A) \[\frac{-8}{9}>\frac{-4}{5}\]
B) \[\frac{-4}{5}<\frac{-8}{9}\]
C) \[\frac{-8}{9}=\frac{-4}{5}\]
D) \[\frac{-8}{9}<\frac{-4}{5}\]
Correct Answer: D
Solution :
Expressing in standard form, we get \[\frac{-8}{9}=\frac{-8}{9}\] and \[\frac{4}{-5}=\frac{-4}{5}\] Express each rational number with L.C.M as denominator. L.C.M of 9 and 5 is \[9\times 5=45\]. \[\therefore \] \[\frac{-8}{9}=\frac{-8\times 5}{9\times 5}=\frac{-40}{45},\] \[\frac{-4}{5}=\frac{-4\times 9}{5\times 9}=\frac{-36}{45}\] Comparing the numerators, we have \[-40<-36\]. \[\therefore \] \[\frac{-40}{45}<\frac{-36}{45}\Rightarrow \frac{-8}{9}<\frac{-4}{5}\]
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