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 ____________.

• A. $\frac{4}{9}$
• B. $\frac{71}{63}$
• C. $\frac{4}{18}$
• D. $\frac{71}{126}$

Answer 1

The correct option is D $\frac{71}{126}$

To arrange the given fractions in ascending order, we have to take LCM of denominators.

LCM of $7,3,9$ $=$ $63$

Therefore $\frac{4}{7}$= $\frac{4\times 9}{7\times 9}$ =$\frac{36}{63}$

$\frac{1}{3}$ $=$ $\frac{1\times 21}{3\times 21}$ $=$ $\frac{21}{63}$

$\frac{4}{7}$ $=$ $\frac{2\times 21}{3\times 21}$ $=$ $\frac{42}{63}$

$\frac{5}{9}$ $=$ $\frac{5\times 7}{9\times 7}$ $=$ $\frac{35}{63}$

In ascending order $=$ $\frac{21}{63}$<$\frac{35}{63}$<$\frac{36}{63}$<$\frac{42}{63}$

Average of two middle numbers$=$ $\frac{\frac{35}{63}+\frac{36}{63}}{2}$

$=$ $\frac{71}{126}$