Question

Q. Verify the following $\left(1\right)\frac{2}{3}\times [\frac{-4}{5}+(\frac{-3}{7}\left)\right]=\frac{2}{3}\times \frac{-4}{5}+\frac{2}{3}\times \frac{-3}{7}$

Answer 1

Dear student
$$\begin{gathered} \mathrm{LHS}=\frac{2}{3}\times \left[-\frac{4}{5}+\left(-\frac{3}{7}\right)\right] \\ =\frac{2}{3}\left(-\frac{{\displaystyle 4}}{{\displaystyle 5}}-\frac{{\displaystyle 3}}{{\displaystyle 7}}\right) \\ =\frac{2}{3}\left(\frac{-28-15}{35}\right) \\ =\frac{2}{3}\left(-\frac{43}{35}\right) \\ =\frac{-86}{105} \\ \mathrm{RHS}=\frac{2}{3}\times \left(-\frac{4}{5}\right)+\frac{2}{3}\times \left(-\frac{3}{7}\right) \\ =-\frac{8}{15}-\frac{6}{21} \\ =\frac{-56-30}{105} \\ =\frac{-86}{105} \\ \mathrm{So},\mathrm{LHS}=\mathrm{RHS} \end{gathered}$$
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