\[\left(\frac{1}{3a}+\frac14\right)\frac{a}{2}=\frac16+\frac{a}{8}.\]
\[\frac16+\frac{7.8}{8}=\frac16+\frac{39}{40}=\frac{137}{120}.\]
Ответ: \(\frac{137}{120}\).