Question

The average of the two middle rational numbers if $\frac{4}{7},\frac{1}{3},\frac{2}{3},\frac{5}{9}$ are arranged in ascending order is…..

Answer 1

Ascending order
Means arangement from lower to higher values.
Given rational no.s $\to \frac{4}{7},\frac{1}{3},\frac{2}{3},\frac{5}{9}$
Take the LCM of denominators.
i.e. 7,3,3,9
LCM=63
$\therefore \frac{4}{7}=\frac{4\times 9}{7\times 9}=\frac{36}{63}\frac{1}{3}=\frac{1\times 21}{3\times 21}=\frac{21}{63}\frac{2}{3}=\frac{2\times 21}{3\times 21}=\frac{42}{63}\frac{5}{9}=\frac{5\times 7}{9\times 7}=\frac{35}{63}\therefore \frac{4}{7},\frac{1}{3},\frac{2}{3},\frac{5}{9}=\frac{36}{63},\frac{21}{63},\frac{42}{63},\frac{35}{63}$
When arranged in ascending order $\to \frac{21}{63},\frac{35}{63},\frac{36}{63},\frac{42}{63}$
$\Rightarrow [\frac{1}{3},\frac{5}{9},\frac{4}{7},\frac{2}{3}]$
$\therefore$ Average of middle two rational nos. =
$\frac{\frac{5}{9}+\frac{4}{7}}{2}-\frac{\frac{35+36}{63}}{2}=\frac{71}{63\times 2}=\frac{71}{126}$