Question

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

• A. $\frac{86}{90}$
• B. $\frac{86}{45}$
• C. $\frac{43}{45}$
• D. $\frac{43}{90}$

Answer 1

The correct option is D $\frac{43}{90}$

The numbers are

$\frac{4}{7},\frac{1}{3},\frac{2}{5}\&\frac{5}{9}$.

To arrange them in ascending order, we make their denominators equal

to the L.C.M. of the denominators.

The L.C.M. of 7, 3, 5 & 9=315.

So $\frac{4}{7}=\frac{4\times 45}{7\times 45}=\frac{180}{315},\frac{1}{3}=\frac{1\times 105}{3\times 105}=\frac{105}{315},\frac{2}{5}=\frac{2\times 63}{5\times 63}=\frac{126}{315}\&\frac{5}{9}=\frac{5\times 35}{9\times 35}=\frac{175}{315}.\therefore \frac{105}{315}<\frac{126}{315}<\frac{175}{315}<\frac{180}{315}i.e\frac{1}{3}<\frac{2}{5}<\frac{5}{9}<\frac{4}{7}$.

Then, the average of the middle numbers

=$\frac{1}{2}(\frac{1}{3}+\frac{2}{5})=\frac{43}{90}$.

Ans- Option D.