Given that $13\frac{3}{4}\% = \frac{55}{4}\%$. Converting this percentage to a fraction: $$ \begin{aligned} \frac{55}{4}\% &= \frac{55}{4} \times \frac{1}{100} \\ &= \frac{55}{400} \\ &= \frac{11}{80} \end{aligned} $$ Thus, the correct option is A.