Question

Find ans using appropriate property 1/5*-3/7-3/5*10/2+1/14*-3/7

Answer 1

$$\begin{gathered} \frac{1}{5}\times \left(-\frac{3}{7}\right)-\frac{3}{5}\times \frac{10}{2}+\frac{1}{14}\times \left(-\frac{{\displaystyle 3}}{{\displaystyle 7}}\right) \\ =\frac{{\displaystyle 1}}{{\displaystyle 5}}\times \left(-\frac{{\displaystyle 3}}{{\displaystyle 7}}\right)+\frac{{\displaystyle 1}}{{\displaystyle 14}}\times \left(-\frac{{\displaystyle 3}}{{\displaystyle 7}}\right)-\frac{{\displaystyle 3}}{{\displaystyle 5}}\times \frac{{\displaystyle 10}}{{\displaystyle 2}}\left[\mathbf{Commutative}\mathbf{}\mathbf{law}\right] \\ =\left(-\frac{{\displaystyle 3}}{{\displaystyle 7}}\right)\times \left[\frac{1}{5}+\frac{1}{14}\right]-\frac{{\displaystyle 3}}{{\displaystyle 5}}\times \frac{{\displaystyle 10}}{{\displaystyle 2}}\left[\mathbf{Distributive}\mathbf{}\mathbf{law}\right] \\ =\left(-\frac{{\displaystyle 3}}{{\displaystyle 7}}\right)\times \left[\frac{14+5}{70}\right]-\frac{{\displaystyle 3}}{{\displaystyle 5}}\times \frac{{\displaystyle 10}}{{\displaystyle 2}} \\ =\left(-\frac{{\displaystyle 3}}{{\displaystyle 7}}\right)\times \frac{19}{70}-\frac{{\displaystyle 3}}{{\displaystyle 5}}\times 5 \\ =-\frac{57}{490}-3 \\ =\frac{-57-1470}{490} \\ =-\frac{1527}{490} \end{gathered}$$