Use the distributive property to evaluate:
(i) $ \frac{9}{13} \times 3 \frac{1}{5}-2 \frac{1}{3} \times \frac{9}{13} $
(ii) $ 6 \frac{2}{5} \times \frac{3}{7}+\frac{4}{7} \times 6 \frac{2}{5} $

Given: $( i).\ \frac{9}{13} \times 3 \frac{1}{5}-2 \frac{1}{3} \times \frac{9}{13}\ \ \ ( ii).\ 6 \frac{2}{5} \times \frac{3}{7}+\frac{4}{7} \times 6 \frac{2}{5}$

To do: To evaluate $( i)$ and $( ii)$ by using distributive property.  

Solution:

$( i).\ \frac{9}{13} \times 3 \frac{1}{5}-2 \frac{1}{3} \times \frac{9}{13}$

$=\frac{9}{13}( 3\frac{1}{5}-2\frac{1}{3})$               [$\because ab-ac=a( b-c)$..... Distributive law]

$=\frac{9}{13}( \frac{16}{5}-\frac{7}{3})$

$=\frac{9}{13}( \frac{48-35}{15})$

$=\frac{9}{13}( \frac{13}{15})$

$=135$

$( ii).\ 6 \frac{2}{5} \times \frac{3}{7}+\frac{4}{7} \times 6 \frac{2}{5}$

$=6 \frac{2}{5}( \frac{3}{7}+\frac{4}{7})$                  [$\because ab+ac=a( b+c)$..... Disributive law]

$=\frac{32}{5}( \frac{3+4}{7})$

$=\frac{32}{5}( \frac{7}{7})$

$=\frac{32}{5}$