Question

If the binary operation ⊙ is defined on the set Q⁺ of all positive rational numbers by $a\odot b=\frac{ab}{4}.\mathrm{Then},3\odot \left(\frac{1}{5}\odot \frac{1}{2}\right)$ is equal to
(a) $\frac{3}{160}$

(b) $\frac{5}{160}$

(c) $\frac{3}{10}$

(d) $\frac{3}{40}$

Answer 1

(a) $\frac{3}{160}$

Given: $a\odot b=\frac{ab}{4}$
$$\begin{gathered} 3\odot \left(\frac{1}{5}\odot \frac{1}{2}\right)=3\odot \left[\frac{\left({\displaystyle \frac{1}{5}}\right)\left({\displaystyle \frac{1}{2}}\right)}{4}\right] \\ =3\odot \left(\frac{1}{40}\right) \\ =\frac{3\left({\displaystyle \frac{1}{40}}\right)}{4} \\ =\frac{3}{160} \end{gathered}$$