3. 0 /a = 0 if a is not equal to 0.

3.4. a / 1 = a

4. Addition & subtraction of integers

5. Multiplication of integers

5.1. (-ve) x (-ve) = +ve

5.2. (-ve) x (+ve) = -ve

5.3. Product of even number of negative integers = Even

5.4. Product of odd number of negative integers = Odd

6. Properties of multiplication of integers

6.1. 0 x a = 0

6.2. Multiplicative identity : a x 1 = a. a is called the multiplicative identity

6.3. Closure : a x b = Integer

6.4. Commutativity :a x b = b x a

6.5. Associativity : a x (b x c) = (a x b) x c

6.6. Distributivity : a x (b + c) = (a x b) + (a x c)

6.7. Distributivity : a x (b - c) = (a x b) - (a x c)

7. Properties of addition and subtraction of integers

7.1. Closure : a + b = Integer

7.2. Closure : a - b = integer

7.3. Commutativity :a + b = b + a

7.4. Subtraction is not commutative

7.5. Associativity : a + (b + c) = (a +b) + c

7.6. Subtraction is not associative

7.7. Additive identity: a+ 0 = a . 0 is the additive identity.