What Have We Discussed?
We now study the properties satisfied by addition and subtraction:
(a) Integers are
(b) Addition is
(c) Addition is
(d) Integer 0 is the
We studied, how integers could be multiplied, and found that product of a positive and a negative integer is a
For example, – 2 × 7 = – 14 and – 3 × – 8 = 24.
Product of even number of negative integers is
Integers show some properties under multiplication.
(a) Integers are closed under multiplication. That is, a × b is an integer for any two integers a and b.
(b) Multiplication is commutative for integers. That is, a × b =
(c) The integer 1 is the identity under multiplication, i.e., 1 × a =
(d) Multiplication is associative for integers, i.e., (a × b) × c =
Under addition and multiplication, integers show a property called
The properties of commutativity, associativity under addition and multiplication, and the distributive property help us to make our calculations easier.
We also learnt how to divide integers. We found that,
(a) When a positive integer is divided by a negative integer, the quotient obtained is
(b) Division of a negative integer by another negative integer gives
For any integer a, we have
(a) a ÷ 0 =
(b) a ÷ 1 =