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Question
Find the greatest and the smallest rational number among the following.
`(-2)/(3) , (-7)/(9) and (-5)/(6)`
Solution
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)`.
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