Question

Find any five rational numbers between `1/4` and `1/5`

Answer 1

Converting the given rational numbers with the same denominators.

`1/4 = (1 xx 30)/(4 xx 30) = 30/120`

`1/5 = (1 xx 24)/(5 xx 24) = 24/120`

Five rational numbers between `30/120` and `24/120` are `25/120, 26/120, 27/120, 27/120, 28/120` and `29/120`

Five rational numbers between `1/4` and `1/5` are `25/120, 26/120, 27/120, 28/120` and `29/120` 

Other Method:

A rational numbers between `1/4` and `1/5`

= `1/2 (1/4 + 1/5)`

= `1/2 ((5 + 4)/20)`

= `1/2 xx 9/20`

= `9/40`

A rational numbers between `1/4` and `9/40`

= `1/2 (1/4 + 9/40)`

= `1/2 ((10 + 9)/40)`

= `19/80`

A rational numbers between `1/4` and `19/80`

= `1/2 (1/4 + 19/20)`

= `1/2 ((20 + 19)/80)`

= `39/160`

A rational numbers between `1/4` and `39/160`

= `1/2 (1/4 + 39/160)`

= `1/2 ((40 + 39)/160)`

= `79/320`

A rational numbers between `1/4` and `79/320`

= `1/2 (1/4 + 79/320)`

= `1/2((80 + 79)/320)`

= `159/640`

∴ Five rational numbers are between `9/40, 19/80, 39/160, 79/320` and `159/640`