Question

find 23 rational number between -4/6 and 1/6​

Answer 1

A rational number between 1/5 and 1/6 would be 1/2(1/5 + 1/6) = 1/2([6+5]/30) = 1/2(11/30) = 11/60

Now, 1/5 < 11/60 < 1/6

A rational number between 1/5 and 11/60 is 1/2([12+11]/60) = 1/2(23/60) = 23/120

And now, a rational number between 11/60 and 1/6 is 1/2([11+10]/60) = 1/2(21/60) = 21/120

That is, 1/5 < 23/120 < 11/60 < 21/120 < 1/6

So the required rational numbers are, 23/120, 11/60 and 21/120.

Answer 2

firstly LCM

LCM = 6

then

-4 × 2 = -8 × 2 = -16

6 2 12 2 24

1 × 2 = 2 × 2 = 4

6 2 12 2 24

so 23 numbers are the numbers between -16

24 and 4

24