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