Integers

Integers are the set of whole numbers and their negatives. It is represented by Z. Z = {…-3, -2, -1, 1, 2, 3, …}. The direction of an integer is indicated by its sign (+ or –), that it is right of 0 or left of 0 on the number line.

Properties of addition and subtraction of integers: a) Integers are closed under addition and subtraction. If a and b are two integers, then (a + b) and (a – b) are also integers.

b) Integers are commutative under addition. {a + b = b + a} c) Integers are associative under addition. {(a + b) + c = a + (b + c)} d) The integer 0 is the additive identity. {a + 0 = a = 0 + a} e) For any integer ‘a’, its additive inverse is ‘–a’.

Multiplication of integers: The product of two positive integers is a positive integer. The product of a negative integer and a positive integer is a negative integer.

The product of two negative integers is a positive integer. The product of even number of negative integers is a positive integer. The product of odd number of negative integers is a negative integer.

Properties of multiplication of integers:

a) Integers are closed under multiplication. { a × b is an integer for any two integers a and b}

b) Multiplication is commutative for integers. { a × b = b × a}

c) The integer 1 is the identity under multiplication. {a × 1= a = 1 × a}

d) Integers are associative under multiplication. {(a × b) × c = a × (b × c)}

Distributive property of integers: a × (b + c) = a × b + a × c Division of a positive integer by a negative integer gives a negative integer as quotient and vice-versa. However, when a negative integer is divided by another negative integer, the quotient obtained is a positive integer. For any integer a, a ÷1 = a and a ÷ 0 is not defined. Keywords: ascending and descending order of integers, predecessor, successor