Question

If the binary operation $*$ is defined on the set $Q^+$ of all positive rational numbers by $a*b=\frac{ab}{4}$. Then, $3 \left(\frac{1}{5} * \frac{1}{2}\right)$ is equal to

• A. $\frac{3}{160}$
• B. $\frac{5}{160}$
• C. $\frac{3}{10}$
• D. $\frac{3}{40}$

Answer 1

Answer: (A)

Given that $a * b =\frac{ab}{4}\,\forall\,a$, $b \in Q'$
$\therefore 3 * \left(\frac{1}{5} * \frac{1}{2}\right)
=3 * \left\{\frac{\frac{1}{5}\times\frac{1}{2}}{4}\right\}$
$=3 * \frac{1}{40}$
$=\frac{\left(3\times\frac{1}{40}\right)}{4}$
$=\frac{3}{160}$