Question 2: \((ii)\) If \(a=\frac{3}{2}\), \(b=\frac{5}{3}\), \(c=\frac{7}{5}\) then verify that \( (a+b)c=ac+bc \)
Solution:
\[
\begin{align*}
L.H.S.&=( a+b) c\\
&=\left(\frac{3}{2} +\frac{5}{3}\right)\frac{7}{5}\\
&=\left(\frac{9+10}{6}\right)\frac{7}{5}\\
&=\left(\frac{19}{6}\right)\frac{7}{5}\\
&=\frac{133}{30}\\
\end{align*}
\]
\[
\begin{align*}
R.H.S.&=ac+bc\\
&=\frac{3}{2} \times \frac{7}{5} +\frac{5}{3} \times \frac{7}{5}\\
&=\frac{21}{10} +\frac{7}{3}\\
&=\frac{63+70}{30}\\
&=\frac{133}{30}\\
\end{align*}
\]
Hence proved \(L.H.S. = R.H.S.\)