Dividing fractions is fairly straightforward: you simply flip the top and bottom numbers of the divisor around (note, the divisor is the second fraction), change the division sign to a multiplication sign, and multiply the two fractions in the usual fashion. Or, “flip the second fraction and multiply” for short.

\begin{aligned}\frac{1}{2}\div\frac{1}{2}&=\frac{1}{2}\times\frac{2}{1} \\[12pt]&=\frac{1\times 2}{2\times 1} \\[12pt]&=\frac{2}{2}=1\end{aligned}

\begin{aligned}\frac{3}{4}\div \frac{3}{5}&= \frac{3}{4}\times\frac{5}{3}=\frac{3\times5}{4\times3}=\frac{15}{12}\end{aligned}

Now we simplify \frac{15}{12} to get the final answer:

\begin{aligned}\frac{15}{12}=\frac{\sout3\times5}{\sout3\times4}=\frac{5}{4}\end{aligned}