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 Mathematics Formulae
Rational Numbers

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.

A + b = b + a where a, b ε Q

(a + b)+ c = a + (b + c)  where a, b, c ε Q

The rational number 0 is such that

a + 0 = 0 + a = a where a ε Q

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 non-zero 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