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Mathematics Formulae
  Rational Numbers
 

 

 

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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 non-zero a ε Q. there corresponds a rational numbers such that

Rational Numbers

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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