Question

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

`(-2)/(3) , (-7)/(9) and (-5)/(6)`

Answer 1

Given numbers : `(-2)/(3) , (-7)/(9) and (-5)/(6)`

The L.C.M. of 3, 9 and 6 is 18.

Thus, numbers are :
`(-2)/(3) = (-2 xx 6)/(3 xx 6)`

= `(-12)/(18); (-7)/(9)`

= `(-7 xx 2)/(9 xx 2)`

= `(-14)/(18); (-5)/(6)`

= `(-5 xx 3)/(6 xx 3)`

= `(-15)/(18)`

Since -12 > -14 > -15, we have `(-2)/(3) > (-7)/(9) > (-5)/(6)`.

Hence, the greatest rational number is `(-2)/(3)` and the smallest rational number is `(-5)/(6)`.