Question 3: If \(a=\frac{4}{3}\), \(b=\frac{5}{2}\), \(c=\frac{7}{4}\) then verify the associative property of real numbers w.r.t. addition and multiplication.
Solution:
Associative Property w.r.t. addition:
\[
\begin{align*}
(a+b)+c&=a+(b+c)\\
\left(\frac{4}{3} +\frac{5}{2}\right) +\frac{7}{4} &=\frac{4}{3} +\left(\frac{5}{2} +\frac{7}{4}\right)\\
\small{\left(\frac{8+15}{6}\right) +\frac{7}{4}} &=\small{\frac{4}{3} +\left(\frac{20+14}{8}\right)}\\
\frac{23}{6} +\frac{7}{4} &=\frac{4}{3} +\frac{34}{8}\\
\frac{92+42}{24} &=\frac{32+102}{24}\\
\frac{134}{24} &=\frac{134}{24}\\
\end{align*}
\]
Associative Property w.r.t. multiplication:
\[
\begin{align*}
(a×b)×c&=a×(b×c)\\
\left(\frac{4}{3} \times \frac{5}{2}\right) \times \frac{7}{4} &=\frac{4}{3} \times \left(\frac{5}{2} \times \frac{7}{4}\right)\\
\frac{10}{3} \times \frac{7}{4} &=\frac{4}{3} \times \frac{35}{8}\\
\frac{70}{12} &=\frac{1}{3} \times \frac{35}{2}\\
\frac{35}{6} &=\frac{35}{6}\\
\end{align*}
\]