Question

Please explain 4 rational numbers between -2/3 and -3/5.

Answer 1

We can use mean method to find rational numbers between any two numbers. (a+b/2).
Here let a= -2/3
       b= -3/5
a+b/2= -2/3+(-3/5)/2
         = -10/15-9/15/2        (LCM)
         = -19/15*2= -19/30
-----(-19/30) is a rational number between -2/3 and -3/5

Now let a= -19/30 and b= -3/5
    a+b/2= -19/30+(-3/5)/2
             = -19/30-18/30/2
             = -37/30*2= -37/60
-----------(-37/60) is a rational number between -19/30 and -3/5

Now let a= -2/3 and b= -19/30
a+b/2= -2/3+(-19/30)/2
         = -20/30-19/30/2
         = -31/30*2
         = -31/60
------(-31/60) is a rational number between -2/3 and -19/30

Now let a= -19/30 and b= -31/60
a+b/2= -19/30+(-31/60)/ 2
         = -38/60-31/60/2
         = -69/60*2
         = -69/120

Therefore the 4 rational numbers between -2/3 and -3/5 are= (-19/30), (-37/60), (-31/60) and (-69/120)