Question

find five rational numbers between 1/4 and 1/6 by mean method

Answer 1

1/4 = 0.25
1/6 = 0.166…
So we can say that five rational numbers between them are 0.17, 0.18, 0.19, 0.20 and 0.21 (you can find more similarly). In p/q form the numbers are 17/100, 18/100, 19/100, 20/100 and 21/100.

Alternate:
LCM of 4 and 6 is 12.
So,
1/4 = 3/12
1/6 = 2/12
3 – 2 = 1. Hence, we’ll multiply the numbers’ N^r and D^r by 5+1 = 6
1/4 = 3/12 = 18/72
1/6 = 2/12 = 12/72
5 rational numbers between 12/72 and 18/72 are 13/72, 14/72, 15/72, 16/72 and 17/72.

Note: Answers may vary