A) \[\frac{4}{9}\]
B) \[\frac{71}{63}\]
C) \[\frac{2}{9}\]
D) \[\frac{71}{126}\]
Correct Answer: D
Solution :
LCM of \[7,\text{ }3,\text{ }3,\text{ }9=63\] \[\therefore \] \[\frac{4}{7}=\frac{4}{7}\times \frac{9}{9}=\frac{36}{63},\frac{1}{3}=\frac{1}{3}\times \frac{21}{21}=\frac{21}{63},\] \[\frac{2}{3}=\frac{2}{3}\times \frac{21}{21}=\frac{42}{63},\frac{5}{9}=\frac{5}{9}\times \frac{7}{7}=\frac{35}{63}\] So, ascending order is \[\frac{21}{63},\frac{35}{63},\frac{36}{63},\frac{42}{63}\] i.e., \[\frac{1}{3}<\frac{5}{9}<\frac{4}{7}<\frac{2}{3}\] Now, the average of \[\frac{5}{9}\] and \[\frac{4}{7}\] is \[\frac{1}{2}\left[ \frac{5}{9}+\frac{4}{7} \right]\] \[=\frac{1}{2}\left[ \frac{35+36}{63} \right]=\frac{71}{126}\]
You need to login to perform this action.
You will be redirected in
3 sec
