Question

Find the greatest and the smallest rational number among the following.

`(6)/(7),(9)/(14) and (23)/(28)`

Answer 1

Given number : `(6)/(7),(9)/(14) and (23)/(28)`

The L.C.M. of 7, 14 and 28 is 28.

Thus, number are :
`(6)/(7) = (6 xx 4)/(7 xx 4)`

= `(24)/(28); (9)/(14)`

= `(9 xx 2)/(14 xx 2)`

= `(18)/(28) and (23)/(28)`.

Since 24 > 23 > 18, we have `(6)/(7) > (23)/(28) > (9)/(14)`.

Hence, the greatest rational number is `(6)/(7)` and the smallest rational number is `(9)/(14)`.