TOPICS
Unit-1(Examples)

Example-1 :-  Find 3/7 + (-6/11) + (-8/21) + 5/22 .

Solution :-
  3/7 + (-6/11) + (-8/21) + 5/22
  L.C.M of 7, 11, 21, 22 is 462 
  Then, (198 - 252 - 176 + 105 )/462 
= (303 - 428)/462
= -125/462
    

Example-2 :-  Find -4/5 x 3/7 x 15/16 x (-14/9)

Solution :-
  -4/5 x 3/7 x 15/16 x (-14/9)
=  [(-4/5) x 3/7] x [15/16 x (-14/9)]
=  (-12/35) x (-35/24)
=  -12/24
=  -1/2
    

Example-3 :-  Write the additive inverse of the following:
(i) -7/19    (ii) 21/112

Solution :-
(i) -7/19
    Here, 7/19 is the additive inverse of -7/19 because -7/19 + 7/19 = 0

(ii) 21/112
    Here, -21/112 is the additive inverse of 21/112 because -21/112 + 21/112 = 0
    

Example-4 :-  Verify that – (– x) is the same as x for
(i) x = 13/17     (ii) x = -21/31

Solution :-
(i) x = 13/17
    The additive inverse of x = 13/17 is -x = -13/17
    Then -13/17 + 13/17 = 0
    Now, - (- x) = - (- 13/17) = 13/17

(i) x = -21/31
    The additive inverse of x = -21/31 is -x = 21/31
    Then -21/31 + 21/31 = 0
    Now, - (- x) = - [- (-21/31] = -21/31
    

Example-5 :-  Find 2/5 x (-3/7) - 1/14 - 3/7 x 3/5 .

Solution :-
   2/5 x (-3/7) - 1/14 - 3/7 x 3/5
=  2/5 x (-3/7) - 3/7 x 3/5 - 1/14      [by commutativity]
=  2/5 x (-3/7) + (-3/7) x 3/5 - 1/14 
=  (-3/7)[2/5 + 3/5] - 1/14             [by distributivity]
=  -3/7 x 1 - 1/14
=  -3/7 - 1/14
=  (-6 - 1)/14
=  -7/14
=  -1/2
    

Example-6 :-  Write any 3 rational numbers between –2 and 0.

Solution :-
   In these numbers, we can multiply and divide by 10 in -2 and 0.
   Then, -2 x 10/10 = -20/10 and 0 x 10/10 = 0 /10
   Since, the numbers in between -20/10 and 0/10 are -19/10, -18/10, -17/10,.....-1/10.
   So, we can take any 3 rational numbers in between them numbers.
    

Example-7 :-  : Find any ten rational numbers between -5/6 and 5/8 .

Solution :-
   Firstly, we convert same denominator of the both values. 
   Then, In -5/6 multiply and divide by 4. I will get (-5 x 4)/(6 x 4) = -20/24.
   Also, In 5/8 multiply and divide by 3. I will get (5 x 3)/(8 x 3) = 15/24.
   So, we can find that ten rational number in -20/24, -19/24, -18/24,......15/24. 
    

Example-8 :-  Find a rational number between 1/4 and 1/2.

Solution :-
   Firstly, We find the mean of the given rational numbers. i.e., (a + b)/2
   since, a = 1/4 and b = 1/2 
   (1/4 + 1/2)/2 = (1 + 2)/8 = 3/8
   So, 3/8 lies in between 1/4 and 1/2. 
    

Example-9 :- Find three rational numbers between 1/4 and 1/2.

Solution :-
   Firstly, We find the mean of the given rational numbers. i.e., (a + b)/2
   since, a = 1/4 and b = 1/2 
   (1/4 + 1/2)/2 = (1 + 2)/8 = 3/8
   So, 3/8 lies in between 1/4 and 1/2. i.e., 1/4 < 3/8 < 1/2
   
   Secondly, we again find the mean in between 1/4 and 3/8. 
   since, a = 1/4 and b = 3/8
   (1/4 + 3/8)/2 = (2 + 3)/16 = 5/16
   So, 5/16 lies in between 1/4 and 3/8.

   Finally, we again find the mean in between 3/8 and 1/2
   (3/8 + 1/2)/2 = (3 + 4)/16 = 7/16
   So, 7/16 lies in between 3/8 and 1/2.

   Now, 5/16, 3/8, 7/16 are be three rational numbers in between 1/4 and 1/2.
    
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