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m Division is an inverse operation of multiplication. So, for any two rational numbers
                                p r             p   r   p   s   ps
                                 ,                ¸   =   ´   =
                                q s             q   s   q   r   qr
              0 is called additive identity and 1 is called multiplicative identity.
                q                          p
             m     is called the reciprocal of
                p                          q
                  p r
             m If  ,  are two rational numbers, then according to the commutative property:
                  q s
                        p   r   r  p                            p    r  r   p
                          +   =  +                                 ´  =   ´
                        q   s   s  q                            q    s  s   q
                  p r      t
             m If   ,  and   are three rational numbers, then according to the associative property
                  q s      u
                        æ  p  r ö  t  p    r æ  t ö          æ  p  r ö  t  p    r æ  t ö
                        ç  + ÷ +    =   + ç  +  ÷            ç  ´ ÷ ´    =   ´ ç  ´   ÷
                        è q  sø   u   q    s è  u ø          è q  sø   u   q    s è  u ø
                                                             p r      t
             m Now again consider the three rational numbers  ,  and   then according to the distributive property,
                                                             q s      u
                   p    r é  t ù  é  p  rù  é p  t ù
                 (i)   ´  +    =  ê  ´  ú  +  ê  ´  ú
                   q   ê  s ë  uû ú  ë q  s û  ë q  u û
                   p    r é  t ù  é p  rù  é p  t ù
                (ii)   ´  -    =  ê  ´  ú  -  ê  ´  ú
                   q   ê  s ë  uû ú  ë q  s û  ë q  u û
             m We can compare and arrange the rational numbers in ascending and descending order.
             m We can find count less rational numbers between any two rational numbers.






                                                     Review Exercise
              1. An swer the fol low ing ques tions.
                 (a) Define a rational number.
                 (b) Write the additive inverse of the rational numbers “a”.
                                                                   p
                                                                      q
                 (c) What is the reciprocal of the rational number   ( ¹0 )?
                                                                   q
                                                             p     r
                 (d) Write the sum of two rational numbers   and   ( ,q r ¹0 )?
                                                             q     s
                 (e) What is the rule to find the product of two rational numbers?
                 (f)  What are the inverse operations of addition and multiplication?
             2. Fill in the blanks.
                 (a)  The________ consists of fractions as well as integers.
                                             p      -p
                 (b)  The rational numbers      and    are called____ inverse of each other.
                                             q      q
                                                                    p
                 (c)  A number that can be expressed in the form of   where p and q are integers and q 0 is called
                                                                    q
                      the________ number.

                 (d)  0 is called additive identity whereas 1 is called ________ identity.
                 (e)  The rational number 0 has no ________ .
                 (f)  The ________ inverse of a rational number is its reciprocal.
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                    Mathematics In Focus - 7
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