Question 2: \((i)\) If \(a=\frac{3}{2}\), \(b=\frac{5}{3}\), \(c=\frac{7}{5}\) then verify that \( a(b+c)=ab+ac \)
Solution:
\[
\begin{align*}
L.H.S.&=a( b+c)\\
&=\frac{3}{2}\left(\frac{5}{3} +\frac{7}{5}\right)\\
&=\frac{3}{2}\left(\frac{25+21}{15}\right)\\
&=\frac{3}{2}\left(\frac{45}{15}\right)\\
&=\frac{3}{2} \times 3\\
&=\frac{9}{2}\\
\end{align*}
\]
\[
\begin{align*}
R.H.S.&=ab+ac\\
&=\frac{3}{2} \times \frac{5}{3} +\frac{3}{2} \times \frac{7}{5}\\
&=\frac{5}{2} +\frac{21}{10}\\
&=\frac{25+21}{10}\\
&=\frac{45}{10}\\
&=\frac{9}{2}\\
\end{align*}
\]
Hence proved \(L.H.S. = R.H.S.\)