Question

1.write five rational numbers between -1 and 2. step by step
using arithmetic mean, write seven rational numbers beween 12/5 and 10/3.

Answer 1

take the LCM -1/1 and 2/1 
if u have to find five rational number between them then multiply with 6 then u will get a perfect 5 rational number so let start the equation like this 
-1/1 x 6/6 = - 6/6 
 2/1 x 6/6 = 12/6 
                 - 6/6 ( -5/6 , - 4/6 , 2/6 , 5/6 ,11/6 ) 12/6 

second question 
take the LCM of 12/5 and 10/3 = 3 x 5 = 15 
12/5 x 3/3 = 36/15 
10/3 x 5/5 = 50/15 
                     36/15 ( 37/15 , 38/15 , 39/15 , 40/15, 41/15 , 42/15 , 43/15 ) 50/15                                     i hope u get the answer 

Answer 2

1. Since -1= -1/1  and   -2= -2/1, these numbers have same denominators so,
Numbers of rational numbers to be written=5 and (5+1=6)
-1x6 = -6/6   
1x6 

-2x6 = -12/6, so, rational numbers between -1 and -2 are the rational numbers
1x6              between -6/6 and -12/6  i.e. -7/6, -8/6, -9/6, -10/6, and -11/6 or                          -7/6, -4/3, -3/2, -5/3, -11/6 (by reducing the numbers into their                            lowest form)

2. 12/5 and 10/3 have different denominators, so LCM of 5 and 3= 15
    =12x3= 36/15
       5x3
 
   =10x5 =50/15 
      3x5

Hence, 7 rational numbers between 12/5 and 10/3 are the rational numbers between 36/15 and 50/15 i.e. 37/15, 38/15, 39/15, 40/15, 41/15, 42/15, 43/15( you can take any 7 rational numbers between 36/15 and 50/15 since there are many rational numbers between them)