# 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]

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

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

$=\frac{32}{5}$

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Updated on: 10-Oct-2022

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