Find 9 rational number between `(1)/(3)and(1)/(2)`.

Answer

N/a

Explanation

Let `a=(1)/(3),b=(1)/(2)" ":.altb`
`b-a=(1)/(2)-(1)/(3)=(1)/(6)`
`and" "n=9" "rArr" "n+1=10`
Divide b - a by 10 and obtain `(b-a)/(n+1)=(1)/(6xx10)=(1)/(60)`
`:."First ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+(1)/(60)=(20+1)/(60)=(21)/(60)=(7)/(20)`
`:."Second ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+2xx(1)/(60)=(20+2)/(60)=(22)/(60)=(11)/(30)`
`:."third ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+3xx(1)/(60)=(20+3)/(60)=(23)/(60)`
`:."Fourth ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+4xx(1)/(60)=(20+4)/(60)=(24)/(60)=(2)/(5)`
`:."Fifth ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+5xx(1)/(60)=(20+5)/(60)=(25)/(60)=(2)/(12)`
`:."Sixth ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+6xx(1)/(60)=(20+6)/(60)=(26)/(60)=(13)/(30)`
`:."Seventh ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+7xx(1)/(60)=(20+7)/(60)=(27)/(60)=(9)/(20)`
`:."Eighth ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+8xx(1)/(60)=(20+8)/(60)=(28)/(60)=(7)/(15)`
`:."Ninth ratinal number between"(1)/(3)and(1)/(2)=(1)/(3)+9xx(1)/(60)=(20+9)/(60)=(29)/(60)`
`:."Required rational number are"`
`(7)/(20),(11)/(30),(23)/(60),(2)/(5),(5)/(12),(13)/(30),(9)/(20),(7)/(15),(29)/(60)`