Rational Numbers: A rational
number is a number which can be expressed in the form of
p/q where p and q are and is not zero. It is denoted by Q.
Properties Law for Addition:
a) Commutative Law for addition:
A + b = b + a
where a, b ε Q
b) Associative Law for addition:
(a + b)+ c = a + (b + c)
where a, b, c ε Q
c) Additive Identity:
The rational
number 0 is such that
a
+ 0 = 0 + a = a where a ε Q d) Additive inverse:
To each a ε Q, there is a
number  a ε Q i.e.
a + (a) = (a) + a = 0
e) Commutative Law for
Multiplication:
a
. b = b . a where
a, b ε Q
f) Associative Law for
Multiplication:
(a . b) . c = a . (b . c) where
a, b c ε Q
g) Multiplicative identity:
The rational number 1
(unity), is such that
1
. a = a . 1 = a where
a ε Q
h) Multiplicative Inverse:
To every nonzero
a ε Q. there corresponds a rational numbers such that
i) Distributive Law:
For a, b, c, ε Q
a .(b + c)
= a . b + a . c and
(a + b).
c = a . c + b . c
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