TOPICS
Exercise - 1.2

Question-1 :-  Represent these numbers on the number line.
(i) 7/4,     (ii) -5/6.

Solution :-
(i) 7/4 on the number line.
   Divide line between two natural number in 4 parts. 
   Thus, the rational number 7/4 lies at a distance of 7 points from 0 towards positive number line.
    number line

(ii) -5/6 on the number line.
   Divide line between two natural number in 6 parts. 
   Thus, the rational number -5/6 lies at a distance of 5 points from 0 towards negative number line.
    number line
    

Question-2 :-  Represent -2/11, -5/11, -9/11 on the number line.

Solution :-
   -2/11, -5/11, -9/11 on the number line.
   Divide line between two natural number in 11 parts. 
   Thus, the rational number -2/11, -5/11, -9/11 lie at a distance of 
   2, 5, 9 points from 0 towards negative number line respectively.
   number line
    

Question-3 :-  Write five rational numbers which are smaller than 2.

Solution :-
   2 can be written as 10/5.
   Thus, 5 natural numbers smaller than 2 are:
   9/5, 8/5, 7/5, 6/5 and 5/5.
    

Question-4 :-  Find ten rational numbers between -2/5 and 1/2.

Solution :-
   -2/5 and 1/2
   Here, L.C.M. of 5 and 2 is 10.
   Since, -2/5 x 2/2 = -4/10 and 1/2 x 5/5 = 5/10.
   Again, -4/10 x 2/2 = -8/20 and 5/10 x 2/2 = 10/20.
   Rational numbers are -7/20, -6/20, -5/20,.........9/20.
   Now, we can take any ten rational numbers in between -2/5 and 1/2.
    

Question-5 :-  Find five rational numbers between.
(i) 2/3 and 4/5
(ii) -3/2 and 5/3
(iii) 1/4 and 1/2

Solution :-
(i) 2/3 and 4/5  
   Here, L.C.M. of 3 and 5 is 15.
   Since, 2/3 x 5/5 = 10/15 and 4/5 x 3/3 = 12/15.
   Again, 10/15 x 4/4 = 40/60 and 12/15 x 4/4 = 48/60.
   Rational numbers are 41/60, 42/60, 43/60, 44/60, 45/60, 46/60, 47/60.
   Now, we can take any five rational numbers in between 2/3 and 4/5.   
          
(ii) -3/2 and 5/3   
   Here, L.C.M. of 2 and 3 is 6.
   Since, -3/2 x 3/3 = -9/6 and 5/3 x 2/2 = 10/6.
   Rational numbers are -8/6, -7/6, -6/6,.........10/6.
   Now, we can take any five rational numbers in between -3/2 and 5/3.   
         
(iii) 1/4 and 1/2
   Here, L.C.M. of 4 and 2 is 4.
   Since, 1/4 x 1/1 = 1/4 and 1/2 x 2/2 = 2/4.
   Again, 1/4 x 6/6 = 6/24 and 2/4 x 6/6 = 12/24.
   Rational numbers are 7/24, 8/24, 9/24, 10/24, 11/24.
   Now, five rational numbers in between 1/4 and 1/2 are 7/24, 8/24, 9/24, 10/24, 11/24. 
    

Question-6 :-  Write five rational numbers greater than -2.

Solution :-
   -2 can be written as -16/8.
   Five rational numbers greater than -2 are:
   -15/8, -14/8, -13/8, -12/8 and -11/8
    

Question-7 :-  Find ten rational numbers between 3/5 and 3/4.

Solution :-
   3/5 and 3/4
   Here, L.C.M. of 5 and 4 is 20.
   Since, 3/5 x 4/4 = 12/20 and 3/4 x 5/5 = 15/20.
   Again, 12/20 x 4/4 = 48/80 and 15/20 x 4/4 = 60/80.
   Rational numbers are 47/80, 48/80, 49/80,.......60/80
   Now, we can take any ten rational numbers in between 3/5 and 3/4.   
    
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