A) \[\frac{9}{-15},\frac{-2}{3},\frac{-4}{5}\]
B) \[\frac{-2}{3},\frac{-4}{5},\frac{-9}{15}\]
C) \[\frac{9}{-15},\frac{-4}{5},\frac{-2}{3}\]
D) \[\frac{-2}{3},\frac{-9}{15},\frac{-4}{5}\]
Correct Answer: A
Solution :
Writing each rational number with a positive denominator, we have \[\frac{-4}{5},\frac{-9}{15}\] and \[\frac{-2}{3}\]. L.C.M of 5, 15 and 3 is 15. \[\therefore \] \[\frac{-4}{5}=\frac{(-4)\times 3}{5\times 3}=\frac{-12}{15}\] \[\frac{-2}{3}=\frac{(-2)\times 5}{3\times 5}=\frac{-10}{15}\] Since \[-12<-10<-9,\] we have \[\frac{-12}{15}<\frac{-10}{15}<\frac{-9}{15}\Rightarrow \frac{-4}{5}<\frac{-2}{3}<\frac{-9}{15}\] \[\Rightarrow \] \[\frac{-9}{15}>\frac{-2}{3}>\frac{-4}{5}\].
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