Question

Solve using appropriate proper properties.

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

Answer 1

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

$=\frac{2}{5}\times \frac{-3}{7}-\frac{3}{7}\times \frac{3}{5}-\frac{1}{14}$ [Commutative property]

$=\frac{3}{7}\times (\frac{-2}{5}-\frac{3}{5})-\frac{1}{14}$ [Distributive property]

$=\frac{3}{7}\times \left(\frac{-5}{5}\right)-\frac{1}{14}$

$=\frac{-3}{7}-\frac{1}{14}$

$=\frac{-6-1}{14}$

$=\frac{-7}{14}$

$=\frac{-1}{2}$

$\therefore \frac{2}{5}\times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}=\frac{-1}{2}$